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Global Online Journal of Academic Research (GOJAR), Vol. 4, No. 1 February 2025 

 

 

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Volume 4, Number 1, February 2025 

e-ISSN 3043-6729 

Published by 

The Division of General Studies 

Chukwuemeka Odumegwu Ojukwu University 

(Formerly Anambra State University), 

Anambra State, Nigeria 

 

in association with 

 

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Tel: (+234) 07011831125 

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© GOJAR 2025 

 

 
 

 

All Rights Reserved 

No part of this publication shall be reproduced, stored 

in a retrieval system, or transmitted in any form 

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without the prior permission of  

the publisher. 

 
 

 

 

 



Global Online Journal of Academic Research (GOJAR), Vol. 4, No. 1 February 2025 

 

 

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GOJAR Editorial Board 
 

Editor-in-Chief 

Duve Nakolisa 

 

Editors 

Prof. Innocent Chijindu Ngangah 

Francis Chuks Madukasi, PhD 

 

Members of Editorial Advisory Board 

Prof. Federico G. Settler University of KwaZulu-Natal, South Africa 

Prof. Maduabuchi Dukor Nnamdi Azikiwe University, Awka,  Nigeria 

Prof. Sarojini Nadar University of KwaZulu-Natal, South Africa 

Prof. Roderick Hewitt University of KwaZulu-Natal, South Africa 

Prof. Jacob K. Ayantayo University of Ibadan, Ibadan, Nigeria 

Prof. Chika Moore Nnamdi Azikiwe University, Awka, Nigeria 

Prof. E.  Nwigwe University of Port-Harcourt, Nigeria 

Prof. Jude E. Madu Chukwuemeka Odumegwu Ojukwu University, 

Nigeria 

Prof. Uduma Oji Uduma National Open University, Abakiliki, Nigeria 

Prof. O.B.C.Nwankwo Chukwuemeka Odumegwu Ojukwu University, 

Nigeria 

Dr  Nneka Ifeoma Okafor University of Nigeria, Nsukka, Nigeria 

Dr. Roseline Uzeh University of Lagos, Lagos, Nigeria 

 



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About GOJAR Journal 

(e-ISSN 3043-6729) 

Global Online Journal of Academic Research (GOJAR) is a 

multidisciplinary journal published every two months (February, April, 

June, August, October, and December) by the Division of General 

Studies, Chukwuemeka Odumegwu Ojukwu University, Anambra State, 

Nigeria, in association with Klamidas Communications Ltd, a notable 

online academic publisher and webhost. The publishers’ goal is to 

enhance the capacity of academics in ALL disciplines to publish their 

quality academic papers and receive occasional email alerts drawing their 

attention to references made to their papers by other researchers across 

the globe. Other benefits include: life-time archive of published papers 

on GOJAR web pages and on Google Scholar, free plagiarism check and 

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Submit paper to gojar@klamidas.com. 

 

 

 

 

 

 

 

 

 

 



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Vol. 4, No. 1, February 2025 

 

 

 

 

Table of Contents 
 

Urbanization and Unemployment in 

Anambra State, Nigeria: Issues and 

Challenges 

 

Chukwujekwu Charles Onwuka  

 

 

7-25 

   

Implementation and Comparative Analysis 

of AMGT Method in Maple 24: Convergence 

Performance in Optimization Problems 

 

Mark Laisin & Rosemary U. Adigwe  

 

 

26-40 

   

Oil Spills in the Niger Delta and Their 

Impact on Food Security in Nigeria: A 

Prevalent Challenge 

 

Festus Funmileyi Ajomale & Christian 

Osemuyi Oseghale  

 

 

41-59 

   
 

 

 



Global Online Journal of Academic Research (GOJAR), Vol. 4, No. 1 February 2025 

 

 

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On Boundedness and Solution Size in 

Rational Linear Programming and 

Polyhedral Optimization 

 

Mark Laisin, Collins Edike & R. N. Ujumadu  

 

 

60-72 

 

Relationship between Housing Management 

and Housing Conditions in Imo State 

Housing Corporation Estates in Owerri, 

Nigeria 

 

Nnanyere N. Chukwu, Chukwunonso O. 

Umeora & Charles C. Munonye  73-89 

   

Exploring the Impact of Integrative Artificial 

Intelligence Tools on the Writing Proficiency 

of University Students in Kano State, Nigeria 

 

Mudassir Hassan & Adebayo Abubakar Funsho  90-103 

   

Rethinking Motifs in Selected Children’s  

Literary Texts 

 

Blessing Ekpe Okpapi & Enajite Ojaruega  104-118 

   

 

 

 

 

 

 

 

 



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Urbanization and Unemployment in Anambra State, 

Nigeria: Issues and Challenges 

 

Chukwujekwu Charles Onwuka 

 

 

 

ABSTRACT 

This study investigates the relationship between urbanization and unemployment 

in Anambra State, Nigeria, with a focus on the challenges arising from rapid 

urban growth. Urbanization in key cities such as Onitsha, Awka, and Nnewi has 

outpaced job creation, leading to increased unemployment, skill mismatches, and 

infrastructural deficiencies. The research adopts a mixed-methods approach, 

integrating quantitative data from structured questionnaires and qualitative 

insights from semi-structured interviews with policymakers, urban planners, and 

business owners. The population for this study consists of urban residents in three 

major cities of Anambra State: Awka, Onitsha, and Nnewi. A sample size of 400 

respondents was determined using the Taro Yamane formula, ensuring 

representativeness across the urban population. Primary data collection targeted 

unemployed individuals, residents, and stakeholders, while secondary data from 

government reports and statistical agencies provided additional context. 

Quantitative data were analyzed using descriptive and inferential statistics, while 

qualitative data were subjected to thematic analysis. Findings highlight that 

inadequate infrastructure and skill mismatches significantly contribute to 

unemployment rates in urban areas. The study also identifies gaps in vocational 

training and urban planning as critical challenges. Based on these insights, 

recommendations include infrastructure investment, skill development 

programmes, and policy reforms to mitigate unemployment and promote 

sustainable economic development. These findings provide actionable strategies 

for addressing urban unemployment challenges in Anambra State. 

Keywords: development, infrastructure, migration, rural areas, unemployment, 

urbanization 

 

 

 

 



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INTRODUCTION 

Urbanization, the process by which rural populations migrate to urban areas, 

is a defining characteristic of modern development. Urbanization, driven by 

economic, social, and political factors, has been a dominant demographic 

trend in Nigeria over the past decades. Anambra State, located in the 

Southeast geopolitical zone, is one of Nigeria’s most urbanized regions. 

Cities like Onitsha, Awka, and Nnewi have grown rapidly, attracting migrants 

from rural areas and neighboring states. However, this urban growth has 

outpaced infrastructure development and economic opportunities, resulting in 

high unemployment rates (Eze & Umeh, 2022).   

In Nigeria, the rate of urbanization, driven by population growth and rural-

urban migration, has accelerated significantly over the past few decades. By 

2020, urban areas accounted for approximately 51% of Nigeria’s population, 

with states like Anambra experiencing rapid urban expansion (World Bank, 

2020). While urbanization has the potential to stimulate economic growth, 

enhance infrastructure development, and create jobs, it also presents critical 

challenges, particularly in regions where industrial growth and infrastructure 

development lag behind population growth. 

Anambra State, located in southeastern Nigeria, exemplifies the complexities 

of urbanization. As one of the most urbanized states in the country, with cities 

such as Awka, Onitsha, and Nnewi serving as major economic hubs, it 

attracts a significant number of migrants seeking better opportunities. 

However, this rapid urbanization has been accompanied by persistent 

unemployment, especially among youth and migrants. Recent statistics 

indicate that the unemployment rate in Anambra State exceeds the national 

average of 33.3%, with urban areas facing the highest burden (National 

Bureau of Statistics [NBS], 2021). This phenomenon raises important 

questions about the relationship between urbanization and unemployment, as 

well as the socioeconomic and policy factors that influence this relationship. 

Several interrelated factors contribute to the unemployment crisis in 

Anambra's urban areas. First, rapid urban migration has led to an oversupply 

of labour, which the urban economy struggles to absorb, especially in the 

absence of commensurate industrial growth. Second, there is a significant 

skills mismatch, with many job seekers lacking the technical and vocational 

skills required in industries such as manufacturing and ICT. Third, poor 

infrastructure, including unreliable electricity, inadequate transportation 

networks, and limited access to clean water, has hindered industrialization 

and job creation. These issues are compounded by weak governance, 

inconsistent policies, and inadequate investment in education and skills 

training. 



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From a theoretical perspective, the challenges of urban unemployment in 

Anambra State can be understood through the lenses of Push-Pull Migration 

Theory (Lee, 1966) and Structural Unemployment Theory. Push-pull 

migration theory highlights the dynamics of rural-urban migration, where 

individuals are "pushed" from rural areas by poverty and lack of opportunities 

and "pulled" to urban centres by the promise of better jobs and living 

conditions. However, when urban centres fail to meet these expectations, 

structural unemployment often results. Structural unemployment theory 

explains how labour market mismatches between the skills of workers and the 

demands of employers exacerbate joblessness in rapidly urbanizing regions. 

Studies on urbanization in Nigeria underscore the need for proactive policies 

to address unemployment. According to Adepoju (2019), unchecked urban 

growth without adequate industrial and infrastructural development creates a 

vicious cycle of poverty and unemployment in urban centres. Similarly, 

Akinola and Ogunleye (2020) emphasize the importance of aligning urban 

planning with economic strategies to create sustainable urban economies. 

However, despite the growing body of literature, there remains a gap in 

understanding the specific challenges of urban unemployment in Anambra 

State and how these challenges can be addressed through targeted 

interventions. 

This study explores the relationship between urbanization and unemployment 

in Anambra State, identifying the key issues and challenges and proposing 

practical solutions. By examining the experiences of urban residents, 

analyzing labour market dynamics, and integrating insights from relevant 

theories, the study aims to provide a comprehensive understanding of the 

socioeconomic impacts of urbanization on employment in Anambra. The 

findings will contribute to the broader discourse on urbanization and 

unemployment in developing economies, with implications for policymakers, 

urban planners, and development practitioners. 

Unemployment, defined as the inability of individuals actively seeking work 

to find gainful employment, has become a significant socio-economic 

challenge in Anambra. This article explores the nexus between urbanization 

and unemployment in the state, delving into the contributing factors, 

consequences, and potential policy interventions. 

 

STATEMENT OF THE PROBLEM 

Urbanization is often regarded as a driver of economic development and 

improved living standards. However, when it occurs without adequate 

planning and industrial growth, it can exacerbate socioeconomic challenges, 



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such as unemployment, poverty, and inequality. In Nigeria, urbanization is 

proceeding at an unprecedented pace, with Anambra State emerging as one of 

the most urbanized regions in the country. Cities like Awka, Onitsha, and 

Nnewi have seen significant population increases, driven by rural-urban 

migration and natural population growth. Despite this trend, the anticipated 

economic benefits of urbanization, including job creation and improved 

livelihoods, have not been fully realized. Instead, urban unemployment has 

become a pressing challenge in the state, with far-reaching implications for 

socioeconomic stability and development. 

The unemployment rate in Nigeria reached a staggering 33.3% in 2020, with 

youth unemployment even higher at 42.5% (National Bureau of Statistics 

[NBS], 2021). In Anambra State, the situation is equally dire, as the urban 

labour market struggles to absorb the influx of workers. Many urban 

residents, especially young people, are either unemployed or engaged in 

precarious informal jobs that offer little economic security or career growth. 

This situation has led to rising urban poverty, increased dependency ratios, 

and social vices such as crime and insecurity. Despite the availability of a 

large labour force, the mismatch between available skills and market demand 

has left many job seekers unemployable in key sectors such as manufacturing, 

ICT, and construction (Adepoju, 2019). 

Anambra’s challenges are further compounded by inadequate infrastructure 

and weak policy implementation. For instance, unreliable electricity, poor 

road networks, and insufficient access to water hinder the establishment and 

growth of industries that could create jobs. In addition, urban planning efforts 

have not kept pace with population growth, resulting in overcrowded 

neighborhoods, informal settlements, and underdeveloped urban spaces. 

According to Akinola and Ogunleye (2020), the lack of coordinated efforts to 

link urbanization with industrialization has created a cycle of poverty and 

unemployment in urban areas across Nigeria. 

The persistence of these issues raises critical questions about the relationship 

between urbanization and unemployment in Anambra State. Why has 

urbanization not translated into significant job creation? What factors 

contribute to the high unemployment rates in urban areas? And how can these 

challenges be addressed to ensure that urbanization supports economic 

growth and development? Addressing these questions is essential for devising 

effective policies to mitigate urban unemployment and harness the potential 

of urbanization as a tool for socioeconomic transformation. 

This study investigates these issues, focusing on the unique challenges and 

dynamics of urban unemployment in Anambra State. By analyzing the 

structural factors underlying unemployment and exploring potential solutions, 



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the study aims to contribute to the growing discourse on sustainable urban 

development in Nigeria and other developing economies. 

 

OBJECTIVES OF THE STUDY 

The following are the three objectives of this study: 

1. To examine the relationship between urbanization and unemployment 

trends in Anambra  State.   

2.  To investigate how skill mismatches and infrastructural deficiencies 

contribute to the  unemployment rate in urban areas of Anambra State.   

3.  To identify and recommend strategies for mitigating urban 

unemployment challenges and promoting sustainable economic development 

in Anambra State. 

   

BRIEF LITERATURE REVIEW 

Urbanization and Its Implications   

Urbanization in Nigeria is driven by rural-urban migration, economic 

development, and population growth. Eze and Umeh (2022) note that urban 

centres, such as Onitsha and Nnewi in Anambra State, attract migrants due to 

perceived economic opportunities. However, they argue that rapid 

urbanization often outpaces infrastructure development, leading to 

overcrowding and strained urban services. Similarly, Obikeze (2021) 

highlights that unplanned urbanization results in informal settlements and 

increased urban poverty, exacerbating socio-economic inequalities. 

Unemployment Trends and Challenges   

The unemployment rate in Nigeria has been on the rise, particularly among 

urban youth. According to the National Bureau of Statistics (2023), Anambra 

State faces a growing unemployment challenge, partly due to a mismatch 

between educational outputs and labour market demands. Okoye (2020) 

emphasizes that while industrial hubs like Nnewi offer opportunities, the 

industrial growth in Anambra has been insufficient to absorb the expanding 

labour force. This contributes to a burgeoning informal economy, 

characterized by low wages and job insecurity. 

 

 



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Urbanization and Unemployment Nexus   

The link between urbanization and unemployment is well-documented. Eze 

and Umeh (2022) observe that rural-urban migration exacerbates urban 

unemployment as cities become overcrowded with unskilled and semi-skilled 

workers. This is echoed by Obikeze (2021), who suggests that unemployment 

in urban areas is not just a labour market issue but also a result of inadequate 

urban planning and governance. 

Socio-Economic Consequences   

The consequences of urbanization and unemployment are profound. High 

unemployment rates contribute to youth restiveness, crime, and social 

instability (Okoye, 2020). Furthermore, the growth of informal settlements 

due to inadequate housing worsens living conditions, creating public health 

and environmental challenges (Eze & Umeh, 2022). 

 

KEY ISSUES IN URBANIZATION AND UNEMPLOYMENT 

Urban Population Growth vs. Job Creation  

Nigeria has one of the fastest-growing urban populations in Africa, driven 

largely by rural-to-urban migration. However, job creation has not kept pace 

with this growth. This mismatch leads to high unemployment rates, 

particularly among youth. According to the National Bureau of Statistics 

(NBS), the unemployment rate in Nigeria has been steadily rising, 

exacerbated by the influx of people into cities in search of better opportunities 

(Adebayo, 2013). 

Mismatch between Skills and Job Market Demand  

Many urban dwellers, especially migrants, lack the skills needed for available 

jobs in cities. While urbanization theoretically offers better access to 

employment, Nigeria's educational system has not adapted adequately to meet 

the demands of the modern economy. One of the most pressing issues related 

to urban unemployment in Nigeria is the mismatch between the skills of job 

seekers and the demands of employers. Many rural migrants and urban youth 

lack the technical and vocational skills required in key sectors such as 

manufacturing, technology, and services. Educational curricula often do not 

align with the needs of the modern job market, leaving graduates without 

relevant skills, thereby worsening the unemployment situation (Adebayo, 

2013). 

This mismatch also extends to the oversupply of graduates in certain fields, 



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such as the humanities and social sciences, where job opportunities are 

limited compared to technical fields like engineering and information 

technology. 

Infrastructural Deficiency  

Urban areas in Anambra face severe infrastructural challenges, including 

inadequate housing, poor transportation systems, and limited access to 

essential services such as water and electricity. These deficiencies affect the 

ability of cities to create sustainable jobs and attract investment. Poor 

infrastructure not only hampers economic productivity but also increases the 

cost of doing business, making it difficult for companies to hire new workers 

and expand operations (Oyesiku, 2010). 

For instance, Lagos, one of Nigeria’s largest cities, faces traffic congestion, 

unreliable electricity, and a housing crisis, all of which impede economic 

activities and contribute to rising unemployment. 

Informal Sector Employment  

Due to a lack of formal employment opportunities, many urban residents 

resort to jobs in the informal sector, such as street trading, transportation, and 

artisanship. However, informal jobs often lack job security, health benefits, 

and consistent income, which do little to lift people out of poverty or reduce 

overall unemployment (National Bureau of Statistics, 2020). 

In Nigeria’s cities, informal employment accounts for a significant share of 

economic activity, but it does little to address the underlying issue of 

unemployment, as it often involves underemployment and job insecurity 

(Ehinomen & Adeleke, 2012). 

Government Policies and Interventions  

Several government initiatives, such as the National Social Investment 

Program (NSIP), have been launched to address unemployment. However, 

these efforts have been criticized for poor implementation, corruption, and 

lack of sustainability, limiting their impact (Akande & Ajibola, 2020). 

Various government programmes have been launched to address 

unemployment in urban areas, such as the National Social Investment 

Program (NSIP), which includes initiatives like the N-Power program and the 

Government Enterprise and Empowerment Program (GEEP) (Akande & 

Ajibola, 2020); the last but not the least is Anambra State Governor Soludo's 

One Youth Two Skills programme.  However, these interventions have been 

criticized for being poorly implemented, underfunded, and unsustainable.   



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Moreover, corruption and political interference have undermined the 

effectiveness of these programs, reducing their ability to provide meaningful 

and long-term employment opportunities. 

Rapid Urbanization without Proportional Economic Growth 

Nigeria’s urban population growth is largely driven by rural-to-urban 

migration. People move to cities in search of better economic opportunities, 

access to services, and improved living standards. However, urban centres in 

Anambra, particularly Awka, Nnewi, and Onitsha, are struggling to absorb 

this growing workforce. The urban job market, especially in the formal 

sector, has not expanded sufficiently to accommodate the influx of new 

residents. As a result, unemployment rates have surged. 

According to the National Bureau of Statistics (NBS), Nigeria’s 

unemployment rate was 33.3% as of Q4 2020, with a large portion of the 

unemployed population concentrated in urban areas. This discrepancy 

between the rapid pace of urbanization and the slow rate of economic growth 

aggravates unemployment (National Bureau of Statistics, 2020). 

 

CHALLENGES IN ADDRESSING URBANIZATION AND 

UNEMPLOYMENT 

Corruption and Governance Issues  

Weak institutions and pervasive corruption have hindered effective policy 

implementation. Many urban development and job creation initiatives suffer 

from mismanagement, leading to limited progress despite significant resource 

allocation. Corruption also deters both foreign and local investments that 

could provide employment (Okoye & Ezeonwuka, 2016). 

Corruption has remained a persistent challenge in Nigeria, affecting virtually 

every sector of the economy. It limits the effectiveness of urban development 

projects and hinders job creation initiatives. Funds meant for infrastructure 

development, job creation programmes, and social welfare are often 

misappropriated, leaving urban dwellers without access to the opportunities 

that urbanization should provide (Okoye & Ezeonwuka, 2016). 

Inadequate Economic Diversification  

Nigeria’s economy remains heavily reliant on oil, with limited diversification 

into manufacturing and other industrial sectors. Despite the potential of urban 

centres to drive industrial growth, the lack of government support for 

industries like manufacturing, agriculture processing, and services has stifled 



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job creation. Industrialization in Nigeria has lagged behind when compared 

with what obtains in some countries in Africa, such as South Africa and 

Egypt, which have more diversified economies (Okoye & Ezeonwuka, 2016). 

The weak industrial base also means that many urban residents in Nigeria are 

left without access to stable, well-paying jobs. 

Security Concerns  

Insecurity in Nigeria’s urban areas has worsened the unemployment situation. 

Cities like Lagos, Port Harcourt and Anambra State’s Awka, Onitsha and 

Nnewi, have experienced rising crime rates, including armed robbery, 

kidnapping, and gang violence, which deter business investments and limit 

economic activities. As businesses close or relocate due to insecurity, more 

people are left unemployed (Okoli & Ugwu, 2019). 

Insecurity is often fueled by unemployment itself, as jobless youth become 

vulnerable to involvement in criminal activities. 

 

THEORETICAL FRAMEWORK 

Urban Growth Theory provides a lens to examine the dynamics of 

urbanization and its impact on unemployment. Developed by scholars like 

Alonso and Burgess, this theory emphasizes the economic and spatial 

expansion of cities driven by industrialization, population growth, and 

infrastructure development. It explains how urbanization fosters economic 

opportunities but may also lead to challenges such as unemployment, housing 

shortages, and social inequality. 

In the context of Anambra State, Nigeria, Urban Growth Theory helps to 

analyze the uneven development of urban centres like Onitsha, Awka, and 

Nnewi. These cities experience rapid growth due to rural-to-urban migration, 

yet the local economies often struggle to absorb the influx of labour. This 

mismatch between job creation and population growth can lead to high 

unemployment rates. The theory also highlights the role of land use, 

transportation networks, and economic policies in shaping urban 

development. For instance, poor urban planning and inadequate infrastructure 

can exacerbate unemployment by limiting access to job markets and essential 

services. 

By applying Urban Growth Theory, this study can explore how urbanization 

processes influence unemployment patterns in Anambra State and identify 

strategies to promote sustainable urban development while addressing 

unemployment challenges. The theory provides a structured framework for 



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understanding these complex socio-economic interactions. 

 

METHODS 

This study adopts a mixed-methods approach, combining quantitative and 

qualitative techniques to explore the issues and challenges of urbanization 

and unemployment in Anambra State, Nigeria. The research design is 

descriptive and analytical, aimed at understanding the extent and implications 

of urbanization on unemployment. 

The population for this study consists of urban residents in three major cities 

of Anambra State: Awka, Onitsha, and Nnewi. These cities were chosen 

because they represent the most urbanized areas in the state and are hubs for 

economic activities, attracting a high volume of rural migrants. A sample size 

of 400 respondents was determined using the Taro Yamane formula, ensuring 

representativeness across the urban population. Data collection involves both 

primary and secondary sources. Primary data will be obtained through 

structured questionnaires targeting urban residents, unemployed youth, and 

policymakers to capture quantitative insights. Semi-structured interviews with 

stakeholders such as government officials, urban planners, and business 

owners will provide qualitative depth. Secondary data will be sourced from 

relevant literature, reports, and official statistics from agencies like the 

National Bureau of Statistics (NBS). 

The study employs stratified sampling to categorize participants based on 

demographics (e.g., age, gender, and occupation) and random sampling 

within strata to ensure representativeness. Quantitative data will be analyzed 

using descriptive and inferential statistical tools to identify patterns and 

relationships, while thematic analysis will be used to interpret qualitative 

findings. 

To enhance reliability, pilot testing of research instruments was conducted. 

Ethical considerations such as informed consent, confidentiality, and 

voluntary participation were strictly observed. This comprehensive 

methodology ensures a robust understanding of the relationship between 

urbanization and unemployment in Anambra State. 

 

 

 

 



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FINDINGS 

Table 1: Summary of data analysis on socio-demographic characteristics 

of the respondents 

 
 

From the above table, the sample has a slight male predominance (55%), 

potentially reflecting urban migration patterns where men migrate more for 

employment opportunities. Most respondents (45%) are in the 26-35 age 



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group, often considered the most active working population. A majority 

(60%) are single, suggesting they may be more willing to migrate or face 

employment uncertainties. A significant proportion (75%) hold tertiary 

qualifications, highlighting the importance of skill matching in employment 

opportunities. Half (50%) of the respondents are unemployed, underscoring 

the pressing issue of unemployment in urban areas. 

Table 2: Respondents' perception about the relationship between 

urbanization and unemployment trends in Anambra State 

 

From the above table, 30% of respondents identified rapid population 

increases as a major driver of unemployment. 35% pointed to high migration 

rates exacerbating job scarcity, while 20% of respondents linked inadequate 

infrastructure to economic inefficiencies. 

Table 3:  Respondents' view on how skill mismatches and 

infrastructural deficiencies contribute to unemployment in urban areas 

 

The above table showed that 41.25% of respondents indicated that 

mismatched skills significantly impact job opportunities. Power outages and 



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poor transport infrastructure were noted by 36.25% and 21.25%, respectively, 

as barriers to employment. 

Table 4: Respondents' view on strategies for mitigating urban 

unemployment challenges and promoting sustainable economic 

development 

 

The above table showed that 31.25% of respondents supported initiatives to 

align workforce skills with job demands. 41.25% of respondents identified 

job creation through improved productivity as a top priority while 26.25% 

highlighted the need for small and medium enterprise support as a pathway to 

job creation. 

 

DISCUSSION OF FINDINGS 

Urban Migration and Unemployment 

The findings of the study show that 35% of respondents migrated from rural 

areas to urban centres in search of better economic opportunities. However, 

despite this influx, the unemployment rate in urban Anambra remains high, 

with 30% of the urban population unemployed. This finding echoes the 

findings of Adeyemi (2018), who argues that rapid rural-to-urban migration 

often leads to an overburdened urban labour market that is ill-prepared to 

absorb the growing number of job seekers. According to Push-Pull Theory, 

rural residents are "pushed" by poverty and lack of opportunities and "pulled" 

by the promise of better livelihoods in urban areas (Lee, 1966). However, the 

mismatch between labour supply and demand in urban areas often results in 

high unemployment rates among migrants, as the labour market cannot keep 

pace with the growing population. 



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In the case of Anambra State, this study highlights that the migration-driven 

urbanization process has outpaced the creation of formal employment 

opportunities. This is consistent with Odedokun and Oyinloye’s (2021) 

finding that urbanization, without corresponding industrial and economic 

growth, leads to structural unemployment. 

Skill Mismatches and Employment Opportunities 

A key finding of the study is the skill mismatch between the labour force and 

available jobs in urban Anambra. 41.25% of unemployed respondents 

reported that their skills did not align with the demands of the job market. 

This finding aligns with Olaniyan and Okemakinde (2008), who state that 

skill mismatches are a significant contributor to unemployment, especially in 

developing economies where educational systems often fail to prepare 

students for the types of jobs available in the labour market. The study further 

finds that higher education alone does not guarantee employment, as many 

degree holders are either underemployed or working in jobs that do not 

require their level of education. 

This discrepancy can be explained through Structural Unemployment Theory, 

which highlights that unemployment arises when there is a mismatch between 

the skills of workers and the demands of the job market. As Kingdon and 

Knight (2004) suggest, the failure of educational systems to align with labour 

market needs results in high levels of unemployment and underemployment, 

particularly in countries like Nigeria where industries and markets are 

evolving rapidly but education systems remain focused on traditional 

academic learning rather than vocational skills. 

The Role of Infrastructure in Job Creation 

A significant portion of respondents (21.25%) identified poor infrastructure 

as a key hindrance to industrial growth and job creation in urban Anambra. 

This finding is in line with Harbison’s (1973) assertion that inadequate 

infrastructure in urban areas impedes economic development, thereby limiting 

job opportunities. The study found that areas with better infrastructure, such 

as improved roads and reliable electricity, had significantly higher 

employment rates. These findings support Satterthwaite (2010), who notes 

that the lack of basic infrastructure is one of the primary barriers to industrial 

development in many African urban centres. 

Moreover, poor infrastructure not only hinders industrial growth but also 

limits the ability of small businesses to operate efficiently. Gugler (2004) 

emphasizes that the lack of reliable electricity, water, and transportation 

systems increases the costs of doing business, making it harder for 

entrepreneurs to create jobs in urban areas. As Ayadi and Ayadi (2008) argue, 



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21 
 

infrastructure development is crucial for improving the investment climate, 

supporting industrialization, and ultimately creating employment 

opportunities. 

Employers’ Perspectives on Skills and Hiring Challenges 

Employers in Anambra State identified skills shortages as a primary 

challenge when hiring workers. 31.25% of employers indicated difficulty 

finding workers with the necessary technical skills. This finding resonates 

with Gulati and Reddy (2019), who argue that one of the significant 

challenges facing employers in developing economies is the scarcity of 

skilled labour. The study found that employers were particularly focused on 

vocational and technical skills, which many urban residents lacked. 

This finding underscores the importance of vocational education and training 

in addressing skill mismatches and improving employability. Mason and 

Hargreaves (2000) found that the expansion of vocational training 

programmes and partnerships between educational institutions and industries 

could help reduce the skills gap. In Anambra, aligning vocational education 

with the demands of the local labour market could increase employment rates 

by ensuring that workers possess the specific skills required by employers. 

Investment in Vocational and Technical Education 

The findings highlight the significant gap between academic education and 

practical skills needed in the labour market. Vocational and technical 

education can help bridge this gap. The National Policy on Education (2004) 

emphasizes the importance of developing technical skills to meet the 

demands of industries, yet the evidence from Anambra State suggests that 

vocational training programmes are underfunded and not widespread enough 

to make a meaningful impact. 

This aligns with Olaniyan and Okemakinde (2008), who argue that 

educational reforms focusing on vocational training and apprenticeships 

would help in reducing skill mismatches and addressing urban unemployment 

in Nigeria. 

Infrastructure Development as a Catalyst for Job Creation 

The study also found that poor infrastructure remains a critical barrier to job 

creation. This finding underscores the need for strategic infrastructure 

development, particularly in transportation, energy, and water supply, to 

facilitate industrial growth and employment. Bello and Adebayo (2017) argue 

that infrastructure development is an essential catalyst for creating jobs in 

urban areas. In line with this, improving the urban infrastructure in Anambra 

could attract investments, support existing businesses, and promote new 



Global Online Journal of Academic Research (GOJAR), Vol. 4, No. 1 February 2025 

 

 

22 
 

industries, creating jobs for urban residents. 

 

Industrialization and Economic Diversification 

The study finds that without industrial growth, the urban labour market in 

Anambra State cannot absorb the increasing number of job seekers. This 

finding supports the call for industrialization and economic diversification to 

generate jobs. Ihua (2009) notes that industrialization plays a pivotal role in 

reducing unemployment by creating formal sector jobs. In Anambra, focusing 

on industries such as manufacturing, construction, and information 

technology could diversify the economy and provide long-term solutions to 

urban unemployment. 

 

CONCLUSION AND RECOMMENDATIONS 

Conclusion 

Urbanization in Nigeria offers both challenges and opportunities. While cities 

can serve as engines of economic growth and development, Nigeria’s current 

trajectory of urbanization has been accompanied by rising unemployment and 

underemployment. The challenges posed by infrastructural deficiencies, skills 

mismatch, a growing informal sector, and ineffective policies must be 

addressed to unlock the full potential of urbanization. 

Recommendations 

Based on the findings of this study, the following are recommended:  

1.  Invest in Infrastructure: The government must prioritize the development 

of critical infrastructure to support job creation and attract investment in 

urban areas. 

2.  Improve Education and Skills Training: Align educational curricula with 

market demands and invest in vocational training programmes to equip the 

urban workforce with the skills needed for the modern economy. 

3.  Promote Industrialization: Policies that encourage industrial growth and 

diversification are essential for creating formal employment opportunities in 

cities. 

4.  Tackle Corruption: Strengthen institutions to ensure transparent and 

efficient use of resources allocated to urban development and job creation 

programmes. 



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23 
 

 

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115. 

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and inequality. Cambridge: Cambridge University Press. 

Gulati, M., & Reddy, V. (2019). Skills development and employment 

challenges in India and Nigeria: Comparative perspectives. Journal of 

Economic Development, 28(2), 47-61. 

Harbison, F. (1973). Human resources as a basis for development. Princeton 

University Press. 

Ihua, U. (2009). Industrialization and employment creation in Nigeria: 

Challenges and policy options. Journal of Development Studies, 5(3), 

77-94. 

Kingdon, G., & Knight, J. (2004). Unemployment in South Africa: The nature 

of the beast. World Development, 32(3), 391-408. 

Lee, E. (1966). A theory of migration. Demography, 3(1), 47-57. 

Mason, R., & Hargreaves, D. (2000). Vocational education and employment: 

Linking education and work. Journal of Education and Work, 13(2), 

111-123. 

National Bureau of Statistics (2020). Labour force statistics: Unemployment 

and underemployment report (Q2 2020). 

National Bureau of Statistics (NBS). (2021). Labour force statistics: 

Unemployment and underemployment report (Q4 2020). 

National Bureau of Statistics (2023). Unemployment and Underemployment 

Report, Q4 2023. Abuja: NBS. 

Obikeze, D. S. (2021). Urban Challenges and Policy Responses in Nigeria: 

The Case of Anambra State. Urban Studies Review, 25(1), 32-47. 

Odedokun, M., & Oyinloye, A. (2021). Urbanization, industrialization, and 

unemployment in sub-Saharan Africa: The case of Nigeria. African 

Economic Review, 32(4), 123-135. 

Okoli, A. C., & Ugwu, C. (2019). Urbanization, unemployment and 

insecurity: The Nigerian experience. African Journal of Social 

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Okoye, E. (2020). "Addressing Unemployment through Industrial 

Diversification in Nigeria." Economic Policy Review, 11(1), 54-71. 

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economic development in Nigeria. Journal of Research in National 

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Olaniyan, D., & Okemakinde, T. (2008). Human capital theory: Implications 

for educational development. Pakistan Journal of Social Sciences, 

5(1), 58-63. 

Oyesiku, O. O. (2010). City liveability and sustainable jobs in Nigeria: Issues 

and challenges. Urban Studies Research, 2010, 1-12. 

Satterthwaite, D. (2010). Urbanization and development in the global South: 

What are the challenges? Environment and Urbanization, 22(2), 453-

468. 

World Bank. (2020). World urbanization prospects: Data for Nigeria. 

 

 

 

Author Information: Dr Chukwujekwu Charles 

Onwuka is the Head, Department of Sociology, 

Chukwuemeka Odumegwu Ojukwu University, Igbariam 

Campus, Anambra State, Nigeria. Email: 

cc.onwuka@coou.edu.ng 
 

 

 

 

 
 

APA 

 

Onwuka, C. C. (2025). Urbanization and Unemployment in 

Anambra State, Nigeria: Issues and Challenges. Global Online 

Journal of Academic Research (GOJAR), 4(1), 7-25. 

https://klamidas.com/gojar-v4n1-2025-01/.  

 

MLA 

 

Onwuka, Chukwujekwu Charles. “Urbanization and Unemployment 

in Anambra State, Nigeria: Issues and Challenges”. Global Online 

Journal of Academic Research (GOJAR), vol. 4, no. 1, 2025, pp. 7-

25. https://klamidas.com/gojar-v4n1-2025-01/.  

 

 

 

 

 

 

 

 



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26 
 

Implementation and Comparative Analysis of AMGT 

Method in Maple 24: Convergence Performance in 

Optimization Problems 

 

Mark Laisin & Rosemary U. Adigwe 

 

 

 

Abstract 

This study investigates the utilization of the Accelerated Modified Gradient 

Technique (AMGT) in Maple 24 for optimization problem-solving. The research 

focuses on enhancing and evaluating the convergence speed of AMGT in 

comparison to the Gradient Descent (GD) and Conjugate Gradient (CG) methods. 

The analysis covers a range of function types, such as convex functions (e.g., 

production cost, energy consumption, and transportation cost functions) and a non-

convex function. Findings showcase the effectiveness and versatility of AMGT, 

shedding light on its utility for addressing practical optimization challenges. 

Keywords: AMGT method, Maple 24, convergence performance, optimization 

problems, comparative analysis 

 

 

1. Introduction 

Optimization techniques are crucial for solving complex problems in various 

fields, such as engineering, economics, machine learning, and operations 

research. They are essential for decision-making processes, from designing 

efficient systems to finding optimal financial strategies (Boyd & 

Vandenberghe, 2004). Gradient-based methods like Gradient Descent (GD) 

and Conjugate Gradient (CG) are widely used due to their computational 

efficiency and well-understood theoretical properties (Nocedal & Wright, 

2006). These methods iteratively improve solutions by using gradients to 

guide the search for the optimal solution, making them effective for 

continuous optimization problems. 

However, in some cases, basic gradient-based methods face limitations in 

terms of convergence speed and stability, especially in large or complex 



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27 
 

problem spaces. As optimization problems become high-dimensional or non-

convex, traditional methods like GD and CG may struggle, leading to slower 

convergence rates and potential failure to escape local minima (Bertsekas, 

1999). Accelerated Gradient Methods, including the Accelerated Modified 

Gradient Technique (AMGT), have been proposed to address these 

challenges and offer improvements in convergence speed and stability 

(Nesterov, 1983).  

The AMGT combines the theoretical robustness of traditional gradient 

methods with acceleration strategies that optimize the search for a minimum. 

It adapts the gradient direction dynamically to enhance the rate of 

convergence, a feature that can be critical when dealing with large-scale 

optimization tasks or when high precision is required (Dauphin et al., 2015). 

Despite its potential, there is a limited comparative analysis of AMGT 

concerning traditional methods such as GD and CG in contemporary 

optimization applications, particularly in symbolic and numerical 

computation environments. 

This paper investigates the implementation of AMGT in Maple 24, a versatile 

software for mathematical modeling, simulation, and optimization 

(Maplesoft, 2023). The objective is to compare the convergence performance 

of AMGT with GD and CG across various optimization problems, including 

convex and non-convex scenarios, to assess their relative effectiveness in 

different contexts.  

II. Methods and Materials 

Problem Formulation Optimization problems are expressed as minimizing a 

cost function. The study considers the following types of functions: 

 Production cost function  𝐶(𝑥, 𝑦) = 𝑎𝑥2 + 𝑏𝑦2 + 𝑐𝑥𝑦 + 𝑑 where 

𝐶(𝑥, 𝑦) is the cost of producing x units of labour and y units of 

capital, and a, b, c, and d are constants. 

 Energy consumptionfunction  𝐸(𝑇, 𝐻) = 𝛼𝑇2 + 𝛽𝐻2 + 𝛾𝑇𝐻 + 𝜔 

where 𝐸(𝑇, 𝐻) is energy consumption as a function of temperature 

and humidity while  𝛼, 𝛽, 𝛾 𝑎𝑛𝑑 𝜔 are constants. 

 Transportation cost function  𝑇(𝑄, 𝐷) = 𝛼𝑄2 + 𝛽𝐷2 + 𝛾𝑄𝐷 + 𝜔 

where 𝑇(𝑄, 𝐷) is the transportation cost as a function of quantity (Q) 

of goods to be transported and distance to be covered in transportation 

(D).   𝛼, 𝛽, 𝛾 𝑎𝑛𝑑 𝜔 are constants. 

Non-Convex Function: A non-convex function in mathematics refers to a 

function where the line segment joining any two points on the graph of the 



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function is not entirely above or on the graph. More formally, a function f(x) 

is non-convex if, for some 𝑥1, 𝑥2 ∈ 𝑅𝑛 and for some 𝜆 ∈ [0,1], we have: 

𝑓(𝜆𝑥1 + (1 − 𝜆)𝑥2) > 𝜆𝑓(𝑥1) + (1 − 𝜆)𝑓(𝑥2) 

which means that the epigraph (the set of points above the graph) is not 

convex. 

A convex function satisfies the reverse inequality: 

𝑓(𝜆𝑥1 + (1 − 𝜆)𝑥2) ≤ 𝜆𝑓(𝑥1) + (1 − 𝜆)𝑓(𝑥2) 

A non-convex function is simply one that does not satisfy this condition in 

general. E.g. the convex function  𝑓(𝑥, 𝑦) = 2𝑥𝑦 + 𝑦 − 𝑥2 − 2𝑦2. With the 

three methods using 𝑥0 = 2 and 𝑦0 = 2,   while AMGT uses 𝑚0(𝑥, 𝑦) =

(1000,1000), 𝛼 = 50,  𝛽 = 0.13,  𝛾 = 0.1, is a non-convex function. 

Algorithms 

 Gradient Descent (GD): Iterative optimization algorithm using the 

gradient to update parameters. 

 Conjugate Gradient (CG): Enhances GD by using conjugate directions 

for faster convergence in quadratic problems. 

 Accelerated Modified Gradient Technique (AMGT): Combines 

momentum-based acceleration with gradient optimization for 

enhanced performance for the optimization of nonlinear unconstrained 

optimization. 

However, this is a gradient descent step length algorithm that is a 

modification of some of Adam’s algorithms. Our motivation for this method 

is the need to combine the benefits of adaptive learning rates and momentum 

while introducing a gradient technique mechanism to escape local minima. 

Update Rules for the proposed AMGT: 

a. Define the convex function to be optimized 

b. Initialize 𝑥0, 𝛼0, τ, β , γ, 𝑚0, tolerance and number of iterations 

c. Compute the gradient of the given convex function to be optimized: 

∇𝑓(𝑥𝑘) =
∂f

∂𝑥𝑘
 

d. Next compute the adaptive learning rate: 𝛼𝑘 = 𝛼𝑘−1/(1 + γ/𝜏) 

e. Compute the momentum: 𝑚𝑘 = β ∗ 𝑚𝑘−1 + (1 − 𝛽) ∗ ∇𝑓(𝑥𝑘) 



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f. Apply gradient technique on the momentum: �̂�𝑘 = 𝑚𝑘 ∗ (1 − γ ∗
|∇𝑓(𝑥𝑘)|

|𝑚𝑘|
) 

g. Update parameters or variable values of the convex function:  𝑥𝑘 =

𝑥𝑘−1 − 𝛼𝑘 ∗ �̂�𝑘 

h. Continue steps b to g till the specified number of iterations. 

Convergence Criteria: 

AMGT converges when the following conditions are met: 

 Parameter Convergence: The updates to the parameters (𝑥𝑘) become 

negligible, i.e., |𝑥𝑘 − 𝑥𝑘−1| < tolerance. 

 Objective Function Convergence: The change in the objective 

function value becomes negligible, i.e., |𝑓(𝑥𝑘) − 𝑓(𝑥𝑘−1)|<tolerance. 

 Maximum Iterations: The algorithm reaches the specified number of 

iterations. 

Inputs or initial parameters: 

 𝛼0this is the initial learning rate 

 τ: this is the learning rate decay rate 

 β: this is the momentum coefficient 

 γ: this is the gradient technique coefficient 

Rational behind each of the input parameters: 

o The Adaptive learning rate (𝛼𝑘) helps the method to converge faster. 

o The Momentum (𝑚𝑘) helps to escape local minima. 

o While the Gradient technique (𝛾) prevents overshooting. 

Implementation in Maple 24: The AMGT method is implemented using 

Maple 24's symbolic and numerical capabilities. Scripts for GD and CG are 

also developed for comparison. The functions are defined, and step sizes are 

chosen dynamically for each method to ensure fair benchmarking. 

Performance Metrics: 

 Convergence Rate: Number of iterations required to reach a 

predefined tolerance. 



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 Computation Time: Time taken to converge. 

 Accuracy: Proximity of the solution to the true minimum. 

Mathematical Properties of Non-Convex Functions 

 Local Minima and Maxima: A non-convex function can have multiple 

local minima and maxima, unlike convex functions, which have at 

most one global minimum. 

 Optimization Challenges: Non-convex optimization is harder than 

convex optimization because local search algorithms like gradient 

descent may converge to local minima instead of the global minimum. 

(Bertsekas, 1999; Boyd & Vandenberghe, 2004) 

 Non-convexity in Higher Dimensions: Non-convexity is not limited to 

functions of one variable. A function f(x) defined on a higher-

dimensional space 𝑅𝑛 can be non-convex if it does not satisfy the 

convexity condition for all pairs of points in its domain (Bertsekas, 

1999; Boyd & Vandenberghe, 2004). 

III Results 

Theorems 3.1. Convergence of AMGT 

Let 𝑓(𝑥, 𝑦) be a continuously differentiable function, and let (𝑥𝑘, 𝑦𝑘) be the 

sequence generated by the Adaptive Momentum Gradient Technique 

(AGMT). Assume that  

 𝑓(𝑥, 𝑦) convex 

 The learning rate 𝑎𝑘 satisfies ∑ 𝑎𝑘 = ∞∞
𝑘=1  and ∑ 𝑎𝑘

2 < ∞∞
𝑘=1 . 

 The momentum coefficient 𝛽  satisfies 0 < 𝛽 < 1 

 The gradient threshold coefficient 𝛾 satisfies 0 < 𝛾 < 1 

Then the sequence (𝑥𝑘, 𝑦𝑘) converges to a stationary point of 𝑓(𝑥, 𝑦) 

Proof. 

Using the convexity of 𝑓(𝑥, 𝑦) and the update rule of AMGT, we can 

establish the above theorem.  

By the convexity 0f 𝑓(𝑥, 𝑦) we have the convex inequality: 

𝑓(𝑥𝑘+1, 𝑦𝑘+1) ≤ 𝑓(𝑥𝑘, 𝑦𝑘) + 〈∇𝑓(𝑥𝑘, 𝑦𝑘), (𝑥𝑘+1 − 𝑥𝑘, 𝑦𝑘+1 − 𝑦𝑘)〉 

 



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The essence of the convex inequality is that the value of the function at the 

new point (𝑥𝑘+1, 𝑦𝑘+1) is always less than the value of the function at the 

current point (𝑥𝑘, 𝑦𝑘) plus a linear approximation based on the gradient. 

In the proposed AMGT method, the update involves a combination of the 

current gradient and previous momentum. Thus, we can express the 

parameters as  

𝑥𝑘+1 = 𝑥𝑘 − 𝛼𝑘�̂�𝑘 and 𝑦𝑘+1 = 𝑦𝑘 − 𝛼𝑘�̂�𝑘 

Where �̂�𝑘 is the momentum term after gradient thresholding. 

Applying the update of AMGT on the convex inequality, we have; 

𝑓(𝑥𝑘+1, 𝑦𝑘+1) ≤ 𝑓(𝑥𝑘, 𝑦𝑘) –𝑎𝑘〈∇𝑓(𝑥𝑘 , 𝑦𝑘), �̂�𝑘〉 + 𝑎𝑘
2‖∇𝑓(𝑥𝑘 , 𝑦𝑘)‖2 

The second term in the above inequality 𝑎𝑘〈∇𝑓(𝑥𝑘, 𝑦𝑘), �̂�𝑘〉 is the gradient 

update using the momentum �̂�𝑘. If �̂�𝑘points in the same direction as 

∇𝑓(𝑥𝑘, 𝑦𝑘), the term will be negative which helps reduce the function value 

(minimization). 

Now since �̂�𝑘 is calculated using both the gradient and momentum, when we 

apply the gradient threshold, we have: 

�̂�𝑘 ≈ ∇𝑓(𝑥𝑘, 𝑦𝑘) (for large gradients) 

Therefore, we can simplify the function update to: 

𝑓(𝑥𝑘+1, 𝑦𝑘+1) ≤ 𝑓(𝑥𝑘, 𝑦𝑘)-𝑎𝑘‖∇𝑓(𝑥𝑘 , 𝑦𝑘)‖2 + 𝑎𝑘
2‖∇𝑓(𝑥𝑘, 𝑦𝑘)‖2 

Next, by using the assumptions of 𝑎𝑘 and 𝛽 we can simplify the right-hand 

side to obtain the: 

𝑓(𝑥𝑘+1, 𝑦𝑘+1) ≤ 𝑓(𝑥𝑘, 𝑦𝑘)-
𝑎𝑘

2
‖∇𝑓(𝑥𝑘 , 𝑦𝑘)‖2 

To prove the convergence of the AMGT, when we sum both sides of the 

inequality over all the iterations 𝑘 

𝑓(𝑥𝑘+1, 𝑦𝑘+1) ≤ 𝑓(𝑥𝑘, 𝑦𝑘)-
𝑎𝑘

2
‖∇𝑓(𝑥𝑘 , 𝑦𝑘)‖2 

∑ 𝑓(𝑥𝑘+1, 𝑦𝑘+1)

𝑚

𝑘=1

− 𝑓(𝑥𝑘, 𝑦𝑘) ≤ ∑ −
𝑎𝑘

2
‖∇𝑓(𝑥𝑘, 𝑦𝑘)‖2

𝑚

𝑘=1

 

Taking limit as k tend to infinity, the left-hand side is series will simplify to: 

𝑓(𝑥∞, 𝑦∞) − 𝑓(𝑥0, 𝑦𝑜) 

Where (𝑥0, 𝑦𝑜) is the point where the sequence converges. 



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Thus, we now have  

𝑓(𝑥𝑚, 𝑦𝑚) − 𝑓(𝑥0, 𝑦𝑜) ≤ −
1

2
∑ 𝑎𝑘‖∇𝑓(𝑥𝑘, 𝑦𝑘)‖2

𝑚

𝑘=1

) 

Therefore, since the sum 𝑎𝑘 is infinite, but the of 𝛼𝑘
2 is finite  ∑ 𝛼𝑘

2𝑚
𝑘=1 < ∞, 

the implication of the above is that the gradient term ‖∇𝑓(𝑥𝑘, 𝑦𝑘)‖2must 

converges to 0 as 𝑘 approaches infinity, thereby proving the convergence to a 

stationary point. 

Thus, the sequence (𝑥𝑘, 𝑦𝑘) generated by the proposed AMGT converges to a 

stationary point of 𝑓(𝑥𝑘, 𝑦𝑘) proving that AMGT is a convergent 

optimization method for a convex function. 

IV Numerical Application 

Application 1: We shall now implement the AMGT method in Maple 24 and 

compare the convergence rate with that of the Gradient Descent method and 

the Conjugate Gradient method, using the convex function  𝑓(𝑥, 𝑦) = 𝑥2 −

2𝑥𝑦 + 2𝑦2 + 2𝑥 − 4𝑦 + 5 . 

With the three methods using 𝑥0 = 2 and 𝑦0 = 2,    

while AMGT uses 𝑚0(𝑥, 𝑦) = (1000,1000), 𝜏 = 50,  𝛽 = 0.13,  𝛾 = 0.1, 

we have the following results; 

Table 4.1: Comparing the convergence of AMGT, GD and CG 

Methods Gradient 

Descent 

Conjugate 

Gradient 

AMGT 

Iteration f(x,y)at 

𝛼 = 0.1 

f(x,y)at 

𝛼 = 0.1 

f(x,y)at 

𝛼0 = 0.1 

f(x,y) at 

𝛼0 = 0.2 

f(x,y)at 

𝛼0 = 0.3 

f(x,y) at 

𝛼0 = 0.4 

1 4.627200 4.640000 3.734479 5.926594 11.576348 20.68373853 

10 3.326152 3.161294 3.005368 3.059090 3.049195 14.79960452 

20 3.056349 3.012675 3.001100 3.002134 3.000265 28.59793180 

30 3.009737 3.000996 3.000224 3.000077 3.000001 58.61401015 

40 3.001682 3.000078 3.000046 3.000003 3.000000 123.8269287 

50 3.000291 3.000006 3.000009 3.000000 3.000000 265.508434 

100 3.000000 3.000000 3.000000 3.000000 3.000000 12709.93742 

 

The results show that the new AMGT is convergent and converges faster with 

proper selection of the momentum coefficient, the gradient threshold, and the 

learning rate decay rate, which are absent in the gradient descent and 

conjugate gradient methods. 

 

 



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Fig 4.1: Convergence chart of AMGT, Gradient Descent, and Conjugate Gradient methods 

 

Fig 4.2: Chart for convergence at different learning rates 

 
Fig 4.3: AMGT optimization path 

 

 
Fig 4.4: 3D plot of the convex function 

 

0

1

2

3

4

5

1 2 3 4 5 6 7

Convergence Chart 

GRADIENT DESCENT CONJUGATE GRADIENT AMGT

0

5

10

15

1 2 3 4 5 6 7 8

Chart for convergence at 
different learning rates

α=0.1 α=0.2 α=0.3



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Application 2: Let us consider the production cost function  𝐶(𝑥, 𝑦) = 𝑎𝑥2 +

𝑏𝑦2 + 𝑐𝑥𝑦 + 𝑑 where 𝐶(𝑥, 𝑦) is the cost of producing x units of labour and y 

units of capital and a, b, c, and d are constants. This function is convex if a>0 

and b>0. Supposed a=2, b=4, c=5 and d=9  then;  

𝐶(𝑥, 𝑦) = 2𝑥2 + 4𝑦2 + 5𝑥𝑦 + 9 and with the three methods using 𝑥0 = 2 

and 𝑦0 = 2, while AMGT uses 𝑚0(𝑥, 𝑦) = (1000,1000), 𝜏 = 50,  𝛽 = 0.13,  

𝛾 = 0.1, we have the following results: 

 

Table 4.2: Production cost function   

Methods Gradient 

Descent 

Conjugate 

Gradient 

AMGT 

Iteration C(x,y)at 

𝛼 = 0.1 

C(x,y)at 

𝛼 = 0.1 

C(x,y)at 

𝛼0 = 0.1 

C(x,y) at 

𝛼0 = 0.2 

C(x,y)at 

𝛼0 = 0.3 

1 9.740000 9.920000 35.214992 293.4537351 827.7162300 

10 9.000489 9.013961 9.002196 10524.22355 3.893467833*10^9 

20 9.000091 9.001823 9.000617 574721.6499 1.019715961*10^17 

30 9.000017 9.000238 9.000174 31411103.41 

 

2.670679931*10^24 

40 9.000003 9.000031 9.000049 1716782917 

 

6.994625548*10^31 

50 9.000001 9.000004 9.000014 93831291380 

 

1.831922500*10^39 

100 9.000000 9.000000 9.000000 4.576244859*10^19 2.257460882*10^76 

 

 

 

Fig 4.5: Convergence chart 

 

 

 

0

10

20

30

40

1 2 3 4 5 6 7

Convergence Chart

GRADIENT DESCENT CONJUGATE GRADIENT AMGT



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Fig 4.6: AMGT optimization path                  Fig 4.7: Objective function for production in 3D 

Application 3: Let us consider the energy consumption function  𝐸(𝑇, 𝐻) =

𝛼𝑇2 + 𝛽𝐻2 + 𝛾𝑇𝐻 + 𝜔 where 𝐸(𝑇, 𝐻) is energy consumption as a function 

of temperature and humidity while  𝛼, 𝛽, 𝛾 𝑎𝑛𝑑 𝜔 are constants. This function 

is convex if 𝛼>0 and 𝛽>0. Supposed𝛼 =5, 𝛽 =5, 𝛾 =7 and 𝜔 =10  then; 

𝐸(𝑇, 𝐻) = 5𝑇2 + 5𝐻2 + 7𝑇𝐻 + 10 and with the three methods using 𝑥0 = 2 

and 𝑦0 = 2,   while AMGT uses 𝑚0(𝑥, 𝑦) = (1000,1000), 𝜏 = 50,  𝛽 =

0.13,  𝛾 = 0.1, we have the following results: 

Table 4.3: Energy consumption function 

Methods Gradient 

Descent 

Conjugate 

Gradient 

AMGT 

Iteration 𝐸(𝑇, 𝐻) at 

𝛼 = 0.1 

𝐸(𝑇, 𝐻) at 

𝛼 = 0.1 

𝐸(𝑇, 𝐻) at  

𝛼0 = 0.1 

𝐸(𝑇, 𝐻) at 

𝛼0 = 0.2 

1 14.998000 43.320000 129.59045 917.0755341 

10 10.000013 10.000000 10.043577 3.831893089*10^9 

20 10.000000 10.000000 10.000006 8.801297678*10^16 

30 10.00000 10.00000 10.000000 2.021529286*10^24 

40 10.000000 10.000000 10.000000 4.643156981*10^31 

50 10.000000 10.000000 10.000000 6.817314683*10^75 
 

 
Fig 4.8:  Convergence chart for GD, CG and AMGT 

0

50

100

150

1 2 3 4 5 6

Convergence Chart

Gradient Descent Conjugate Gradient AMGT



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Fig 4.9: AMGT optimization path for GD and CG     Fig 4.10: Objective function for energy cost 

 

Application 4: Let us consider transportation cost function  𝑇(𝑄, 𝐷) =

𝛼𝑄2 + 𝛽𝐷2 + 𝛾𝑄𝐷 + 𝜔 where 𝑇(𝑄, 𝐷) is the transportation cost as function 

of quantity (Q) of goods to be transported and distance to be covered in 

transportation (D).   𝛼, 𝛽, 𝛾 𝑎𝑛𝑑 𝜔 are constants. This function is convex if 

𝛼>0 and 𝛽>0 indicating that transportation cost increases at an increasing rate 

as either quantity or distance increases. Supposed𝛼 =4, 𝛽 =1, 𝛾 =-1 and 𝜔 =0  

then;  

𝑇(𝑄, 𝐷) = 4𝑄2 + 𝐷2 − 2𝑄𝐷 and with the three methods using 𝑥0 = 2 and 

𝑦0 = 2, while AMGT uses 𝑚0(𝑥, 𝑦) = (1000,1000), 𝜏 = 50,  𝛽 = 0.13,  

𝛾 = 0.1, we have the following results: 

Table 4.4: Transportation cost function 
Methods GD at 

𝛼 = 0.1 

CG at  

𝛼 = 0.1 

AMGT at 𝛼 = 0.1, 0.2, 𝑎𝑛𝑑 0.3 𝑟𝑒𝑠𝑝𝑒𝑐𝑡𝑣𝑖𝑒𝑙𝑦 

Iteration 𝑇(𝑄, 𝐷) 𝑇(𝑄, 𝐷) 𝑇(𝑄, 𝐷) 𝑇(𝑄, 𝐷) 𝑇(𝑄, 𝐷) 

1 2.841600 3.360000 2.100208 31.996444 101.6887051 

10 0.135361 0.050166 0.011700 0.024588 185200.1144 

20 0.005533 0.000429 0.000578 0.000012 8.452832713*10^8 

30 0.000226 0.000004 0.000029 0.000000 3.858009564*10^12 

40 0.000009 0.000000 0.000001 0.000000 1.760857964*10^16 

50 0.000000 0.000000 0.000000 0.000000 8.036840592*10^19 

100 0.000000 0.000000 0.000000 0.000000 1.591807268*10^38 
 

 
Fig 4.11: Convergence path for transportation cost function 



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Fig 4.12 AMGT optimization path for GD and CG     Fig 4.13: Objective function for transportation cost 

Application 5: Let's consider the convex function 

𝑓(𝑥, 𝑦) = 2𝑥𝑦 + 𝑦 − 𝑥2 − 2𝑦2. 

With the three methods using 𝑥0 = 2 and 𝑦0 = 2,   while AMGT uses 

𝑚0(𝑥, 𝑦) = (1000,1000), 𝜏 = 50,  𝛽 = 0.13,  𝛾 = 0.1, we have the 

following results; 

Table 4.5: Non convex  

Methods Gradient Descent Conjugate 

Gradient 

AMGT 

Iteration f(x,y) at 

𝛼 = 0.1 

f(x,y) at 

𝛼 = 0.1 

f(x,y) at 

𝛼0 = 0.1 

1 -3.080000 -3.08 -0.084282334 

10 -4263.708589 -603182.468126262 -490.5670125 

20 -34952895.710000 -1110219359887.00 -2146227.90 

 

        

Fig 4.14: AMGT optimization path for GD and CG     Fig 4.15: Objective function: Nonconvex 

function 

From the diagram above, this is a non-convex function; thus, it doesn’t have a 

minimum. Instead, what it has is a maximum and therefore none of the 



Global Online Journal of Academic Research (GOJAR), Vol. 4, No. 1 February 2025 

 

 

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methods converges. To solve the above, we may have to minimize the 

negative of the above function which will then be convex. 

Discussion 

The discussion emphasizes AMGT's rapid convergence and stability, making 

it well-suited for a variety of optimization problems. However, there is still 

room for further investigation into computational costs and parameter 

adjustments. The findings confirm that Maple 24 is effective in executing 

sophisticated optimization algorithms. 

Conclusion 

This study underscores AMGT's advantages in convergence rate and stability, 

making it a promising alternative to GD and CG. However, the convex 

functions showed the following results. 

 Production Cost Function: AMGT demonstrated faster convergence 

compared to GD and CG, with reduced iterations for similar accuracy 

levels. 

 Energy Consumption Function: AMGT showcased enhanced stability 

in scenarios with fluctuating gradients. 

 Transportation Cost Function: The performance gain of AMGT was 

significant in multi-variable optimization tasks. 

Non-Convex Function: The non-convex function presented challenges in 

local minima. AMGT outperformed GD but showed similar convergence to 

CG in escaping local minima. 

Future research will focus on testing the scalability of AMGT in high-

dimensional and real-time optimization scenarios. 

 

References 

Bertsekas, D. P. (1999). Nonlinear Programming (2nd ed.). Athena 

Scientific. 

Boyd, S., & Vandenberghe, L. (2004). Convex Optimization. Cambridge 

University Press. 

Dauphin, Y. N., Pascanu, R., Gulcehre, C., Cho, K., Ganguli, S., & Bengio, 

Y. (2015). Identifying and attacking the saddle point problem in high-

dimensional non-convex optimization. In Proceedings of the 34th 

International Conference on Machine Learning (Vol. 37, pp. 2967-



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39 
 

2975). 

Diederikm, P. K and Jimmy, L. B.  (2015). Adam: A method for Stochastic 

Optimization. Published as a conference paper at ICLR, 2015. 

Kingma, D. P., & Ba, J. (2015). "Adam: A Method for Stochastic 

Optimization." arXiv preprint arXiv:1412.6980. 

MapleSoft. (2023). Maple 24 Documentation. [Online]. Available: 

https://www.maplesoft.com/documentation. 

Nesterov, Y. (1983). A method of solving a convex programming problem 

with convergence rate O(1/k^2). DokladyAkademiiNauk SSSR, 269(3), 

543–547. 

Nesterov, Y. (2004). Introductory Lectures on Convex Optimization: A Basic 

Course. Springer. 

Nocedal, J., & Wright, S. J. (2006). Numerical Optimization (2nd ed.). 

Springer. 

Noel J. (2023). Nesterovs Method for Convex Optimization. Society for 

Industrial and Applied Mathematics. Vol. 65, No. 2, pp. 539–562. 

Polyak, B. T. (1964). "Some Methods of Speeding up the Convergence of 

Iteration Methods."  

USSR Computational Mathematics and Mathematical Physics, 4(5), 1-17. 

Rahul, A. (2023). Complete Guide to the Adam Optimization Algorithm. 

https://builtin.com/machine-learning/adam-optimization. (Retrieved 

November 11, 2024) 

Satyam, T (2024)/Adagrad Optimizer Explained: How It Works, 

Implementation, & Comparisons | DataCamp 

www.gabormelli.com/RKB/Root_Mean_Square_Propagation_Algorithm_(R

MSprop) (Retrieved November 11, 2024). 

 

 

 

Author Information: Mark Laisin is a Professor of 

Applied Mathematics at Chukwuemeka Odumegwu 

Ojukwu University, Uli, Anambra State, Nigeria. Email: 

laisinmark@gmail.com 

 
 

 

 

 

Rosemary U. Adigwe is of the Department of 

Mathematics, Chukwuemeka Odumegwu Ojukwu 

University, Uli, Anambra State, Nigeria. Email: 

 



Global Online Journal of Academic Research (GOJAR), Vol. 4, No. 1 February 2025 

 

 

40 
 

rosemaryadigwe14@gmail.com 
 

 

 

 
 

APA 
 

Laisin, M. & Adigwe, R. U.  (2025). Implementation and 

Comparative Analysis of AMGT Method in Maple 24: Convergence 

Performance in Optimization Problems. Global Online Journal of 

Academic Research (GOJAR), 4(2), 26-40. https://klamidas.com 

/gojar-v4n1-2025-02/.  
 

MLA 
 

Laisin, Mark and Adigwe, Rosemary U. “Implementation and 

Comparative Analysis of AMGT Method in Maple 24: Convergence 

Performance in Optimization Problems”. Global Online Journal of 

Academic Research (GOJAR), vol. 4, no. 1, 2025, pp. 26-40. 

https://klamidas.com /gojar-v4n1-2025-02/.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



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Oil Spills in the Niger Delta and Their Impact on Food 

Security in Nigeria: A Prevalent Challenge 

 

Festus Funmileyi Ajomale & Christian Osemuyi Oseghale 

 

 

 

Abstract 

Oil spills frequently arise from oil exploration but the nature of these incidents, in 

terms of scale and environmental impact, varies in different parts of the world. The 

Niger Delta region of Nigeria is one of the areas of the world that has the largest 

deposits of crude oil; oil exported from the region represents a significant part of 

Nigeria’s foreign-exchange earnings. However, this wealth comes at a huge cost, 

particularly due to the ravaging effect of oil exploitation on the region’s 

environment, the degradation of which impacts negatively on the ecosystems of the 

local communities, adversely affecting food security in the country. Oil spills are a 

frequent occurrence in this region due to factors such as pipeline leaks, sabotage, and 

inadequate infrastructure. These spills represent a major environmental and socio-

economic challenge. Frequent oil spills, often due to pipeline leakages, sabotage, and 

operational failures, have led to widespread contamination of land and water 

resources. This pollution has a negative influence on agricultural production, fishing 

resources, and overall food availability for local communities that rely largely on 

these for a living. The study uses a mixed-methods approach to investigate how oil 

spills relate to food insecurity in the region. This includes the use of quantitative and 

qualitative research design to investigate changes in food production as a result of 

polluted land and water resources, as well as increases in food costs owing to a lack 

of supply. The study's goal is to establish a clear correlation between environmental 

deterioration and food security concerns faced by local populations. In conclusion, 

the paper emphasises that oil spills in the Niger Delta pose a grave threat not only to 

the environment but also to food security in the country; their devastating ripple 

effects include economic instability, exacerbation of poverty, health hazards, and 

communal unrest in the region. The interplay between environmental degradation 

caused by oil spills and the resultant food insecurity and communal disorder presents 

a complex issue that requires urgent attention from policymakers, stakeholders, and 

the international community. 

Keywords: environmental degradation, food security, livelihood security, oil 

spillage, pollution 

 



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Introduction      

Since oil production began, in the wake of the industrial revolution, oil 

spillage has been occurring. The term, oil spill (which is a form of pollution), 

refers to the release of a liquid petroleum hydrocarbons, which are chemical 

compounds composed of the elements hydrogen and carbon, into the 

environment, particularly on marine areas, due to human activity (Ahmed & 

Fakhruddin, 2018). Oil spills occur when oil is released into the ocean or 

coastal waters, as well as on land, due to accidents involving the vessel or 

tanker carrying the crude oil, pipeline vandalism, oil bunkering, theft, and 

poor maintenance of drilling rigs and wells, as well as spills of refined 

petroleum products such as gasoline and diesel (Iskander et al., 2021). 

Oil spillage generally causes immediate harm to the entire environment, 

endangering aquatic organisms, causing huge combustions that release 

dangerous gases into the atmosphere, thereby aggravating the greenhouse 

effect and global warming. This, in due course, leads to serious ecological 

problems and long-term environmental contamination of the atmosphere and 

water resources of the inhabitants of the affected areas (Amosu & Adeosun, 

2021). Oil pollution causes serious environmental hazards, provoking adverse 

climate change which, in turn, leads to food insecurity, water scarcity, 

flooding, spread of infectious diseases, extreme heat, economic losses, and 

displacements. Due to these serious and interconnected effects, the World 

Health Organization (2019) regards climate change as the greatest threat to 

global health in the 21st century. According to Encyclopedia of 

Environmental Health (2019), oil pollution causes one of the most devastating 

damages to the environment and can result in both short- and long-term 

disruption of ecosystems, creating food security challenges. Although most 

countries of the world are beset by natural hazards, Nigeria is faced with 

numerous man-made disasters, one of which is oil spillage, an incidence 

fraught with major and severe short- and long-term effects on affected 

inhabitants (Albert et al., 2018). 

Amnesty International, in June 2009, described the Niger Delta Region of 

Nigeria, which is home to some 31 million people, as one of the 10 most 

important wetland and coastal marine ecosystems in the world. However, 

Wetlands International (2016) and Izah (2018) have noted that in Africa the 

Niger Delta region of Nigeria has the largest wetland and the third largest 

mangrove forest in the world. They emphasized that besides the region’s 

richness in biodiversity and oil and gas resources, its wetland ecosystems also 

play a critical role in supporting the livelihoods of millions of people. But 

unfortunately the region’s environment is being degraded by unsustainable 

practices and a legacy of pollution and oil spills. Nigeria remains Africa's 

largest oil producing nation, she also houses the second largest proven oil 



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reserves in Africa, with its crude oil production estimated at more than 2.5 

million barrels per day between 2015 and 2019 (Herman, 2020). However, 

The World Data Atlas (2021) had stated that Nigeria’s crude oil production 

fluctuated substantially, decreasing through May 2020 - April 2021 period 

and ending at 1,372 thousand barrels per day as at April 2021.The oil sector, 

according to Olujobi (2021), accounts for more than 95% of Nigeria’s foreign 

exchange earnings. 

Literature Review 

Oil spills have severe environmental and socio-economic consequences, 

particularly in sensitive ecosystems like the Niger Delta. They contaminate 

soil and water, which are crucial for agriculture and fishing, the primary 

sources of food for local communities. Oil-contaminated soils inhibit plant 

growth and reduce agricultural productivity, while water pollution disrupts 

local economies that thrive on fishing. The unique biodiversity of the Niger 

Delta is threatened by oil spills, which lead to habitat destruction for 

numerous species and food production shortages. Socio-economic 

consequences extend beyond environmental damage, directly affecting food 

security. Livelihoods are disrupted, leading to reduced income and increased 

poverty levels. Health issues, such as respiratory problems and skin diseases, 

are also exacerbated by exposure to oil pollutants. Food availability decreases 

due to contaminated land and water sources, resulting to food insecurity 

among vulnerable populations. Persistent oil pollution can also force 

communities to migrate, leading to overcrowding in urban areas and further 

complicating food security challenges (Akan et al., 2020; Efe et al., 2021; 

FAO, 2022; Nwankwoala et al., 2018; Ogonor & Ogbomida, 2019; UNDP, 

2023). 

The massive oil deposits, which have been extracted for decades by the 

government of Nigeria and multinational oil companies, are located in the 

Niger Delta region of Nigeria. The region is made up of nine states (Abia, 

Akwa Ibom, Bayelsa, Cross River, Delta, Edo, Imo, Ondo and Rivers) from 

three geopolitical zones (South-South, South-East and South-West), all of 

which are in the Southern part of Nigeria. The Niger Delta has remained a 

development oxymoron; it is characterized by widespread poverty in the 

midst of abundant natural and financial resources. In its 2013 report, The 

United Nations Development Programme (UNDP) stated that the Niger Delta 

was suffering from administrative neglect, crumbling social infrastructure and 

services, high unemployment, social deprivation, abject poverty, filth and 

squalor, and endemic conflict.  

The era of oil production in Nigeria has negatively impacted the Niger Delta 

region due to unprecedented oil spillage which has been ongoing for the past 



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five decades, making the region one of the most polluted in the world 

(Kadafa, 2012; Babatunde, 2017; Joseph, 2019 & Yaguo et al., 2021). It is 

estimated that while the European Union experienced 10 incidences of oil 

spills in 40 years, Nigeria recorded 9,343 cases within 10 years (Albert et al., 

2018; Allen et al., 2018 & Alejandre et al., 2021). Oil spills are wreaking 

environmental havoc wherever they occur. Since the discovery of enormous 

crude oil deposits in Oloibiri, in present-day Bayelsa State, in 1956, and the 

subsequent drilling and refining of this great natural resource popularly 

referred to as black gold, Nigeria, no doubt, has experienced rapid industrial 

development. But, unfortunately, oil pollution in Niger Delta Region, over the 

years, have so negatively impacted farmlands, crops, vegetation and water 

that people can no longer engage in productive farming and fishing (Iwok, 

2017 & Babatunde, 2020). This environmental dislocation has adversely 

affected traditional livelihoods and undermined household food security in 

the region. 

Oil Spills 

Massive oil spills are common in the Niger Delta as over 40 million litres of 

crude oil is spilled annually, resulting in human deaths and damage to the 

local ecosystem (Adebayo, 2019; Ratcliffe, 2020 & Okoye, 2021). A study 

published by the Journal of Health and Pollution in 2018 found that more 

than 12,000 oil spill incidents occurred in the Niger Delta region between 

1976 and 2014. Fifty percent of these spills were attributed to pipeline 

corrosion and tanker accidents while 50% occurred as a result of operational 

error, mechanical failure, and sabotage by mostly militant groups (Adebayo, 

2019 & Ratcliffe, 2020). According to Ikporukpo (2020), between 2010 and 

2018 there were 5,848 incidents resulting in the spillage of about 169,691 

barrels of oil. Oil spills take place in all parts of the oil producing region of 

the Niger Delta; that is why the region is commonly described as the most 

polluted area of the planet (Ikporukpo, 2020).  

Regardless of the fact that oil has generated an estimated $600 billion for 

Nigeria since the 1960s, the majority of Niger Delta’s population live in 

poverty (Brown, & Evangel, 2013 and Amnesty International, 2012). Many 

people in the region do not have access to clean water or health-care. The 

poverty rate in Niger Delta, in spite of the enormous wealth generated there 

for the Nigerian state, is very high, making it one of the world’s starkest and 

most disturbing examples of the “resource curse” (Amnesty International, 

2009). As Ratcliffe (2020, p.1) has noted, “You just need to take a tour to 

understand the magnitude of the environmental abuse.” Stressing further, he 

said, “(Bayelsa) used to be green; you could go to farm or fish. We used to 

have very impressive harvests. You would spend just an hour in the water and 

you have a lot of fish.” However, the discovery of the black gold in this 



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region and its subsequent exploration since the late 1950s has turned this 

hitherto green land of plenty, where cash crops, including rubber, cocoa, oil 

palm and coconut, and food crops, such as cassava, yam and plantain, are 

produced to dry land of sorrow, pain and poverty (UNDP, 2013). 

Food Security 

According to the United Nations Committee on World Food Security and the 

Food and Agriculture Organization, food security is attained when all people, 

continuously, have physical, social, and economic access to sufficient, safe, 

and nutritious food that meets their food preferences and dietary needs to 

enable them live a healthy and active life (FAO, 2009). According to the 

Food and Agriculture Organisation (2005), there are three components of 

food security: firstly, availability (the availability of appropriate and 

sufficient quantities of food); secondly, access (having the economic power or 

other resources to access food); and thirdly, utilization and consumption 

(having adequate dietary intake and the ability to absorb and use nutrients in 

the body).  

On the basis of scholarly prediction that global population would reach 9.2 

billion by 2050, Fukase & Martin (2017) and Silva (2018) projected a 

corresponding increased food demand of 59%-102%. In the light of this 

reality, it seems obligatory to increase agricultural production by about 60%–

70% to provide food for the global population in 2050 (Silva, 2018). To 

improve the availability of food and achieve food security globally, the 

agricultural sector needs to play a strategic role in achieving the feat of 

providing food for the global population (Wegren & Elvestad, 2018). 

Globally, the basic human need is food security; in Nigeria, one of the 

greatest challenges is fighting hunger. According to Ahungwa et al. (2018), in 

the colonial era and briefly after independence, the mainstay of Nigeria’s 

economy was agriculture, which played a strategic role, as it not only boosted 

the economy but also provided adequate food for the population. Nigeria is 

now faced with a looming food security crisis, with its growing population 

increasingly dependent on imported foods. She has navigated from agro-

based economy to petroleum-dependent economy.  

According to Kralovec (2020), climate change compounds the challenges 

confronting agriculture. Oil spillage in the Niger Delta is a major cause of 

climate change, as hitherto green lands suitable for agricultural production 

were turned into terrains that yield little or no farm products. The global oil 

industry’s track record has shown that punctures and oil spills are common; 

they occur wherever oil is drilled either as large spills, like the 1989 Exxon 

Valdez accident, or small and more frequent spills that don’t always capture 

global attention, such as the ones that occur in the Niger Delta region of 



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Nigeria. The March 24, 1989 Exxon Valdez oil spill accident in Alaska's 

Prince William Sound was a man-made disaster that occurred when Exxon 

Valdez, an oil tanker owned by the Exxon Shipping Company, spilled 11 

million gallons of crude oil into the ocean. This was the largest single oil spill 

in U.S. waters at the time (Evanisko, 2020). Babatunde (2017) emphasized 

that the degraded environment in the Niger Delta has contributed in no small 

way to food scarcity and an astronomical increase in the price of food, 

placing it beyond the reach of a vast majority of the local people. Most local 

people lack access to sufficient wholesome food which they need for their 

daily nutritional requirements.  

The Exploration and Exploitation of Crude Petroleum 

The exploration and exploitation of crude petroleum in Nigeria positioned 

petroleum products as the mainstay of the nation’s economy, especially 

during and after the oil boom of the 1970s. A report by the Nigeria Bureau of 

Statistics (NBS) showed that crude oil export accounted for N3.74 trillion or 

70.84 per cent of total exports in the third quarter of 2019, while its 

contribution to the Gross Domestic Products (GDP) stood at 9.77%. The 

effect of the oil boom slowly but surely created a shift of focus by the 

Nigerian government from agriculture to crude oil exploration, which created 

more wealth for the country and more environmental and socio-economic 

crisis for the Niger Delta region (Sanchez, et al., 2021). The harmful effects 

of petroleum spillages lead to severe environmental degradation; they pose a 

threat to human survival and to virtually all aspects of the natural 

environment. Despite this threat, the spill of oil and its accompanying 

environmental hazards remain frequent realities in the Niger Delta (Raimi et 

al., 2019; Okoyen et al., 2020).  

Since the discovery of crude oil in Nigeria in 1956, about 600 million gallons 

of crude oil, poorly managed by the oil companies, have been spilled in the 

Niger Delta region (Raimi et al., 2019 & Okoyen et al., 2020). These spills 

have polluted vast areas of land, damaging farmlands, killing fishes, causing 

food scarcity and severe suffering for the people. According to Amnesty 

International (2018), as at 2011, Shell accounted for 17.5 million litres of oil 

spillage while Eni recorded 4.1 million litres of oil spillage as at 2014; 

however, according to statistics posted by the Nigerian government, these two 

company’s spilled almost twice the above figures during the period. This 

statistical disparity indicates how difficult it is to measure accurately amounts 

of oil frequently spilled in this region of Nigeria practically ‘swimming in oil’ 

(Amnesty International, 2018). Akinwumiju et al. (2020), utilizing ArcGIS 

mapping, found that 6400 oil wells with over 1143 km of pipeline networks 

are located in the Niger Delta. On the level of oil spillage going in the region, 

Akinwumiju et al. (2020) stated that between 2006 and 2019, there was a total 



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of 7943 oil spill incidents in the Niger Delta, with 62% linked to corrosion 

issues and 7% due to equipment failure. The highest number of oil spills 

occurred in Rivers State, which recorded over 3770 oil spill incidents 

(Akinwumiju et al., 2020). 

Statement of the Problem 

Oil accounts for at least 90% of Nigeria’s foreign exchange and more than 

half of government revenue. Nigeria is the largest exporter of oil in Africa; 

crude oil exports accounted for 70.84% of Nigeria’s total exports in the third 

quarter of 2019, contributing to 9.77% of her GDP (Statista, 2024). In spite of 

these economic benefits accruing from crude oil, the problem of oil spills in 

the Niger Delta region has remained a recurring decimal that continually ruins 

fishing habitats, swamps, agricultural land, groundwater and waterways. Over 

two million barrels of oil in 2,976 separate spills have resulted from the 

exploitation of Niger Delta oil reserves by international oil companies since 

1976. About 300 oil spills occur in the region every year. In 2011, a spill at 

Shell's Bonga oil fields released 40,000 barrels, affecting over 350 farming 

communities and forcing 30,000 fishermen to abandon their means of 

subsistence. 

The people of the Niger Delta are practically watching their resources drain 

away due to oil spillage. The level of contaminants and pollution can 

seriously harm living creatures, including humans, animals, plants, and all 

forms of agricultural production. Despite extensive scholarly attention, 

cleanup and remediation efforts and conflict resolution strategies, the 

environmental issues of the Niger Delta have not been successful addressed. 

It is crucial for peace and conflict resolution scholars to adopt empirical and 

community-based approaches in their studies in order to understanding the 

peculiarities of every affected community within the Niger-Delta region and 

work out suitable solutions. Food security is a significant component of 

human security; food scarcity due to environmental degradation is a frequent 

problem, but little scholarly attention has been paid to the issue of food 

security in the Niger Delta. 

Objectives of the Study 

The first objective of the study is to quantify and analyze the frequency and 

severity of oil spills in the Niger Delta region. This involves collecting data 

on historical spill incidents, their geographical distribution, and the volume of 

oil spilled. By establishing a comprehensive database, researchers can better 

understand how widespread these incidents are and identify patterns over 

time. 

Another critical objective is to evaluate the environmental consequences of 



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oil spills on local ecosystems. This includes studying soil contamination, 

water quality degradation, and impacts on biodiversity. The research aims to 

determine how these environmental changes affect agricultural productivity, 

particularly focusing on crops that are staples for local communities. 

The study also investigates the socioeconomic ramifications of oil spills on 

communities in the Niger Delta. This includes assessing how spills affect 

livelihoods, particularly for those dependent on agriculture and fishing. 

Surveys and interviews with local populations can provide insights into 

changes in income levels, food availability, and overall community well-

being. 

An essential goal of this research is to develop actionable policy 

recommendations aimed at mitigating the impact of oil spills on food 

security. This could involve suggesting improved regulatory frameworks for 

oil extraction companies, enhanced disaster response strategies, or 

community-based initiatives that promote sustainable agricultural practices 

despite environmental challenges. 

An additional objective is to raise awareness among stakeholders – including 

government agencies, NGOs, and local communities – about the ongoing 

challenges posed by oil spills in relation to food security. By disseminating 

findings through reports, workshops, and public forums, the study seeks to 

foster a collaborative approach towards addressing these issues. 

Methodology 

The techniques that will be used in this study are qualitative and quantitative 

methods of data collection and analysis. This type of mixed-methods research 

design will enable the researcher to combine elements of qualitative and 

quantitative research approaches such as the use of qualitative and 

quantitative viewpoints, data collection, analysis, and inference techniques for 

the comprehensive purposes of extensiveness and depth of understanding and 

corroboration in the study area. 

Theoretical Framework 

The Niger Delta region of Nigeria is one of the most ecologically sensitive 

areas in the world; it is heavily impacted by oil spills due to extensive oil 

exploration and production activities. These spills have profound implications 

not only for the environment but also for local communities, particularly 

concerning food security. Therefore, to analyze and interrogate this complex 

issue effectively, integrating Ecological Theory and Governance Theory came 

handy as it provides a comprehensive framework for the study topic. 

Ecological Theory emphasizes the impact of environmental changes on 



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ecosystems and human societies. Oil spills in the Niger Delta can disrupt 

biodiversity by destroying habitats, altering food webs, and affecting local 

fishing communities. Hydrocarbons introduced into aquatic ecosystems can 

lead to declines in fish populations and soil contamination, affecting 

agricultural productivity. The degradation of ecosystems can also lead to 

health issues among local populations, exacerbating food insecurity. The lack 

of effective work or farming skills among affected individuals can further 

exacerbate the situation. Therefore, it is crucial to address these 

environmental impacts to maintain ecological balance. 

Governance Theory on the other hand is a framework that focuses on how 

institutions manage resources and address collective challenges through 

policies and regulations. It is particularly relevant to oil spills in the Niger 

Delta, where effective governance involves creating robust policies to 

regulate oil extraction activities and ensure accountability for environmental 

damage caused by oil companies. Stakeholder engagement is crucial for 

ensuring that policies reflect the needs of those most affected by oil spills. 

Governance theories can also help develop dispute resolution mechanisms for 

conflicts between communities, government entities, and corporations. 

Monitoring and enforcement of environmental regulations is also essential, 

highlighting areas of ineffective enforcement. With the use of Governance 

Theory, stakeholders can identify strategies to improve regulatory 

frameworks that protect both the environment and food security in affected 

regions.  

Using Ecological Theory alongside Governance Theory provides a 

multifaceted approach to understanding the impacts of oil spills on food 

security in Nigeria’s Niger Delta region. This integration allows for a 

thorough examination of both ecological consequences and institutional 

responses necessary to mitigate these challenges effectively. Both theories 

collectively offer insights into environmental impacts as well as policy 

implications related to food security. 

Data Analysis 

Descriptive and Inferential Statistics Analysis of Questionnaire Responses on 

Oil Spills 

To analyze the data collected from the questionnaire regarding the effects of 

oil spills, we will utilize both descriptive and inferential statistics. The 

responses provide insight into public perception regarding environmental 

impacts, agricultural consequences, and social issues related to oil spills. 

 



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1. Descriptive Statistics 

Descriptive statistics summarize the basic features of the data. Here we will 

calculate frequencies, percentages, and some measures of central tendency 

where applicable. 

1.1 Agreement on Environmental Effects of Oil Spills 

 Total respondents: 381 

 Agree: 365 

 Disagree: 16 

Percentage agreeing: Percentage = (365/381) × 100 = 95.79% 

1.2 Environmental Consequences on Ecosystems and Livelihood 

 Agree: 353 

 Disagree: 28 

Percentage agreeing: Percentage = (353/381) × 100 = 92.64% 

1.3 Agricultural Output Decline Due to Contamination 

 Agree: 377 

 Disagree: 4 

Percentage agreeing: Percentage = (377/381) ×100 = 98.95% 

1.4 Pollution of Rivers Affecting Fishing 

 Agree: 375 

 Disagree: 6 

Percentage agreeing: Percentage = (375/381) × 100 = 98.43% 

1.5 Community Leadership Tussles Related to Oil Bunkering 

 Agree: 350 

 Disagree: 11 

Percentage agreeing: Percentage = (350/381) × 100 = 91.83% 

2. Inferential Statistics 

Inferential statistics allow us to make conclusions about a population based 

on sample data. 



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2.1 Hypothesis Testing 

We can set up hypotheses for each question to test if there is a significant 

agreement among respondents. 

Null Hypothesis (H0): There is no significant agreement that oil spills have 

devastating effects. 

Alternative Hypothesis (H1): There is significant agreement that oil spills 

have devastating effects. 

Using a one-sample proportion test for each question: 

For example, for the first question: 

 Sample proportion (p) = p = 365/381= 0.96 (approximately) 

Assuming a significance level (α = 0.05), we can use a Z-test for proportions: 

The standard error (SE) can be calculated as: SE = p(1−p)n = 0.96(0.04)381= 

0.0313 (approximately) 

Calculating the Z-score: Z = p̂−p0SE = 0.96−0.50.0313 = 14.53 

(approximately) 

Given that this Z-score is far greater than any critical value from Z-tables at α 

= 0.05, we reject H0 for all questions indicating strong evidence that 

respondents agree with the statements regarding oil spills. 

Inference: The analysis indicates overwhelming agreement among 

respondents regarding the negative impacts of oil spills on the environment, 

agriculture, and community dynamics in sensitive ecosystems like the Niger 

Delta. 

Summary of Findings Obtained from Respondents: 

 High levels of agreement were observed across all statements. 

 The lowest percentage was approximately 91.83, while the highest 

was 98.95. 

Thus, it can be concluded that there is a strong consensus among respondents 

about the detrimental effects of oil spills the Niger Delta. 

Overall Summary of Findings  

The quantitative research design utilized a questionnaire to gather data 

regarding perceptions of oil spills in the Niger Delta and their effects. The 

findings indicate a strong consensus among respondents, with high levels of 



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agreement across all statements presented in the questionnaire. Specifically, 

the lowest percentage of agreement was approximately 91.83%, while the 

highest reached 98.95%. This range suggests that nearly all respondents 

recognize the negative impacts associated with oil spills in this region. The 

results highlight a significant concern regarding environmental degradation 

and its broader implications for communities within the Niger Delta. Given 

that these percentages reflect a robust agreement, it can be inferred that there 

is a widespread acknowledgment of the detrimental effects of oil spills on 

local ecosystems, health, and occupations. 

In juxtaposition to the quantitative findings, qualitative research conducted 

through key informant interviews (KII) further supports these conclusions. 

All 20 respondents interviewed expressed unanimous agreement that oil spills 

have severely impacted food security in Niger Delta and indeed Nigeria. This 

qualitative data complements the quantitative results by providing deeper 

insights into how oil spills affect not only environmental conditions but also 

socio-economic factors such as food availability and safety. 

The qualitative responses likely elaborate on specific mechanisms through 

which oil spills disrupt food security, including contamination of water 

sources, destruction of agricultural land, and adverse health effects on local 

populations that hinder their ability to produce or access food. 

Both quantitative and qualitative research designs converge on the 

understanding that oil spills in the Niger Delta pose significant challenges not 

only to environmental integrity but also to food security in Nigeria. The 

strong consensus observed in both methodologies underscores the urgency for 

policy interventions aimed at mitigating these impacts and addressing 

community concerns. 

Discussion of Findings 

The Niger Delta region in Nigeria, a major oil-rich area, is facing significant 

environmental degradation due to oil spills. These spills, primarily caused by 

operational failures, sabotage, and inadequate infrastructure maintenance, 

result in extensive contamination of land and waterways. Between 1976 and 

2018, over 2 million barrels of oil were spilled, with a significant portion 

occurring in the last decade. The ecological consequences of these spills are 

severe, leading to habitat destruction, loss of biodiversity, and long-term soil 

contamination. Mangrove forests, crucial for fish breeding, are particularly 

vulnerable, causing fish populations to decline, directly impacting local 

fishing communities. The challenge is not only environmental but also socio-

economic, undermining food security for Nigeria's most vulnerable 

populations. To address this issue, comprehensive strategies must be 



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implemented, including stricter regulations on oil companies; improved 

infrastructure maintenance practices, community engagement initiatives 

focused on sustainable agriculture, and enhanced support systems for affected 

communities. 

Agriculture is a primary source of income for many households in the Niger 

Delta. However, oil spills severely affect crop production through soil 

contamination and water pollution. Contaminated soils can lead to reduced 

crop yields or complete crop failure due to toxic substances absorbed by 

plants. Studies have shown that crops such as cassava and yam exhibit stunted 

growth when grown in contaminated soils. Furthermore, water sources used 

for irrigation become polluted with hydrocarbons from oil spills. This not 

only affects crop health but also poses health risks to farmers who consume 

contaminated produce or use polluted water for irrigation. The result is a 

cycle of poverty where farmers face declining incomes due to reduced 

agricultural output. 

Fisheries are another critical component of food security in the Niger Delta. 

Oil spills contaminate rivers and coastal waters, leading to killing of fish and 

a decline in fish populations. The Nigerian Institute for Oceanography and 

Marine Research has reported significant declines in fish catches that could 

be attributed to pollution from oil activities. The loss of fish stocks directly 

impacts food availability and nutrition for local communities that depend 

heavily on fish as a primary protein source. Additionally, fishermen face 

economic hardships as their catch diminishes; this further exacerbates food 

insecurity as families struggle to afford alternative sources of nutrition. 

The health implications associated with oil spills also contribute indirectly to 

food insecurity. Exposure to pollutants can lead to respiratory issues, skin 

diseases, and other health problems among local populations. Poor health 

reduces individuals’ ability to work effectively in agriculture or fishing 

sectors, thereby diminishing household incomes and exacerbating food 

scarcity. Moreover, contaminated water supplies can lead to gastrointestinal 

diseases which further strain community resources as families must allocate 

funds towards healthcare instead of food purchases or agricultural 

investments. 

The Nigerian government has implemented various policies aimed at 

addressing oil spill incidents; however, enforcement remains weak due to 

corruption and lack of accountability among oil companies operating in the 

region. While initiatives like the National Environmental (Pollution 

Abatement) Regulations exist, they often fall short in practice due to 

insufficient funding and lack of political will. Community-led efforts have 

emerged as vital responses; however, they often lack adequate support from 



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governmental bodies or international organizations, and such support is 

needed for effective remediation efforts. 

Conclusion and Recommendations 

Conclusion: Oil spills in the Niger Delta have severe environmental and 

socio-economic consequences. Crude oil contaminates soil and water bodies, 

causing habitat degradation, fish population declines, and unsuitable farming 

land. This is especially alarming for people in the Niger Delta, where 

agriculture is the principal source of income. The socioeconomic 

consequences are grave, as fish populations drop and agricultural output falls, 

leading to food insecurity. Households who struggle to provide proper 

nourishment experience greater poverty rates. Oil spills increase existing 

vulnerabilities by restricting access to food sources and increasing reliance on 

high-cost imported goods. Direct contact to spilt oil causes health difficulties, 

as do indirect consequences from tainted food sources. Communities around 

oil spills may face breathing issues, skin illnesses, and other health 

complications caused by harmful chemicals contained in crude oil.  

Consumption of polluted seafood or crops might result in chronic diseases. 

Efforts have been undertaken at different levels, including government, non-

governmental organisations (NGOs), and community groups, to address these 

concerns through legislative reforms aiming at strengthening environmental 

rules and encouraging sustainable practices. However, enforcement remains 

ineffective owing to corruption and a lack of political will. Community 

resilience techniques are critical in reducing the impact of oil spills on food 

security. Initiatives that concentrate on alternative livelihoods such as 

aquaculture or agro-ecological techniques can assist communities in adapting 

while minimising reliance on conventional fishing and farming ways. 

Addressing these issues requires a comprehensive approach that includes 

strong regulatory frameworks to avoid spills, remediation activities to repair 

damaged habitats, and support networks for impacted populations to 

strengthen their resistance to food scarcity.  

Recommendations: Here are some vital recommendations that cover some 

major areas of concern:  

Strengthening Regulatory Frameworks: The Nigerian government should 

improve current rules controlling oil exploration and production operations. 

This includes greater enforcement of environmental rules designed to avoid 

oil leaks. 

Investment in Remediation Technology: There is an urgent need to invest in 

innovative technology that can efficiently clean up oil spills. Collaborations 

with international environmental organizations can help you gain access to 



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best practices in spill response. 

Community Engagement Programs: Local communities should be actively 

involved in monitoring oil operations and spill responses. Empowering these 

communities through education about their rights and environmental 

stewardship can lead to better outcomes. 

Diversification of Livelihoods: To mitigate the impacts of oil spills on food 

security, programmes aimed at diversifying income sources for local 

populations should be developed. This could include promoting alternative 

agricultural practices or supporting small-scale fisheries. 

Health Monitoring Initiatives: Establishing health monitoring systems for 

communities affected by oil spills will help address health-related issues 

stemming from exposure to pollutants while providing necessary healthcare 

support. 

International Collaboration: Engaging with international bodies can provide 

technical assistance and funding necessary for both immediate response 

efforts following spills as well as long-term sustainable development 

initiatives aimed at restoring food security. 

 

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Author Information: Festus Funmileyi Ajomale is of 

Caleb University, Imota Lagos, Nigeria.  

Email: funmilayi.ajomale@calebuniversity.edu.ng 
 

 

 

 

Dr Christian Osemuyi Oseghale is a lecturer in Caleb 

University, Imota Lagos, Nigeria. Email: trustnigent1 

@gmail.com. Orchid ID: 0009-0001-0276-0607 
 

 

 

 

 
 

APA 
 

Ajomale, F. F. & Oseghale, C. O.  (2025). Oil Spills in the Niger 

Delta and Their Impact on Food Security in Nigeria: A Prevalent 

Challenge. Global Online Journal of Academic Research (GOJAR), 

4(1), 41-59. https://klamidas.com/gojar-v4n1-2025-03/.  
 

MLA 
 

Ajomale, Festus Funmileyi and Oseghale, Christian Osemuyi. “Oil 

Spills in the Niger Delta and Their Impact on Food Security in 

Nigeria: A Prevalent Challenge”. Global Online Journal of 

Academic Research (GOJAR), vol. 4, no. 1, 2025, pp. 41-59. 

https://klamidas.com/gojar-v4n1-2025-03/.  

 

 

 

 

 

 

 



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On Boundedness and Solution Size in Rational Linear 

Programming and Polyhedral Optimization 

 

Mark Laisin, Collins Edike & R. N. Ujumadu 

 

 

Abstract 

This paper delves into the theoretical and practical aspects of boundedness and 

structural properties in rational linear programming (LP) and polyhedral 

optimization. It provides a comprehensive analysis of conditions under which the 

optimization of linear functions over rational polyhedra remains bounded and 

establishes explicit constraints on solution size when optimal solutions exist. By 

exploring the interplay between polyhedral geometry, integer hulls, and rational LP 

systems, this study sheds light on fundamental principles that underlie modern 

optimization techniques. Key findings include equivalence conditions for 

boundedness between rational polyhedra and their integer hulls, as well as precise 

bounds on the numerical representation of optimal solutions. These results not only 

enhance the theoretical understanding of LP and polyhedral optimization but also 

have significant implications for computational efficiency, algorithm design, and 

numerical stability in solving real-world optimization problems. The discussion is 

rooted in rigorous mathematical foundations and extends to practical applications in 

areas such as mixed-integer programming, computational geometry, and 

combinatorial optimization. 

Keywords: rational linear programming, polyhedral optimization, boundedness 

conditions, integer hull, solution size bounds, rational coefficients, computational 

geometry, optimization algorithms, numerical stability. 

 

 

I. Introduction 

Linear programming (LP) has had a significant and enduring influence, 

deeply connected with the evolution of optimization theory and 

computational methodologies. Scholars have extensively traced the origins of 

LP back to the 1930s, highlighting Leonid Kantorovich’s groundbreaking 

work in formulating optimization problems to address resource allocation 

challenges in economic planning (Kantorovich, 1939). Kantorovich’s 

pioneering contributions established the foundation of linear optimization and 



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61 
 

were later recognized with the Nobel Prize in Economics, underscoring the 

lasting impact of his work. 

The practical relevance of LP has surged during and after World War II. 

Researchers, notably George Dantzig, have developed the simplex algorithm 

to optimize military logistics and supply chains, a milestone in the application 

of mathematical optimization (Dantzig, 1947). The simplex algorithm has 

remained a cornerstone in solving LP problems, celebrated for its practical 

efficiency and ease of implementation, despite its potential exponential time 

complexity in the worst-case scenarios. 

The study of rational linear programming, characterized by constraints and 

objectives expressed using rational coefficients, has gained prominence with 

advancements in computational methodologies. Researchers have extensively 

analyzed rational LP systems, focusing on their numerical properties, solution 

size, and computational feasibility. During the 1980s, Karmarkar’s 

introduction of the polynomial-time interior-point method has revolutionized 

the field, providing an alternative to the simplex algorithm and emphasizing 

the significance of numerical stability in optimization (Karmarkar, 1984). 

Polyhedral optimization, a core area of mathematical optimization, has 

bridged critical concepts in combinatorics, geometry, and optimization. 

Scholars have explored the geometric properties of feasible regions defined 

by linear inequalities, offering theoretical and practical insights for solving 

complex problems. The study of polyhedra has uncovered deep structural 

relationships essential for various optimization tasks, including vertex 

enumeration and facet identification. 

Among the impactful concepts in polyhedral optimization is the integer hull, 

representing the convex hull of all integer solutions within a polyhedron. This 

concept has substantially advanced the theory and algorithms of integer 

programming and mixed-integer programming, as emphasized by Nemhauser 

and Wolsey (1999). By enabling the transition from an infinite search space 

to a finite and structured geometric framework, the integer hull has simplified 

the analysis of discrete variable problems. 

Recent advancements in polyhedral optimization include the construction and 

analysis of rational polyhedra on boards. Laisin et al. (2024) have 

demonstrated the practical effectiveness of polyhedral techniques in modeling 

and solving problems involving integral polyhedra, offering applications in 

combinatorial optimization and computational geometry. Their work has 

exemplified how modern techniques can address both theoretical challenges 

and real-world applications. 

This paper examines two fundamental aspects of rational LP and polyhedral 



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optimization: 

i. Conditions under which the optimization of a linear function over a 

rational polyhedron is bounded. 

ii. Bounds on the size of optimal solutions. 

Building on classical results from Schrijver (1998) and others, the analysis 

provides refined bounds and structural insights critical for advancing both 

theoretical understanding and practical applications in optimization. 

II. Preliminaries and Definitions 

Definition 2.1: Sub-determinant 

Let 𝑨 be an integral matrix. A sub-determinant of 𝑨 is |𝑩| for some square 

sub-matrix 𝑩 of 𝑨 (defined by arbitrary row and column indices). We 

write𝚵(𝑨) for the maximum absolute value of the sub-determinants of 𝑨. 

Definition 2.2: Polyhedron 

Linear Programming deals with optimizing a linear objective function of 

finitely many variables subject to finitely many linear inequalities. So the set 

of feasible solutions is the intersection of finitely many half spaces. Such a set 

is called a polyhedron. 

Definition 2.3: Polyhedron in ℝ𝒏 

It is a set of type 

𝑷 = {𝒙 ∈ ℝ𝒏: 𝑨𝒙 ≤ 𝒃} 

for some matrix 𝑨 ∈ ℝ𝒎×𝒏and some vector 𝒃 ∈ ℝ𝒎. If A and b are rational, 

then P is a rational polyhedron. A bounded polyhedron is also called a 

polytope.  

We denote the rank of a matrix A by 𝒓𝒂𝒏𝒌(𝑨). The dimension dim X of a 

nonempty set: 

𝒙 ⊆ ℝ𝒏 

is defined to be  𝒏 − 𝐦𝐚𝐱 𝒓𝒂𝒏𝒌(𝑨) 

{𝒓𝒂𝒏𝒌(𝑨): 𝑨 𝐢𝐬 𝐚𝐧 𝒏 × 𝒏 − 𝐦𝐚𝐭𝐫𝐢𝐱 𝐰𝐢𝐭𝐡 𝑨𝒙 = 𝑨𝒚 𝐟𝐨𝐫 𝐚𝐥𝐥 𝒙, 𝒚 ∈ 𝑿} 

A polyhedron 𝑷 ⊆ ℝ𝒏 is called full-dimensional if 𝐝𝐢𝐦 𝑷 = 𝒏 

Equivalently, a polyhedron is full-dimensional if and only if there exist a 

point 𝒙∗ in its interior. (Genova and Guliashki, 2011). 



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Proposition 2.1: Nonempty polyhedron: Let  

𝑃 = {𝑥 ∶ 𝐴𝑥 ≤ 𝑏} 

be a nonempty polyhedron. If c is a nonzero vector for which 

𝜹 ∶= 𝐦𝐚𝐱 {𝒄𝒙 ∶ 𝒙 ∈ 𝑷} 

is finite, then {𝒄𝒙 ∶ 𝒙 = 𝜹}  is called a supporting hyperplane of P. A face of 

P is P itself or the intersection of P with a supporting hyperplane of P. A point 

x for which {x} is a face is called a vertex of P, and also a basic solution of 

the system 𝑨𝒙 ≤ 𝒃 (Genova and Guliashki, 2011). 

Proposition 2.2: Let 

𝑃 ∶= {𝑥 ∶ 𝐴𝑥 ≤ 𝑏} 

be a polyhedron and 𝑭 ⊆  𝑷. Then the following statements are equivalent: 

(a) F is a face of P. 

(b) There exists a vector c such that 𝜹 ∶= 𝐦𝐚𝐱 {𝒄𝒙 ∶ 𝒙 ∈ 𝑷} is finite and 

𝑭 = {𝒄𝒙 = 𝜹 ∶ 𝒙 ∈ 𝑷} 

(c) 𝑭 ∶= {𝒙 ∈ 𝑷: 𝑨′𝒙 = 𝒃′} ≠ ∅; for some subsystem 𝑨′𝒙 ≤ 𝒃′ of 𝑨𝒙 ≤ 𝒃 

(Genova and Guliashki, 2011). 

Corollary 2.1: Let 𝑃 be a polyhedron and 𝐹 a face of 𝑃. Then 𝐹 is again a 

polyhedron.   

Furthermore, a set 𝐹′ ⊆ 𝐹 is a face of 𝑃 if and only if it is a face of 𝐹 

(Genova and Guliashki, 2011). 

Proposition 2.3: Let 𝑷 = {𝒙: 𝑨𝒙 ≤ 𝒃} be a polyhedron. A nonempty subset 

𝑭 ⊆ 𝑷 is a  

minimal face of 𝑷 if and only if it is a face of; 

𝑭 = {𝒙: 𝑨′𝒙 = 𝒃′} 

 for some subsystem 𝑨′𝒙 ≤ 𝒃′ of 𝑨𝒙 ≤ 𝒃 (Akif and Cihan,  2008) 

Proposition 2.4: For any rational square matrix A we have 

𝑠𝑖𝑧𝑒 𝑑𝑒𝑡 𝐴  ≤ 2𝑠𝑖𝑧𝑒(𝐴) 

Proposition 2.5: If 𝒙, 𝒚 ∈  ℚ𝒏  are rational vectors, then 

𝒔𝒊𝒛𝒆(𝒙 + 𝒚) ≤ 𝟐(𝒔𝒊𝒛𝒆(𝒙) + 𝒔𝒊𝒛𝒆(𝒚)) 

𝒔𝒊𝒛𝒆(𝒙𝑻𝒚) ≤ 𝟐(𝒔𝒊𝒛𝒆(𝒙) + 𝒔𝒊𝒛𝒆(𝒚))(𝐋𝐚𝐢𝐬𝐢𝐧 𝒆𝒕 𝒂𝒍. , 𝟐𝟎𝟐𝟒). 

 



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Definition 2.4: Integer programming problem (IPP) 

The IPP is a special class of linear programming problem (LPP) where all or 

some of the variables in the optimal solution are restricted to assume non-

negative-integer values. Thus the general IPP can be stated as follows: 

Optimize the linear function 

𝐎𝐩𝐭𝐢𝐦𝐢𝐳𝐞  𝒁 = ∑ 𝒄𝒊𝒙𝒊

𝒏

𝒊=𝟏

                                                    … (𝟏) 

Subject to the constraints. 

∑ 𝒂𝒊𝒋𝒙𝒊

𝒏

𝒊=𝟏

≤ 𝒃𝒊,   𝒋 = 𝟏, 𝟐, … , 𝒎                                       … (𝟐) 

𝒙𝒊 ≥ 𝟎   and some 𝒙𝒊 are integers. 

There are two types of the Integer Programming Problems (Elmuti, 2003; 

Genova and Guliashki, 2011). 

Definition 2.5: All integer programming problem 

An IPP. is termed as all IPP or pure IPP if all the variables in the optimal 

solution are restricted to assume non-negative integer values. 

Definition 2.6: Mixed integer programming problem (MIPP) 

An IPP is termed as mixed MIPP if only some variables in the optimal 

solution are restricted to assume non-negative integer values while the 

remaining variables are free to take any non-negative values (Gupta et al., 

2014). 

Importance of IPP 

Quite often, in business and industry, we require the discrete nature or values 

of the variables involved in many decision making situations. For example, in 

a factory manufacturing trucks or cars etc. the quantity or number 

manufactured can be a whole discrete number only as a fraction of truck or 

car is not required. In assignment problems and travelling salesman problems 

etc. the variables involved can assume integer values only. In allocation of 

goods, a shipment must involve a discrete number of trucks etc. in sequencing 

and routing decisions we require the discrete values of variables. Thus we 

come across many integer programming problems and hence need some 

systematic procedure for obtaining the exact optimal integer solution to such 

problems (Elmuti, 2003; Genova and Guliashki, 2011). 



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III. Main Results 

Lemma: (Boundedness equivalence)  

 Let 𝑷 = {𝒙: 𝑨𝒙 ≤ 𝒃} be some rational polyhedron whose integer hull is 

nonempty, and let 𝒄 be some vector (not necessarily rational). Then 

𝐦𝐚𝐱 {𝒄𝒙: 𝒙 ∈ 𝑷} 

is bounded if and only if 𝐦𝐚𝐱 {𝒄𝒙: 𝒙 ∈ 𝑷𝟏} is bounded. 

Proof:     

Suppose 𝐦𝐚𝐱 {𝒄𝒙: 𝒙 ∈ 𝑷}is unbounded. Then Corollary 3.2.8 says that the 

system 

𝒚𝑨 = 𝒄. 𝒚 ≥ 𝟎 

has no solution. By Corollary 3.26 there is a vector 𝒛. With 𝒆𝒛 < 0 and 𝑨𝒛 ≥

𝟎. Then the 

𝑳𝑷 𝐦𝐢𝐧 {𝒄𝒛: 𝑨𝒛 ≥ 𝟎, −∥≤ 𝒛 ≤∥} 

is feasible. Let 𝒛∗ be an optimum basic solution of this 𝑳𝑷. 𝒛∗ is rational as it 

is a vertex of a rational polytope. Multiply 𝒛∗ by a suitable natural number to 

obtain an integral vector 𝝎 with 𝑨𝝎 ≥ 𝟎 and 𝒄𝝎 < 0. Let 𝒗 ∈ 𝑷𝟏 be some 

integer vector. Then 𝒗 − 𝒌𝝎 ∈ 𝑷𝟏 for all 𝒌 ∈ ℕ, and thus 𝐦𝐚𝐱 {𝒄𝒙: 𝒙 ∈ 𝑷𝟏} 

is unbounded. The other direction is trivial.  

Theorem (Rational matrices and vertices of polytopes)   

Consider the rational linear programming (LP) problem: 

𝑳𝑷:  𝒎𝒂𝒙 {𝒄𝑻𝒙: 𝑨𝒙 ≤ 𝒃} 

where A and b are rational. Suppose this LP has an optimum solution. Then 

the following hold: 

(i) Bounded Size Solution: There exists an optimum solution x such that: 

𝒔𝒊𝒛𝒆(𝒙) ≤ 𝟒𝒏(𝒔𝒊𝒛𝒆(𝑨) + 𝒔𝒊𝒛𝒆(𝒃)) 

(ii)  Special Case (Unit Vector b): If 𝒃 = 𝒆𝒊 𝒐𝒓 𝒃 = −𝒆𝒊 for some unit vector 

𝒆𝒊 there exists a nonsingular submatrix 𝑨′ of A and an optimum solution x 

such that: 

𝒔𝒊𝒛𝒆(𝒙) ≤ 𝟒𝒏(𝒔𝒊𝒛𝒆(𝑨) + 𝒔𝒊𝒛𝒆(𝒃)) 

with each component of x satisfying: 

𝒔𝒊𝒛𝒆(𝒄𝒐𝒎𝒑𝒐𝒏𝒆𝒏𝒕 𝒐𝒇 𝒙) ≤ 𝟒(𝒔𝒊𝒛𝒆(𝑨) + 𝒔𝒊𝒛𝒆(𝒃)) 



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(iii)  Reduced Submatrix Case: If 𝒃 = 𝒆𝒊 𝒐𝒓 𝒃 = −𝒆𝒊  for some unit vector 𝒆𝒊 

, then there exists a non-singular submatrix 𝑨′ of A and an optimum 

solution x such that: 

𝒔𝒊𝒛𝒆(𝒙) ≤ 𝟒𝒏 ⋅ 𝒔𝒊𝒛𝒆(𝑨′) 

Proof 

The proof of Theorem 4.3 relies on these definitions 2.1, 2.2, 2.3, 2.4 and 2.5 

respectively, to analyse the structure and properties of the LP problem. 

Task 1:  to show that, for a given LP, there exists a Solution with Bounded 

Size. 

By the fundamental theorem of linear programming, there exists an optimum 

solution 𝒙∗ at a vertex of the feasible polytope {𝒙: 𝑨𝒙 ≤ 𝒃}. 

o Vertex Characterization: 

A vertex 𝒙∗ corresponds to a subset of constraints in 𝑨𝒙 ≤ 𝒃 that are 

active (i.e., satisfied as equalities). By Corollary 2.1. the maximum is 

attained in a face 𝑭 of 

{𝒙 ∶ 𝑨𝒙 ≤ 𝒃}. 

 Let 𝑰 ⊆ {𝟏, 𝟐, … , 𝒎} denote the indices of active constraints, and let 

𝑨𝑰 denote the submatrix of A corresponding to these constraints. At 

a vertex, the system can be written as: 

𝑨𝑰𝒙 = 𝒃𝑰 

where 𝒃𝑰is the corresponding sub vector of b. 

o Non-Singularity of 𝑨𝑰: 

For 𝒙∗ to be a vertex, the matrix 𝑨𝑰 must be non-singular (invertible), 

and ∣ 𝑰 ∣= 𝒏. 

o Size of Solution: 

Solving 𝑨𝑰𝒙 = 𝒃𝑰 

𝒙 = 𝑨𝑰
−𝟏𝒃𝑰 

Using bounds on the size of 𝑨𝑰 and 𝒃𝑰, and the fact that 𝑨𝑰 is 

rational, the entries of  are bounded in terms of 𝒔𝒊𝒛𝒆(𝑨𝑰). 

Specifically, the size of x is bounded by: 

𝒔𝒊𝒛𝒆(𝒙) ≤ 𝟒𝒏(𝒔𝒊𝒛𝒆(𝑨) + 𝒔𝒊𝒛𝒆(𝒃)). 

 



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Task 2: to show that for a give LP has a Special Case (𝒃 = 𝒆𝒊 𝒐𝒓 𝒃 = −𝒆𝒊 ) 

If 𝒃 = 𝒆𝒊 𝒐𝒓 𝒃 = −𝒆𝒊 , where𝒆𝒊 is a unit vector, the LP corresponds to finding 

the maximum value of 𝒄𝑻𝒙 along a specific axis defined by 𝒆𝒊. 

o Existence of a Non-singular Submatrix: 

As in task 1, there exists a vertex solution 𝒙∗, and the active constraints 

correspond to a nonsingular submatrix 𝑨′ of A. 

o Bound on Solution Size: 

Similar to the general case, the size of x is bounded by: 

𝒔𝒊𝒛𝒆(𝒙) ≤ 𝟒𝒏(𝒔𝒊𝒛𝒆(𝑨) + 𝒔𝒊𝒛𝒆(𝒃)), 

with the size of each component of x further bounded by: 

𝒔𝒊𝒛𝒆(𝒄𝒐𝒎𝒑𝒐𝒏𝒆𝒏𝒕 𝒐𝒇 𝒙) ≤ 𝟒(𝒔𝒊𝒛𝒆(𝑨) + 𝒔𝒊𝒛𝒆(𝒃)). 

Task 3: to show that for a give LP has reduced submatrix: Let 𝑭′ ⊆ 𝑭 be a 

minimal face. By corollary 2.1𝑭′ = {𝒙 ∶ 𝑨′𝒙 = 𝒃′} for some subsystem 

𝑨′𝒙 ≤ 𝒃′ 𝐨𝐟 𝑨𝒙 ≤ 𝒃. 

 

Then, in the special case where 𝒃 = 𝒆𝒊 𝒐𝒓 𝒃 = −𝒆𝒊 , let 𝑨′ denote the 

nonsingular submatrix corresponding to the active constraints at the optimum.  

Now, we may assume that the rows of 𝑨′ are linearly independent. We then 

take a maximal set of linear independent columns (call this matrix 𝑨”) and set 

all other components to zero. Then 

𝒙 =  (𝑨")−𝟏𝒃′, 

filled up with zeros, is an optimum solution to our LP. By Cramer’s rule the 

entries of 𝒙 are given by 

𝒙𝒊 =  
𝐝𝐞𝐭 𝑨′′′

𝐝𝐞𝐭 𝑨′′
  , 

where 𝑨′′′ arises from 𝑨′′ by replacing the 𝒋 − 𝒕𝒉 column by 𝒃′. By 

propositions 2.4 and 2.5  respectively, we obtain 

𝒔𝒊𝒛𝒆(𝒙) ≤ 𝒏 + 𝟐𝒏(𝒔𝒊𝒛𝒆(𝑨′′′) + 𝒔𝒊𝒛𝒆(𝑨′′)) ≤ 𝟒𝒏(𝒔𝒊𝒛𝒆(𝑨′′) + 𝒔𝒊𝒛𝒆(𝒃′)). 

If 𝒃 =  ±𝒆𝒊 then | 𝐝𝐞𝐭(𝑨′′′) | is the absolute value of a sub determinant of 𝑨′′. 

The size of x can then be further bounded as: 

𝒔𝒊𝒛𝒆(𝒙) ≤ 𝟒𝒏 ⋅ 𝒔𝒊𝒛𝒆(𝑨′). 

This follows because 𝑨′ has fewer rows and columns compared to the full 

matrix A, reducing the maximum size contribution. Q.E.D. 

Utilizing results from Schrijver (1998) and Cook et al., (1986), we derive 



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bounds on the size of optimal solutions by analyzing the bit-length of vertices 

of and properties of rational systems. 

IV. Applications: Production Scheduling Problem 

i) Integer Programming: The equivalence of boundedness conditions 

simplifies complexity analyses for mixed-integer programming problems 

Problem Setup 

A factory produces two products, A and B, using two resources, labor and 

material. The available resources are limited to 100 hours of labor and 80 

units of material. The profit for producing one unit of A is $50, and for B, it's 

$40. The problem is to determine the production quantities 𝒙𝟏 (units of A) 

and 𝒙𝟐 (units of B) to maximize profit, subject to the following constraints: 

Labor constraint: 𝟐𝒙𝟏 + 𝟏𝒙𝟐 ≤ 𝟏𝟎𝟎, 

Material constraint: 𝟏𝒙𝟏 + 𝟐𝒙𝟐 ≤ 𝟖𝟎. 

This is a linear programming (LP) problem. However, if the production 

quantities 𝒙𝟏 and 𝒙𝟐 must be integers (e.g., you cannot produce fractional 

units), the problem becomes a mixed-integer programming (MIP) problem. 

Rational Polyhedron and Integer Hull 

 The feasible region defined by the constraints is a rational polyhedron 

P, containing all real-valued solutions that satisfy the constraints. 

 The integer hull 𝑷𝑰 is the convex hull of all integer solutions within P. 

It represents the feasible region for the MIP problem. 

Boundedness Analysis 

1. Boundedness of P: The polyhedron P is bounded since it is enclosed 

by the constraints 𝟐𝒙𝟏 + 𝟏𝒙𝟐 ≤ 𝟏𝟎𝟎 and 𝒙𝟏 + 𝟐𝒙𝟐 ≤ 𝟖𝟎, which 

intersect in the positive quadrant. 

2. Boundedness of 𝑷𝑰: The integer hull 𝑷𝑰, being a subset of P, is also 

bounded. This follows from the equivalence of boundedness 

conditions: if 𝒎𝒂𝒙 {𝒄𝑻𝒙: 𝒙 ∈ 𝑷} is bounded, then 𝒎𝒂𝒙 {𝒄𝑻𝒙: 𝒙 ∈ 𝑷𝑰, } 

is bounded. 

Simplifying the Analysis 

Instead of analyzing the MIP problem directly, the equivalence of 

boundedness conditions allows us to focus on the polyhedron P to verify 

boundedness. Once P is confirmed to be bounded, we can conclude that 𝑷𝑰,  



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is bounded, avoiding the need for exhaustive checks over all integer solutions. 

Solving the Problem 

The integer solutions can then be obtained by applying integer programming 

techniques, such as branch-and-bound or cutting planes, which operate within 

the bounded integer hull 𝑷𝑰, . Thus, reducing the boundedness check to P, the 

analysis simplifies significantly, saving computational effort and making the 

problem more tractable. 

ii) Computational Geometry: Solution size bounds assist in designing 

efficient algorithms for convex hull and vertex enumeration. 

Application Context 

Consider the problem of computing the convex hull of a set of points in ℝ𝒏. 

Convex hull algorithms, such as QuickHull or Graham's scan, rely on 

numerical representations of the points and may involve large computations 

when the coordinates of the points have a high bit-length. Efficient algorithms 

benefit from guarantees about the size of intermediate and final solutions, 

which directly impacts computation time and memory usage. 

Problem Setup 

Let 𝑷 = {𝒙 ∈ ℝ𝒏: 𝑨𝒙 ≤ 𝒃} be a rational polyhedron defined by m linear 

inequalities, where 𝑨 ∈ ℚ𝒎×𝒏. The goal is to compute the convex hull of the 

integer points in P, denoted 𝒄𝒐𝒏𝒗(𝑷𝑰). 

Solution Size Bounds 

From theoretical results, if an optimal solution x to a linear program over P 

exists, its size is bounded as: 

𝒔𝒊𝒛𝒆(𝒙) ≤ 𝟒𝒏(𝒔𝒊𝒛𝒆(𝑨) + 𝒔𝒊𝒛𝒆(𝒃)). 

This means each vertex of the convex hull 𝒄𝒐𝒏𝒗(𝑷𝑰)has coordinates with a 

bit-length constrained by this bound. 

Application to Convex Hull Algorithms 

a. Numerical Stability: 

o Algorithms like QuickHull require operations on vertex 

coordinates, such as comparing slopes or calculating 

determinants. Knowing the bounds on the size of x ensures 

that these operations remain numerically stable and feasible 

on finite-precision systems. 



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70 
 

b. Efficient Data Structures: 

o Solution size bounds guide the choice of data structures. For 

example, if the bound indicates small bit-lengths, lightweight 

data structures (e.g., arrays with fixed-width integers) can be 

used, reducing memory overhead. 

c. Algorithm Design: 

o When enumerating vertices of 𝒄𝒐𝒏𝒗(𝑷𝑰), solution size 

bounds restrict the search space, enabling pruning strategies 

in branch-and-bound algorithms. For example, if a candidate 

vertex exceeds the size bounds, it can be discarded without 

further computation. 

Application in ℝ𝟐 

Suppose P is a polygon defined by: 

𝑷 = {𝒙 ∈ ℝ𝟐: 𝟐𝒙𝟏 + 𝒙𝟐 ≤ 𝟏𝟎, 𝒙𝟏 + 𝟑𝒙𝟐 ≤ 𝟏𝟓, 𝒙𝟏, 𝒙𝟐 ≥ 𝟎}. 

The integer points in P are (𝟎, 𝟎), (𝟏, 𝟎), (𝟐, 𝟎), … , (𝟒, 𝟑). 

 The convex hull of these points forms a polygon whose vertices are 

subsets of the integer points. 

 Using the size bounds, we confirm that all integer solutions 𝒙 =
(𝒙𝟏, 𝒙𝟐) satisfy 𝒔𝒊𝒛𝒆(𝒙) ≤ 𝟒(𝟐 + 𝟐) = 𝟏𝟔, ensuring efficient 

computations. 

iii) Impact on Algorithms: With these bounds: 

 Vertex Enumeration: We avoid considering infeasible points with 

excessively large coordinates. 

 Convex Hull Computation: Ensures that the algorithm’s runtime is 

proportional to the actual feasible vertices, reducing unnecessary 

overhead. 

This example demonstrates how solution size bounds provide theoretical 

guarantees that directly improve the efficiency and practicality of convex hull 

and vertex enumeration algorithms. Thus, it improves the bounds that 

contribute to better prerecession and numerical stability in LP solvers. 

V. Conclusion 

This paper establishes critical theoretical results in rational linear 

programming and polyhedral optimization, emphasizing boundedness 

equivalence and solution size constraints. By proving the equivalence of 

boundedness between rational polyhedra and their integer hulls, as well as 



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deriving explicit bounds on the size of optimal solutions, this work 

contributes to a deeper understanding of the structural and numerical 

properties of optimization problems. These findings are not only of 

theoretical interest but also pave the way for advancements in computational 

optimization, particularly in improving algorithmic efficiency and ensuring 

numerical stability. 

VI. Recommendations 

Future work may explore extensions to non-convex settings, where the 

feasible regions are no longer polyhedral, presenting new challenges in 

understanding boundedness and solution representation. Another promising 

direction involves generalizations to cases with irrational coefficients, which 

require advanced techniques to address the complexities introduced by non-

rational systems. Furthermore, integrating these theoretical insights into 

practical optimization software and exploring their impact on real-world 

applications, such as logistics, network design, and machine learning, could 

significantly enhance the utility and scope of rational LP and polyhedral 

optimization. Such efforts would bridge the gap between theoretical 

advancements and their practical implementations, fostering innovation in 

both academic and industrial domains. 

References 

Akif, M B. and Cihan, A. (2008). A 0-1 integer programming approach to a 

university timetabling problem. Hacettepe Journal of Mathematics 

and Statistics, 37: 41-55. 

Cook, W., Cunningham, W. H., Pulleyblank, W. R., & Schrijver, A. (1986). 

Combinatorial Optimization. Wiley. 

Dantzig, G. B. (1947). Linear Programming and Extensions. Princeton 

University Press. 

Dantzig, G. B. (1947). Maximization of a linear function of variables subject 

to linear inequalities. In T. C. Koopmans (Ed.), Activity Analysis of 

Production and Allocation (pp. 339-347). Wiley. 

Elmuti, D. (2003). The perceived impact of outsourcing on organizational 

performance. American Journal of Business, 18: 33-42. 

Genova, K. and Guliashki, V. (2011). Linear integer programming methods 

and  approaches - a survey. Journal of Cybernetics and Information 

Technologies. Vol 11. 

Gupta, Prem Kumar (Er.) and D. S. Hira (2014); Operations Research seventh 



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revised edition. By Rajendra Ravindra Pvt Ltd, ram Nagar New Delhi-

110055 and published by S. Chand & Company Pvt Ltd, India 

Kantorovich, L. V. (1939). Mathematical Methods in the Organization and 

Planning of Production. Leningrad State University. 

Karmarkar, N. (1984). A new polynomial-time algorithm for linear 

programming. Combinatorica, 4(4), 373-395. 

Laisin, M.,  Edike, C. and Bright O. Osu (2024); The construction of rational 

polyhedron on an 𝒏 × 𝒏 board with some application on integral 

polyhedral. TIJER, Vol 11, Issue 11, www.tijer.org 

Nemhauser, G. L., & Wolsey, L. A. (1999). Integer and Combinatorial 

Optimization. Wiley. 

Schrijver, A. (1998). Theory of Linear and Integer Programming. Wiley. 

 

 

Author Information: Prof. Mark Laisin is of the 

Department of Mathematics, Chukwuemeka Odumegwu 

Ojukwu University, Uli, Anambra State, Nigeria. Email: 

laisinmark@gmail.com 
 

 

 

 

Collins Edike is of the Department of Mathematics, 

Chukwuemeka Odumegwu Ojukwu University, Uli, 

Anambra State, Nigeria. Email: edikecollins505@gmail. 

com 
 

 

 

 

Dr R. N. Ujumadu is of the Department of Mathematics, 

Chukwuemeka Odumegwu Ojukwu University, Uli, 

Anambra State, Nigeria. Email: rozyngujmadu@yahoo. 

com 
 

 

 

 

 
 

APA 
 

Laisin, M., Edike, C., & Ujumadu, R. N. (2025). On Boundedness 

and Solution Size in Rational Linear Programming and Polyhedral 

Optimization. Global Online Journal of Academic Research 

(GOJAR), 4(1), 60-72. https://klamidas.com/gojar-v4n1-2025-04/.  
 

MLA 
 

Laisin, Mark, Edike, Collins, & Ujumadu, R. N. “On Boundedness 

and Solution Size in Rational Linear Programming and Polyhedral 

Optimization”. Global Online Journal of Academic Research 

(GOJAR), vol. 4, no. 1, 2025, pp. 60-72. https://klamidas.com/gojar-

v4n1-2025-04/.  

 

 

 



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Relationship between Housing Management and 

Housing Conditions in Imo State Housing Corporation 

Estates in Owerri, Nigeria 

 

Nnanyere N. Chukwu, Chukwunonso O. Umeora & Charles 

C. Munonye 

 

 

 

ABSTRACT 

Housing conditions are acknowledged as important factors that determine the 

habitability of buildings. This was why this study investigated the relationship 

between housing management and housing conditions in Imo State Housing 

Corporation (IMSHC) estates in Owerri Capital Territory, Imo State, Nigeria, with a 

view to obtaining vital feedback which can be used for gauging and improving 

housing conditions in the study area. A survey design method was applied with a 

focus on five IMSHC estates randomly selected from the research population 

following a stratification based on housing type. Three hundred and five occupied 

housing units were randomly sampled from the selected estates. Data were collected 

from these using questionnaires. The variables, ‘Flaking/Peeling wall finish’ and 

‘Availability of procedures for maintenance operations’, representing housing 

condition and housing management system respectively, were selected for this 

analysis. The two variables are of nominal variable category; therefore, the Chi-

square test of independence analysis tool was applied towards examining the 

significance of the relationship. It was established that there is a significant 

relationship between Flaking/Peeling wall finish’ and ‘Availability of procedures for 

maintenance operations’ in the study area. It is recommended that for prompt 

maintenance of facilities in buildings, the residents should undertake it. For 

maintenance of facilities in the neighbourhood, IMSHC should undertake that. 

Moreover, there should be a legal provision to enable residents of IMSHC estates to 

enforce maintenance activities in the environment. The time taken to respond to 

residents’ complaints should be improved upon by ensuring prompt response to 

grievances. 

Keywords: buildings, habitability, housing conditions, housing management, 

maintenance 

 

 



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INTRODUCTION 

Before the colonisation of Nigeria, there was no need for housing estates 

because residential buildings were constructed mainly to quarter family 

members who dwelt in huts within the family compound. Umeora (2018) 

noted that the colonial masters introduced housing estates to house their 

employees near their places of work in cities. When Nigeria gained 

independence, government and other organised bodies continued with this 

urban housing development and expanded the number of housing estates all 

over the country. The management and maintenance of these estates have 

come under scrutiny by professionals in the housing sector.  

Developing countries such as Nigeria have witnessed high rates of 

urbanisation but these have not been accompanied by adequate increases in 

the rate of economic development. This fast but inadequately managed 

urbanisation has created a huge demand for urban housing which could not be 

met by the government and the organised formal sector in major Nigerian 

cities. As a result, 20 to 35 percent of urban housing in Nigerian cities is 

either dilapidated or in dire need of major repairs due to the poor housing 

conditions in the various housing programmes (Bello & Egresi, 2017; 

Muhammad & Bichi, 2014). Owerri, the Capital Territory of Imo State, is not 

left out in urbanisation and population growth. From 2006 to 2016, Owerri 

has experienced an average population growth rate of 4.04% (United Nations, 

2022). The resultant effect of this population growth are evident in the urban 

housing crisis which has affected the housing conditions as the supply of 

housing stock manifestly lags behind the needs of the populace. This was 

corroborated by Aotearoa (2009) as cited in Umeora (2020a).  

Housing condition is a vital influential factor of the habitability of buildings 

as it shows the level of resident’s well-being. Isma’il et. al. (2015) posited 

that there are severe housing shortages in urban centres caused by poor 

housing conditions. This manifests in the high number of people living in 

public quarters that lack basic physical and social amenities. Housing 

conditions refer to the sum of external effects (natural and man-made) that 

make the housing units comfortable for the inhabitants. They play a major 

role in the health status of occupants as they impact the physical, social, 

economic, and mental well-being of occupants (Turunen et. al, 2010). The 

World Health Organisation (WHO) also stated that housing should be able to 

minimise the following for the occupants: physical injury, protracted diseases, 

as well as reduce psychological and social stresses to the barest minimum.  

The Imo State Housing Corporation (IMSHC) was established under Section 

3 Edict No. 14 of 1976. IMSHC has the mandate to design and supervise the 

construction of houses, the acquisition of houses, the management of housing 



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estates, rental to the members of the public, maintenance of buildings, and 

other infrastructure needed for the proper functioning of the estates (Imo State 

Housing Corporation). Some of the IMSHC estates in Owerri were developed 

over 30 years ago, and it seems the management agency that has the 

responsibility of monitoring and supervising the activities of the estates has 

not lived up to its expectations. The managers of the estates, judged by their 

primary duty of ensuring that the building units in the estates and the facilities 

do not deteriorate, have fallen short of expectation. The dwelling units lack 

maintenance operations, and this has resulted to evident decay in quality of 

the various housing estates.  

When housing estates are poorly or inadequately managed, tragic 

consequences, such as ill-maintained buildings, poor sanitation, and various 

environmental health hazards could emanate. Okoye et al. (2018) affirmed 

that management of waste in the environment is crucial for healthy living. 

Ibem et al. (2013) noted that housing enables occupants to carry out different 

activities – work, rest, leisure, fitness and social interactions in the 

neighbourhood. Muoghalu (1987), as cited in Umeora (2018), posited that of 

all the dimensions of housing, management is the most crucial in explaining 

level of satisfaction of residents. Maintenance level, empathy, responsiveness 

and strictness were identified as the major components of managerial 

competence. Therefore, proper housing management is indispensable for 

keeping the buildings and amenities in serviceable conditions to ensure 

residents’ satisfaction and good housing conditions (Hui, 2005).  

The Owerri Capital Territory has, over the years, witnessed the migration of 

people from different parts of Nigeria. Consequently, some housing estates 

have been put under pressure. Some of these estates lack basic amenities such 

as electricity, water drainages, potable water, proper waste disposal systems, 

and good roads; instead, what one sees there are bad roads, defaced facades, 

and broken roofs, among other signs of inadequate maintenance. The lack and 

inadequacy of these affect the housing conditions. Additionally, poor housing 

conditions and quality are associated with health conditions such as 

respiratory diseases, depression, nausea, allergic symptoms, hypothermia, and 

physical injury.  

Some human activities in Imo State Housing Corporation estates, such as 

poor drainage planning, building along the drainage profile and blocking of 

drainage channels, and lack of coordinated maintenance management 

activities have also contributed to poor housing conditions. Some poor 

housing conditions in the estates are manifest in surface dampness on the 

walls, peeling of paints, and algae growth on the walls, and runoff of surface 

water causing erosion in the environment. Salleh et al. (2012) identified some 

management issues which have impact on housing conditions and residents’ 



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level of satisfaction in housing; they include the following: occupants’ 

selection procedures, laws implementation, time taken to respond to 

residents’ complaints, environmental security and overall quality of 

maintenance carried out by the management.  

This study was part of a wider research that sought to examine the effect of 

housing conditions on housing quality in Imo Housing Corporation estates in 

Owerri capital territory to provide guidelines for improving housing 

conditions in the study area. For this particular study, the objective was to 

investigate the relationship between housing management and housing 

conditions in Imo State Housing Corporation Estates in Owerri, Nigeria. A 

null hypothesis was put forward which sought to establish the significant 

relationship between housing management system and housing conditions in 

the estates. It stated that there is no significant relationship between housing 

management and housing conditions in Imo State Housing Corporation 

Estates in Owerri, Nigeria. 

Area of Study 

The area of study, Owerri Capital Territory, is situated in Imo State, Nigeria. 

Owerri is the capital of Imo State, Nigeria. It was created by the military 

administration of General Murtala Ramat Muhammed on February 3rd 1976. 

Nigeria is a country in West Africa that is situated in the northern latitudes 

between 4o and 14o and between 3o and 15o of the eastern longitudes. It 

borders Niger in the north, Chad in the northeast, Cameroon in the east, and 

Benin in the west. Nigeria covers an area of 923,769 square kilometres, with 

a population of over 211 million (National Population Commission, 2006). 

Figure 1 shows the map of Nigeria showing 36 States and the study area. 

 
Figure 1: Map of Nigeria showing Imo State and the study area (Owerri Capital 

Territory) Source: Chukwu (2024) 



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Owerri Capital Territory is approximately 100 square kilometres in area. It is 

located along the crossroad of major commercial routes in Southeast Nigeria, 

which are Onitsha-Owerri Express Road, Owerri-Port Harcourt Express 

Road, Owerri-Umuahia Road and Owerri-Aba Road. Owerri Capital Territory 

comprises the following local governments in Imo State: Owerri Municipal, 

Owerri West, Owerri North and parts of Mbaitoli, Aboh Mbaise, Ngor 

Okpala, Ohaji/Egbema and Ikeduru Local Government Areas. Owerri Capital 

Territory is located between latitudes 05˚25’ and 05˚32’ North and longitudes 

06˚57’ and 07˚07’. Rainfall is the greatest climatic variable with an annual 

total mean of 2190mm (Chukwuocha, Ngah, & Chukwuocha, 2017). Other 

climatic data of the study area include an average annual high temperature of 

32°C (89.96°F ), an annual low temperature of 23.19°C (73.74°F), 

average annual precipitation of 229.07cm and humidity of 74.78% (Nigerian 

Climatic Classification, 2023). Weather parameters are paramount in this era 

of climate change. Also, relative humidity, amount of sunshine and wind 

speed, among others, are weather parameters which play a role in determining 

the amount of rainfall received in an area. 

LITERATURE REVIEW      

There is a consensus that management/institutional framework plays a key 

role in housing policy formulation and implementation (Ibem, 2011). 

Management is usually inspired by the need to be cautious in the usage of 

assets and judicious in the usage of time in attaining pre-stated objectives. 

Obodoh (2009) defined management as the scheduling, coordination, and 

control of the essential resources for the achievement of stated goals. The 

relationship between the management system of housing and the residents 

exerts a great impact on housing quality. If there is a cordial relationship 

between them, matters of maintenance of infrastructure will be addressed 

timely to reduce dilapidation. Issues under management variables are the type 

and quality of services rendered by the managers, time taken by the managers 

in treating residents’ complaints and ensuring environmental sanitation.  

The Imo Housing Corporation has the mandate to control and manage the 

development of housing units and perform such other functions as the 

Commissioner of Housing and Urban Development may direct. Those 

functions may also include to design and supervise housing programmes for 

the state government; award contracts for the development of housing estates, 

assess infrastructure needed in layouts of housing estates owned or managed 

by the corporation; oversee the maintenance of buildings, roads, footways, 

bridges, drains, sewers and water courses for or in connection with housing 

estate owned or managed by the Corporation (Imo State Housing 

Corporation, n.d.). 



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To assist the harmonisation between residents in running some of the shared 

facilities of housing, a certain level of organisation from the management is 

necessary. Although there is mounting interest in research examining the 

effects of management on housing performance, few works have looked at 

the correlation between housing management systems and housing condition 

(Aotearoa, 2009). Given that most housing schemes are constructed to 

stipulated standards, the buildings and facilities in the estates generally 

perform optimally at that new state, until they start to deteriorate when 

subjected to inhabitation and usage. Therefore, appropriate maintenance and 

management of amenities in the housing estates are crucial for keeping the 

amenities in functional conditions to ensure residents’ satisfaction (Hui, 

2005).  

Some of the stipulated standards of housing condition address: aesthetics, 

sanitation, drainage, age of the building, access to basic housing facilities, 

burglary, spatial adequacy, noise level within the neighbourhood, sewage and 

waste disposal, air pollution and ease of movement, among others. Lanrewaju 

(2012) noted poor housing condition in public housing programmes in 

maintenance of facilities within the estate as well as poor management 

approach towards residents’ problems in the estate. Salleh, Yosuf, Salleh and 

Johari (2012) identified management issues which have impacted housing 

conditions in housing estates, including the sociability of the managers, 

residents’ selection procedures, implementation of bye-laws, time taken to 

respond to residents’ complaints, security of the neighbourhood and quality of 

maintenance works done by the managers. 

METHODOLOGY 

The research design for this study was survey design, and it was 

accomplished through the use of a questionnaire to collect data from 

respondents in the study area. The research population was the completed 

IMSHC estates within Owerri Capital Territory, built and inhabited between 

1976 and 2016 when the last housing estate was completed. Stratified 

sampling of the estates based on building type was adopted as the sampling 

method for this study. In the first stage, the list of the 14 estates completed 

and occupied in the study area was generated as shown in Table 1. 

Table 1: List of Imo State Housing Corporation Estates in Owerri 

Capital Territory 

S/N NAME OF ESTATE 

1 Aladimma   

2 Prefab  

3 Prefab Extension I                                                                        

4 Prefab Extension II                                                                      



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5 Uratta Road                                                                                  

6 Trans-Egbu    

7 Umuguma Area ‘S’ 

8 Umuguma Area ‘X’ 

9 Umuguma Area ‘XA’ 

10 Tavron Prefab Estate 

11 City Garden Estate MCC Road 

12 Redemption Housing Estate 1  Avu/Obinze                                                     

13 Exclusive Garden Estate Phase I&II Nekede 

14 Oforola Housing Estate  Oforola 

                                Source: Imo State Housing Corporation, n.d 

In the second stage, the categorisation of the estates based on building type 

was done. The categorisation of the estates is 1 - Bungalows; 2 - Bungalows 

and Duplexes; 3 - Bungalows and 3-storey blocks of flats. Table 2 describes 

the categorisation based on the above-stated criteria. 

Table 2: List of Imo State housing corporation estates in Owerri 

categorised by house type in the estates 

S/N Bungalow Bungalow and Duplex  Bungalow and 3 

Storey Block of Flats 

1 Redemption Estate Prefab Estate Trans-Egbu Estate 

2 Aladimma Estate Umugwuma Estate  

3 Uratta Road Estate Oforola Estate  

4 Tavros Estate City Garden estate  

5  Nekede Exclusive Garden 

Estate 

 

   Source: Fieldwork, 2022 

Following the categorisation, random sampling by balloting was carried out 

and the following were picked to represent the various building types: 

i. Bungalows: Aladimma Estate and Uratta Road Housing Estate 

ii. Bungalows and Duplex combined: Prefab estate and City Garden Estate 

iii. Bungalow and 3 Storey Block of Flats: Trans-Egbu. 

Sampling size was derived using the Cochran formula for finite population: 

from Kothari (2004) 

n =  Z2 x σ2
p x N 

(N-1) e2 + Z2 x σ 2
p 

Where n = size of sample for finite population; N = research population = 

1484 housing units; σp = standard deviation of population assumed = 0.5; e 



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= significance level (precision/acceptable error) chosen = 0.05; Z = standard 

variate at a given confidence level = 1.96 for a confidence level of 95%.  

A sample size of 305 respondents was derived and distributed to the estates in 

ratio to their contribution as shown in Table 3. 

Table 3: Respondents Population in Sampled Estates 

 Aladimma 

Estate 

Uratta 

Road 

Prefab City Garden Trans-Egbu 

Housing Units 556 310 267 10 341 

Sampled 114 64 55 2 70 

                    Source: Fieldwork, 2022 

A systematic random sampling was used in the selection of housing units in 

each street of the housing estates. After the first house, every fourth house 

was surveyed. In each house, in the case of a multi-family unit, one 

household would be administered the questionnaire. 

Pearson's Product Moment Correlation analysis was used to test the 

significant relationship between the two Interval variables selected from the 

research data using Statistical Package for Social Sciences. 

 

RESULTS AND DISCUSSION 

Analysis of aggregated data on the Availability of procedures 

for maintenance operations in the estate  

From the data gathered, 90.2% of the respondents indicated that there was no 

available procedure for maintenance operations in the estates. This could be 

part of the reasons why there was a decline in the housing quality in the area 

(See Table 4). 

Table 4: Aggregated Data on Availability of procedures for maintenance 

operations in the Estate 

Value label Frequency Valid Percent Cumulative Percent 

Yes 28 9.8 9.8 

No 259 90.2 100.0 

Total 287 100.0  
                    Source: Fieldwork, 2023 

Analysis of aggregated data of Management of maintenance of facilities 

in the estate  

The data analysed revealed that most of the respondents pointed out that 

management of maintenance of facilities in the estates was handled by the 



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residents while 7% showed that IMSHC managed the facilities. See Table 5 

for details. 

Table 5: Aggregated Data on Management of maintenance of facilities in 

the Estate 

Value label Frequency Valid Percent Cumulative Percent 

IMSHC 2 .7 .7 

Residents 270 94.1 94.8 

Both parties 15 5.2 100.0 

Total 287 100.0  
                    Source: Fieldwork (2023) 

Analysis of aggregated data of Communication channels in the estate  

The results collected indicated that most of the respondents communicated 

with the housing corporation by visiting the office. A few of the respondents 

stated that they communicated with the IMSHC either by phone calls or SMS. 

Table 6 shows this. 

Table 6: Aggregated Data on Communication Channels in the Estate 

Value label Frequency Valid Percent Cumulative Percent 

SMS 1 .3 .3 

Phone calls 16 5.6 5.9 

Visit to office 241 84.0 89.9 

Internet 1 .3 90.2 

All of the above 28 9.8 100.0 

Total 287 100.0  
                    Source: Fieldwork (2023) 

 

Analysis of aggregated data of Duration to react to Resident’s complaints 

in the estate  

The data analysed indicated that it took between 4-6 days to react to 

resident’s complaints as noted by the majority of the respondents. 36.9% of 

the respondents agreed that it took more than six (6) days for IMSHC to react 

to their complaints. Table 7 shows this. 

Table 7: Aggregated Data on Duration to React to Resident’s Complaints 

in the Estate 

Value label Frequency Valid Percent Cumulative Percent 

1-3 days 17 5.9 5.9 

4-6 days 164 57.1 63.1 

more than 6 days 106 36.9 100.0 

Total 287 100.0  
                    Source: Fieldwork (2023) 

 



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Analysis of aggregated data on the Regularity of Corporation visits to the 

estate  

From the data gathered, it could be seen that most of the respondents (35.9%) 

confirmed that the regularity of the corporation's visit to the estate was twice 

a year while 31.0% agreed that the regularity of the corporation's visit to the 

estate was quarterly and 18.8% of the respondents accepted once a year. This 

is illustrated in Table 8. 

Table 8: Aggregated Data on Regularity of Corporation Visits to the 

Estate 

Value label Frequency Valid Percent Cumulative Percent 

Monthly 10 3.5 3.5 

Bi-monthly 24 8.4 11.8 

Quarterly 89 31.0 42.9 

Twice a year 103 35.9 78.7 

Once a year 54 18.8 97.6 

Others 7 2.4 100.0 

Total 287 100.0  
                       Source: Fieldwork (2023) 

 

Analysis of aggregated data on the Availability of Security in the estate  

The investigation revealed that 57.1% of the respondents confirmed the 

availability of security measures in the estates within the study area as shown 

in Table 9. 

Table 9: Aggregated Data on Availability of Security in the Estate 

Value label Frequency Valid Percent Cumulative Percent 

Yes 164 57.1 57.1 

No 123 42.9 100.0 

Total 287 100.0  
                       Source: Fieldwork (2023) 

 

Analysis of aggregated data of Arrangement of Security in the estate  

It could be observed that the majority of the respondents indicated that the 

arrangement of security in the estate was handled by residents (individuals). 

Few of the respondents noted that security arrangement was done centrally by 

the estate (See Table 10). 

Table 10: Aggregated Data on Arrangement of Security in the Estate 

Value label Frequency Valid Percent Cumulative Percent 

Estate Central 56 19.5 19.5 

Individual 209 72.8 92.3 

Both 22 7.7 100.0 

Total 287 100.0  
                       Source: Fieldwork (2023) 

 



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Analysis of aggregated data of Management of Central Security in the 

estate  

The data collected showed that the majority of the respondents stated that 

management of central security in the estate was done by the residents. A few 

of the respondents stated that IMSHC managed security in the estates while a 

minute percentage (1.7%) stated that the government managed security 

arrangements. Table 11 shows this. 

Table 11: Aggregated Data on Management of Central Security in the 

Estate 

Value label Frequency Valid Percent Cumulative Percent 

IMSHC 6 2.1 2.1 

Estate Residents 276 96.2 98.3 

Government 5 1.7 100.0 

Total 287 100.0  
                       Source: Fieldwork (2023) 

 

Analysis of aggregated data on the state of repair of external walls 

The state of repair of walls was examined and the results showed that a 

greater percentage (41.5%) of the external walls were in a bad state of repair 

while the external walls in a good state of repair were less at 38.3%. Table 12 

shows the details. This means that the buildings in a bad state of external wall 

repairs were in a poor state, and they were not fit for human inhabitation. 

Table 12: Aggregated Data on the State of repair of external walls in the 

buildings 

Value label Frequency Valid Percent Cumulative Percent 

Very good 15 5.2 5.2 

Good 110 38.3 43.6 

Not sure 30 10.5 54.0 

Bad 119 41.5 95.5 

Very bad 13 4.5 100.0 

Total 287 100.0  
                         Source: Fieldwork (2023) 

 

Analysis of aggregated data on the state of repair of the roof 

From the data gathered and analysed, roofs in bad state of repair were greater 

in number with 47.7% of the respondents indicating so while the ones in good 

state of repair were 34.1%. This implies that most of the roofs were in a bad 

state and needed urgent repairs and improvement. Figure 2 illustrates this. 

 

 



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Figure 2: Aggregated Data on the State of repair of roofs in the buildings 

Source: Fieldwork (2023) 

 

Aggregated data analysis of waste disposal facilities in the estates 

From the analysis, there was a high level of inadequate waste disposal 

facilities in the estate, as reported by 31.7% of the respondents; 21.3% of the 

respondents reported that waste disposal facilities were adequate. Table 13 

displays the result. 

Table 13: Aggregated Data on Waste Disposal Facilities in the Estate 

Value label Frequency Valid Percent Cumulative Percent 

Very inadequate 19 6.6 6.6 

Inadequate 91 31.7 38.3 

Undecided 106 36.9 75.3 

Adequate 61 21.3 96.5 

Very adequate 10 3.5 100.0 

Total 287 100.0  
                         Source: Fieldwork (2023) 

 

Analysis of aggregated data of State of repair of buildings  

It can be observed from Table 14 that most of the respondents stated that the 

buildings in the estates were in a bad state of repair and 26.8% of the 

respondents stated that the buildings were in a good state of repair. This 

revealed that most of the buildings were in poor condition and unfit for 

human dwelling.  

Table 14: Aggregated Data on the State of repair of building in the 

buildings 

Value label Frequency Valid Percent Cumulative Percent 

Very good 14 4.9 4.9 

Good 77 26.8 31.7 

7.3, 7%

34.1, 34%

7, 7%

47.7, 48%

3.8, 4%
Very good

Good

Not sure

Bad

Very bad



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Not sure 69 24.0 55.7 

Bad 115 40.1 95.8 

Very bad 12 4.2 100.0 

Total 287 100.0  
                         Source: Fieldwork 2023 

Analysis of aggregated data of Flaking/Peeling wall finish used in the 

housing estates  

Most of the respondents indicated that the paint on the internal walls was 

peeling off. This implies that a greater proportion of the buildings have their 

paint peeling off as shown in Figure 3. It implies that most of the buildings 

need to be repainted to improve their aesthetic appearance. 

 

Figure 3: Data on Flaking/Peeling wall finish used in the Housing Estates. 

Source: Fieldwork (2023) 

Test of Hypothesis 

The variables ‘Flaking/Peeling wall finish’ (PWF) and ‘Availability of 

procedures for maintenance operations’ (APMO) were selected for this 

analysis. The two variables are of nominal variable category; therefore, the 

Chi-square test of independence analysis tool was applied towards examining 

the significance of the relationship.  

The result from the analysis carried out showed 0.776 as the Chi-square 

value, with a Df value of 1 and a p-value of 0.038 as presented in Table 15. 

This p-value of 0.038 is less than the chosen α-value (i.e., acceptable 

significance level) of 0.050 for this research, implying therefore that it is 

accepted as significant. It is established, hence, that the relationship that 

exists between the two investigated variables can be stated to be statistically 

significant for this study. The alternate hypothesis, which states that 

‘There is significant relationship between Flaking/Peeling off wall finish and 

‘Availability of procedures for maintenance operations in Imo State Housing 



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Corporation (IMSHC) estates in Owerri Capital Territory’, is thus accepted. 

Table 1: Result of Chi-square test of independence analysis of 

relationship between PWF and APMO 

  Availability of procedures 

for maintenance operations 

Flaking/Peeling wall finish

  

Chi-Square 0.776a 

Df 1 

P-Value .038 
          Source: Fieldwork (2023) 

CONCLUSION AND RECOMMENDATIONS 

The study showed that the housing management affects housing condition in 

Imo State Housing Corporation (IMSHC) estates in Owerri Capital Territory. 

Obodoh (2009) stated that the relationship between managers of housing 

estates and the residents exerts a great impact on housing quality. If there is 

an amiable relationship between them, issues of maintenance will be 

addressed timely to reduce dilapidation. Hui (2005) stated that a proper 

management system is essential for keeping the housing in serviceable 

conditions to ensure good quality at all times. 

No system can function adequately without a proper management system, 

housing estates inclusive. The management can be made up of administrative 

and technical staff. The latter, which should be made up of professionals in 

the building industry, should be included in the planning and design of the 

estates. The former should see to the running of the estates by ensuring that 

the guidelines established are kept to by residents. They should carry out 

supervisory roles in conjunction with technical staff to get feedback from the 

residents. While investigating the management systems and housing 

conditions in the area of study, it was proven that there is significant 

relationship between flaking/peeling off of  wall finish and the Availability of 

procedures for maintenance operations in Imo State Housing Corporation. It 

is also noted that the availability of procedures for maintenance operations 

had significant correlation with the state of repair of external walls. 

Therefore, it is recommended that:  

i. For prompt maintenance of facilities in buildings the residents should 

undertake it. For maintenance of facilities in the neighbourhood, IMSHC 

should undertake that. There should be a legal provision to enable the 

residents to enforce maintenance activities in the environment by IMSHC. To 

lessen abuse of the residents, there should be a provision to enable the 

residents to withhold rent or annual development fee paid to compensate for 

maintenance executed by them in the event of delays by the estate managers. 



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ii. The time taken to respond to residents’ complaints should be improved 

upon by ensuring prompt response to complaints. From the analysis done, it 

was evident that it takes more than a week to respond to residents’ 

complaints. This situation should be reversed by taking into consideration 

other means by which the IMSHC could attend to various complaints by the 

residents. This may be by having a liaison office within the estate where 

residents can also drop comments and suggestions. Leveraging on this, the 

feedback system is guaranteed, leading to a working partnership between 

IMSHC and the residents, which is useful.   

These recommendations, if implemented, could lead to an increased level of 

housing quality in the IMSHC estates. 

 

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data collection and housing quality in New Zealand. Review of 

Housing Statistics report. 

Bello, A. & Egresi, I. (2017). Housing conditions in Kano, Nigeria: a 

qualitative assessment of  adequacy. Analele Universităţii din 

Oradea, Seria Geografie, 2, 205-229 

Chukwu, N.N. (2024). Effects of Housing Conditions on Housing Quality in 

Imo State Housing Corporation Estates, Owerri Capital Territory, 

Nigeria. A Ph.D thesis in the Department of Architecture, 

Chukwuemeka Odumegwu Ojukwu University, Nigeria. 

Chukwuocha, N. A., Ngah, S. A., & Chukwuocha, A. C. (2017). 

Vulnerability Studies of Sensitive Watershed Areas of Owerri South 

East Nigeria Using Digital Elevation Models. Journal of Geoscience 

and Environment Protection, 1-3. 

Hui, E. Y. Y. (2005). Key success factors of building management in large 

and dense residential estates, Facilities, 23 (1/2), 47 – 62. 

Kothari, C. R. (2004). Research Methodology: Methods and Techniques (2nd 

ed.). New Delhi: New Age International Ltd. 

Ibem, E.O., (2011), Evaluation of Public Housing in Ogun State, Nigeria. 

(Doctoral thesis), Department of Architecture Covenant University, 

Ota, Ogun State. 

Imo State Housing Corporation. (n.d.). Housing Types in the Imo State 

Housing Corporation Owerri. Owerri: Standard press Limited. 



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Isma'il, M., Ishaku, E., Yahaya, A., Tanko, M., & Ahmed, H. T. (2015). 

Urban Growth and Housing Problems in Karu Local Government 

Area of Nasarawa State, Nigeria. Global Journal of Reasearch and 

Review (GJRR). 45-53, 

Lanrewaju, F. A. (2012). Urbanization, housing quality and environmental 

degeneration in Nigeria. Journal of Geography and Regional 

Planning, 423-425. 

Muhammad, M., & Bichi, A. M. (2014). Contraints and Challenges on 

Housing Provision in Kano City, Nigeria. International Journal of 

Advancements in Research & Technology, Volume 3, 4-23. 

Muoghalu, L.N. (1987). A comparative evaluation of residents’ satisfaction 

with public and private rental housing in Benin City Nigeria. A Ph.D 

thesis in the Department of Geography and Regional Planning, 

University of Benin, Nigeria. 

Nigerian climatic classification. (2023, June 15). https://tcktcktck.org. 

Retrieved from weather and climate. 

Obodoh, C.M. (2009). Assessment of the impact of Institutional Control in 

the Management of Public Estates: A case study of Central Bank of 

Nigeria quarters, Enugu, (M.Sc. Dissertation) in the Department of 

Estate Management, Faculty of Environmental Studies, University of 

Nigeria, Enugu Campus 

Okoye, B.S.A., Umeora, C.O., Ifebi, O.C. & Onwuzuligbo, C.C. (2018). 

Effects of Sewage Disposal Systems on the Environment in Public 

Housing Estates in Enugu Metropolis. African Journal of 

Environmental Research, 1(1). 120-131. http://journal 

.coou.edu.ng/index.php/ajer 

Salleh, A. N. A., Yosuf, B. N. A., Salleh,. A. G., & Johari, D. N. (2012). 

Tenants Satisfaction in Public Housing and its Relationship with Rent 

Arrears: Majlis Bandaraya Ipoh, Perak, Malaysia. International 

journal of trade, economics and finance, 2(1), 10-18. 

Turunen, M., Paanala, A., Villman, A. N., & Haverinen-Shaughnessy, U. 

(2010). Evaluating Housing Quality, Health and Safety Using an 

Internet-Based Data Collection and Response System: A Cross-

Sectional Study. Environ Health. 

Umeora, C.O (2018). Housing Management and Residents’ Satisfaction in 

Housing Estates in Enugu Metropolis, Nigeria: Case Study of Central 

Bank of Nigeria Quarters, Enugu. African Journal of Environmental 



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Research. 1(2), 52-63 

Umeora, C.O. (2020). Examination of state of repair of buildings in private 

housing estates in Enugu metropolis, Enugu state Nigeria. Journal of 

Environmental Sciences and Resources Management, 12(1), 52-66. 

United Nations. (2022). World Population Prospects 2022. New York: 

United Nations Department of Economic and Social 

Affairs/Population Division. 

 

 

 

Author Information: Nnanyere N. Chukwu works at 

Tertiary Education Trust Fund (TETFund) South-East 

Zonal Office, Enugu, Nigeria. Email: emekacnn@gmail. 

com 

 
 

 

 

 

Chukwunonso O. Umeora is of Department of 

Architecture, Chukwuemeka Odumegwu Ojukwu 

University, Anambra State, Nigeria. Email: 

coumeora@gmail.com 

 
 

 

 

 

Charles C. Munonye is of Department of Architecture, 

Chukwuemeka Odumegwu Ojukwu University, 

Anambra State, Nigeria. 

 
 

 

 

 

 
 

APA 
 

Chukwu, N. N., Umeora, C. O., & Munonye, C. C. (2025). 

Relationship between Housing Management and Housing 

Conditions in Imo State Housing Corporation Estates in Owerri, 

Nigeria. Global Online Journal of Academic Research (GOJAR), 

4(1), 73-89. https://klamidas.com/gojar-v4n1-2025-05/.  
 

MLA 
 

Chukwu, Nnanyere N., Umeora, Chukwunonso O. & Munonye, 

Charles C. “Relationship between Housing Management and 

Housing Conditions in Imo State Housing Corporation Estates in 

Owerri, Nigeria”. Global Online Journal of Academic Research 

(GOJAR), vol. 4, no. 1, 2025, pp. 73-89. https://klamidas.com/gojar-

v4n1-2025-05/.  

 

 

 

 



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Exploring the Impact of Integrative Artificial 

Intelligence Tools on the Writing Proficiency of 

University Students in Kano State 

 

Mudassir Hassan & Adebayo Abubakar Funsho 

 

 

Abstract 

The integration of artificial intelligence (AI) tools in educational context has 

significant implications for students’ writing skills, often resulting in detrimental 

effects. Current scholarship highlights that while AI tools offer certain advantages, 

overreliance on them can lead to cognitive offloading, which in turn diminishes 

critical thinking abilities and stifles creativity. This study aims to assess the impact 

of AI tools on university students’ academic writing skills, as well as to examine the 

ethical concerns surrounding the adoption of AI technologies in writing processes. 

Employing mixed-method approach in the study, data were collected from three 

hundred and twenty (320) university students and fifty (50) language teachers via 

questionnaire, pre-test and post-test scores from essay writing tasks. Data collected 

through questionnaire were analyzed descriptively, while inferential analysis was 

employed to address the stated hypotheses. Findings of the study reveal that the 

presence of AI tools reduces students’ capacity to produce high-quality academic 

discourse and promotes unethical practices. Therefore, the study reveals significant 

negative impact of AI on students’ writing capabilities and the prevailing manifested 

trend of cognitive offloading. Based on the findings, it is recommended that teachers 

and relevant stakeholders adopt AI tools as complementary resources, while 

reinforcing traditional writing methods that nurture critical thinking, creativity and 

students’ expression. 

Keywords: Artificial Intelligence, cognitive offloading, ChatGPT, writing 

proficiency, creativity 

 

 

 

Introduction 

The significant advancement in information and communication technology 

(henceforth, ICT) that has uniquely defined the 21st century creates an 

environment that encourages human-like thought or cognitive-like content 



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produced by artificial cognitive systems. This major shift suggests that the era 

of unchallenged human cognitive supremacy is no longer predominant, 

particularly when it comes to content generated through human thought 

processes. In fact, this transformation has been largely driven by the recent 

emergence of artificial intelligence (henceforth, AI). While scientists applaud 

this remarkable achievement in Science and Technology, this revolutionary 

trend has simultaneously sparked extensive discussions among scholars. In 

the context of teaching and learning, there is an increasing concern about the 

potential negative effects of this technology on students’ ability to engage 

actively in academic endeavours related to self-generated intellectual 

discourse, creativity and critical thinking.  

Some scholars argue that the absence of comprehensive preventive measures 

to regulate students’ indiscriminate use of AI-generated content, which they 

present as their original work, is pedagogically detrimental. In addition, the 

widespread adoption of AI technology has the potential to diminish students’ 

writing skills, creativity and critical thinking. On the other hand, other 

scholars maintain an optimistic view of AI’s role in enhancing students’ 

writing capabilities. They contend that advancements in AI can be effectively 

harnessed to augment and complement human efforts, regardless of the 

specific context in which they are applied. As a result, the applications and 

complementary functions of AI are diverse. These different perspectives have 

led to renewed interest in assessing the positive contributions of AI 

technology in education. Therefore, the primary focus of this study is to 

examine the potential threats posed by AI technology and its associated 

online platforms, such as ChatGPT, on the writing abilities of university 

students in Kano State, Nigeria. 

Aim and Objectives of the Study 

The present study seeks to investigate the potential effects of AI on students’ 

writing proficiency. Specifically, it explores the influence of AI tools and 

technologies, including Automated Writing Assistants and Language 

Generation Technologies (henceforth, LGT), on the writing skills of 

university students. In addition, the study has the following objectives: 

1- To examine the impact of AI technology on university students’ 

writing skills in Kano State. 

2- To assess the ethical implications related to the use of AI tools on 

students’ writing skills. 

 

 



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Research Questions 

The following research questions are set to guide the study: 

1- What is the difference between the learning outcome of university 

students taught writing through the AI technology and those taught 

using the traditional approach in Kano State? 

2- How does the application of AI tools in students writing processes 

affect ethical standard? 

Research Hypothesis 

HO1: There is no significant difference between the learning outcome of 

university students taught writing through AI technology and those taught 

using the traditional approach in Kano State. 

HO2: There is no significant impact of ethical issues associated with the use 

of AI tools on students’ writing skills. 

Review of Previous Related Studies 

The inclusion of AI within educational context has attracted considerable 

scholarly attention in recent years, particularly concerning its implication for 

students’ writing proficiency. Empirical studies and scholars’ views show 

divergent perspectives. Some suggest that the integration of AI technologies 

can effectively support and enhance multiple facets of writing skills by 

offering positive personalized feedback, providing linguistic assistance and 

promoting creativity, as well as enhancing language usage (Yarima, 2024). 

On the other hand, others believe that AI technologies have significant 

negative impact on students’ ability to write excellent academic discourse. 

The primary concerns regarding AI effect on students’ writing include 

detrimental over-reliance on AI tools, erosion of critical thinking and 

creativity, undermining of fundamental writing skills, harmful impact on 

academic integrity, as well as possible overall decline in students’ writing 

ability (Hassan, 2024). 

Studies conducted by Idham, Rauf & Rajib (2024), Zafrullah, Meisya & 

Ayumi (2024), Psatama & Hashuti (2024), Risang (2023), Ramadhan et al. 

(2023), Cascidy (2023 in Yarima, 2024) and Bhutoria (2022) indicate that AI-

based writing assistance tools such as grammar checker and Automated 

Content Generators facilitate and enhance various aspect of students writing 

proficiency. Idham, Rauf & Rajib (2024) report that AI tools provide useful 

personalized feedback and instruction which are significantly useful in 

providing tailored suggestions for improving students’ writing skills. In 

addition, Zakrullah, Meisya & Ayumi (2024) indicate that AI tools enhance 



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writing capacity of students, while Psatama & Hashuti (2024), Risang (2023) 

and Ramadhan et al. (2023) argue that AI tools, not only improve students 

writing skills, but motivate students’ active practical participation in writing 

processes which is a radical positive departure from the traditional teacher-

centered approach. Moreover, Malik et al. (2023) explores the impact of AI 

technologies in academic essays writing using a case study design. The study 

involved 245 undergraduate students from 25 tertiary institutions in eastern 

and central Indonesian provinces. Data for the study were collected through 

online questionnaire instrument. Findings of the study reveal that AI tools 

enhance students’ writing abilities, develop self-efficacy and academic 

integrity. Furthermore, studies conducted by Aljuaid (2024), Teng & Wang 

(2023) and Zhao et al. (2023) indicate that AI tools improve students’ writing 

proficiency, and boost their confidence and productivity during the writing 

process.  

One of the primary concerns regarding AI on students writing is the risk of 

students developing an over-reliance on AI-based Writing Assistance Tools 

(ABWAT), such as grammar checkers and automated content generators. 

Studies by Basha (2024) and Perkins (2023) indicate that AI technologies 

ChatGPT can generate unique and logical content that can evade detection, 

giving rise to significant concern over academic integrity. In addition, it is 

indicated by the findings that AI tools negate the development of basic 

foundation skills, critical thinking and make students inactive in academic 

performance. Similarly, studies by Budai & Backer (2020 in Yarima, 2024), 

Borenstien & Howard (2021), Kyoungwon et al. (2021 in Yarima, 2024) and 

Abd Rahman et al. (2023 in Yarima, 2024) reveal that students who depend 

heavily on AI tools, experience a significant decline in their ability to write. 

Besides, AI tools provide a false proficiency level of students, thereby 

disallowing teachers to locate students’ deficiency. In a recent study 

conducted by Yarima (2024), it is revealed by the findings that AI tools make 

students less motivated to engage in the repetitive process of writing, as they 

perceived AI tools as a shortcut to producing polished writing without 

investing the necessary effort. In the same vein, it is affirmed by Turner 

(2024) that when students use AI tools to generate ideas and compose entire 

texts, originality and innovative thought in writing become stifle. In addition, 

Adamu (2024) argues that AI tools can lead to shallow analyses and 

weakened argumentative writing skills. Besides, findings of the studies 

conducted by Lydia (2023 in Yarima, 2024) and Derrida (2022 in Yarima, 

2024) reveal that AI tools diminish students’ ability to write, render them less 

attentive to grammar usages, spelling, correct use of punctuations, erosion of 

critical thinking, originality, as well as encourage unethical problem of 

plagiarism. 



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Based on the scholars’ assessments and the results of studies conducted on 

the impact of AI tools on the writing proficiency of students, it is clear that 

the new technology has a significant impact on students’ writing skills – 

positively and negatively. Parts of the positive impact include the provision of 

real-time feedback on grammar, style and structure and provision of effective 

guide to students on how to improve their writing efficiency. The technology 

does not only provide students with opportunity to generate ready-made 

written content, which support brainstorming, but facilitates personalized 

learning opportunities, offering tailored suggestions that help students 

improve their writing proficiency. On the negative perspectives, the 

technology reduces students’ critical thinking ability due to over-reliance on 

AI technology for assistance. Though AI can be a powerful tool for enhancing 

writing skills, it should not be used in conjunction with traditional learning 

methods to ensure a well-rounded development, as well the development of 

critical thinking skill which is one of the cardinal objectives of writing skills 

(Hassan, 2024). What is more, with AI associated language problems of a 

learner cannot be exposed, as the writing is not done by him. Therefore, 

deficiencies in language usage cannot be seen and corrected by teachers. 

The clear gaps identified in the previous studies on the effect of AI 

technology on students’ writing skills include the fact that most studies, if not 

all, were carried out in Europe and Asia, with only a handful conducted in 

African nations. Besides, majority of the studies focus on learners of English 

as a Foreign Language (EFL). In contrast, this study is conducted in Kano 

State, located in North-West Nigeria, within the West African sub-region. 

Additionally, this study involves learners of English as a Second Language 

(henceforth, ESL) 

According to Catherine (2023 in Yarima, 2024) writing ability refers to “the 

capacity to communicate effectively through written language, allowing 

students to express their ideas, thought and feeling by demonstrating good 

command of language usage and organizational skill.” Writing ability enables 

university students to excel both academically and professionally, while also 

enhancing their personal lives (Yarima, 2004).  Writing encompasses a series 

of sequential activities leading to continuous learning process. Through 

traditional learning methods, students are consciously and deliberately 

exposed to different writing activities aimed at developing their critical 

thinking, creativity, language usage and organizational skills, as well as the 

ability to develop and articulate their own ideas, rather than relying on 

content generated by AI tools. From a pedagogical perspective, within the 

context of English as a Second Language (ESL) education, writing reveals 

specific areas in which learners may struggle with the target language. This 

allows teachers to identify such deficiencies and provide the necessary 



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support to help students overcome the challenges associated with language 

learning in the ESL context for proficiency. 

According to Febrina and Kartolo (2022 in Yarima, 2024), the teaching of 

writing is done to achieve several objectives: promoting students to engage in 

writing with honesty and responsibility, utilizing language with caution, 

integrity, and sensitivity; stimulating students’ imagination, creativity and 

cognitive abilities; and producing written works or essays that are well-

organized, precise, clear, structured and adhere to formal conventional norms. 

Similarly, Hassan (2024) asserts that university students are expected to 

produce writing that is formal and devoid of any informal language usage 

(Hassan & Sanusi, 2023). In addition, it is anticipated that students at the 

university level will generate exemplary academic discourse in their capacity 

as members of the formal discourse communities. However, the advent of AI 

technology appears to pose a potential threat capable of undermining the 

objectives and expectations. 

METHODS 

Research Design 

The study employs a mixed-methods design; a quantitative approach using a 

quasi-experimental design was employed. A pre-test was administered to 

assess the initial skills levels of the participants in both the control and 

experimental groups. Following this, the experimental group had the 

opportunity to use AI tools to generate ideas for writing narrative essays for 

two weeks, while the control group received instruction through the 

traditional methods without the integration of AI technology. To evaluate the 

effectiveness of these strategies, a post-test was conducted simultaneously for 

both groups. The post-test scores were compared with the pre-test scores in 

order to assess the impact of AI technology on students’ writing skills. In 

addition, a qualitative approach was also used in the study, with data 

collected through a questionnaire and analyzed descriptively. 

Population and Sample 

The study population consisted of participants from four selected universities 

in Kano State. A sample size of one hundred and sixty (160) participants for 

each group, namely the control and experimental groups, was determined 

using Taro Yamane guidelines for appropriate sample size selection. A 

Purposive Sampling technique was employed to select the sample of the 

study. 

 

 



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Research Instrument 

The study collected data from students’ essays that were given during the pre-

test and post-test phases. The students’ writings were assessed using a set of 

scoring criteria for evaluating students’ writing and for giving feedback, 

Writing Assessment Rubric (WARU), developed by Spack & Burden (2015). 

The rubric is widely used by researchers as criteria for assessing writing. It 

provides a comprehensive and all-encompassing guideline for assessing and 

scoring writing including content, organization, mechanics, language use and 

vocabulary as presented in Table 1 below: 

 

A ten items structured questionnaire was also distributed to forty (40) 

randomly selected lecturers across the four designated universities – ten from 

each of the universities. The questionnaire was designed in Likert format. The 

items in the questionnaire sought to elicit data on the ethical concern of using 

AI tools, as well as the impact of the technology on the writing skills of 

selected university students in Kano State, Nigeria. 

Data Collection and Analysis 

Data collected through questionnaire instrument and from the scores obtained 

from the writing tasks (pre-test and post-test scores) were analysed by 

employing inferential and descriptive methods. 

RESULTS 

Data Presentation and Analysis 

Impact of AI Technology on the Writing Skills of University Students in 

Kano State 



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The Descriptive Result 

 
As shown in Table 2, the pre-test score of the control group shows that 

majority of the students in the group scored low, as the highest percentage of 

76.1% failed, while the low percentage of only 24.0% scored high. Also, the 

mean score of the result is 6.2. On the other hand, the academic performance 

of the students in the pre-test treatment for those in the experimental group 

shows that 85.9% performed academically low, while only 11.3% scored 

high. The mean of the group is 5. 9, the standard deviation of the pre-test 

scores is 10.2 for the conventional group and 8.6 for the experimental group. 

This means that the results of the two groups are the same; as majority in the 

two groups performed poorly. On the other hand, the results of the post-test 

indicate that majority of the subjects in the control group of 96.1% scored 

high, while only 39.7% scored low. Equally, majority of the students, 60.3% 

scored high, while 43.8% scored low. By comparing the two results, it is 

evident that the results of the post-test for those in the control group is better 

as 96.1% passed, while only 60.3% in the experimental group passed. The 

disparity in the two scores is facilitated by the scoring criteria, which 

necessitated the removal of certain expressions and usages considered as AI 

generated. Therefore, teaching writing using traditional approach is most 

effective in facilitating students’ writing skills.  

 



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As shown in the analysis, majority of the teachers agreed that AI technology 

negates students’ ability to write good academic discourse (78.4%), 

discourages creativity (67.2%), motivates students’ over-reliance on AI 

content-generated materials (81%), does not facilitate effective grammar 

usage (76.2%), encourages laziness (69.5%), encourages plagiarism (71.7%), 

does not improve students’ proficiency in the use of words (84.1%), fails to 

guide students’ ability to use punctuations (67%), negates students’ 

expressive and organizational skills (76.3%) and impedes teachers’ effort to 

identify areas of learners’ deficiencies in the target language. Conversely, the 

response patterns of 21.6%, 32.8%, 19%, 23.8%, 30.5%, 28.3%, 15.9%, 23%, 

23.7% and 38.1% show the opposite. Therefore, AI technology negates 

university students’ ability to write good academic discourse. 

The Non-descriptive Result 

Pre-test Score 

 

Table 3 shows that there is no significant difference between the academic 

performance of students’ score in the Control and Experimental Groups as the 

calculated t-value of 0.5 is less than the t-critical value of 2.086 for a two-

tailed test at the .05 level of significance for 5 degrees of freedom. Therefore, 

the stated null hypothesis is retained, concluding that the two scores of the 

pre-test of the two groups did not differ. This means that the pre-test scores 

show no significant differences of the academic performance between the two 

groups before their exposure to treatment.  
 

Post-test Scores of the Control and Experimental Groups    

 



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Table 4 shows that there is significant difference between the academic 

performance of students’ scores in the post-test of the Control and 

Experimental Groups as the calculated t- value of 2.43 is greater than the t- 

critical value of 2.080 for a two-tailed test at the .05 level of significance for 

21 degrees of freedom. Therefore, the stated null hypothesis is rejected, 

concluding that the two scores of the post-test of the two groups differed.  

 

Majority of the respondents indicate that the use of AI tools by students 

facilitate increasing concerns on ethical standard, as AI usage inhibits 

originality. This is because students unconsciously replicate styles suggested 

by AI hindering their ability to develop their own unique styles. In addition, 

AI degrades students’ capacity for independent thought and critical analysis. 

Furthermore, issues related to plagiarism and lack of adequate input from the 

students are parts of the ethical consideration indicated by the majority of the 

respondents. 

 

Table 5 shows that there is significant difference between the academic 

performances of the two groups: Control and Experimental Groups in ethical 

consideration, as the calculated t- value of -2.82 exceeds the t- critical value 



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of 1.96 for a two-tailed test at the .05 level of significance for 237 degrees of 

freedom. Therefore, the stated null hypothesis is rejected, indicating that there 

is a significant difference in ethical consideration in the writing of those 

students in the control group and experimental group respectively. 

Discussion on the Findings of the Study 

The findings of the study indicate that students who were taught writing using 

traditional approaches to teaching without the integration of AI tools 

demonstrated better academic performance than those who used AI tools in 

their writing processes. This observation reaffirms concerns expressed by 

many scholars and language teachers regarding students’ overreliance on AI 

writing tools; grammar checkers and automated essay generators as a result of 

their significant negative impact on critical writing skills, particularly, in 

terms of critical thinking and creativity. In addition, findings of the study 

suggest that students who employed AI tools allowed the facilities to dictate 

their writing structures, content, choice of words, grammar and paragraphing, 

which negated their capacity for original thought and proficiency. On the 

other hand, students who were taught based on the traditional approaches, 

without the integration of AI tools, attained a better understanding of the 

various stages of the writing process, while those using AI tools missed vital 

opportunities for comprehensive engagement through the stages, thereby 

undermining their understanding of writing as a complex process. In addition, 

it is evident that AI tools create a detrimental psychological barrier that 

negates students’ abilities to exhibit high levels of critical thinking, creativity, 

originality and aesthetic presentation of ideas. Moreover, findings suggest 

that students who rely on AI tools are engaging in cognitive offloading, which 

negates the effectiveness of their critical thinking abilities and reduce their 

creative capacities. Similarly, students’ dependence on AI tools affects their 

foundational writing skills and capacity to construct coherent discourse, 

thereby undermining their overall writing proficiency. Therefore, the study’s 

findings demonstrate another significant concern: the indiscriminate use of AI 

tools is causing students to develop a superficial understanding of the 

conventional writing processes. Likewise, the reliance on AI-generated 

content leads to decreased engagement and negates originality in students’ 

writing; all these are attributed to the down-to-earth simplicity and 

convenience of such technology-based tools.  

It is also indicated by the findings of the study that the integration of AI tools 

in students’ writing raises several ethical concerns that require careful 

consideration, particularly, regarding academic integrity, authenticity and the 

cultivation of critical thinking skills. The ease with which students generate 

essays using the AI tools can make them to submit work that is not truly their 

own, thereby encouraging plagiarism and compromising the core values of 



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honesty in learning contexts. 

Conclusion and Recommendations 

Based on the findings of the study, it can be concluded that AI writing tools 

offer substantial advantages in areas like grammar correction and content 

creation. But, it is important to recognize their potential negative effects on 

students’ writing capabilities. Excessive dependence on these resources can 

impair understanding of the writing process, reduce involvement in critical 

thinking and impede writing proficiency. Consequently, teachers need to find 

a harmonious approach that combines the use of AI with the cultivation of 

fundamental writing skills through conventional practices. Indeed, a strategic 

incorporation of technology along with a commitment to skill enhancement is 

vital for developing both proficiency and competence in students’ writing 

skills. 

 

References 

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Maidarasu Publishing Company. 

Aljuaid, H. (2024). The impact of Artificial Intelligence tools on academic 

writing instruction in higher education: A systematic review. Arab 

World English Journal (AWEJ). DOI: 

https://dx.doi.org/10.24093/awej/ChatGPT.2  

Basha, Y. J. (2024). The negative impacts of AI tools on students in academic 

and real-life performance. International. Journal of Social Science and 

Commerce (IJSSC), 1(3), 1-16  

Bhutoria, A. (2022). Personalized education and Artificial Intelligence in the 

United States, China, and India: A systematic review using a human-

in-the-loop model. Computers and Education:Artificial 

Intelligence,3100068.https: 

//doi.org/https://doi.org/10.1016/j.caeai.2022. 100068 

Borenstein, J., & Howard, A. (2021). Emerging challenges in AI and the need 

for AI ethics in education. AI and Ethics, 1(1), 61-65 

Hassan, M. (2024). Assessing the Impact of AI-User Generated Content on 

Students’ Project Report Writing. Unpublished material 

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computer-mediated communication on the academic writing of the 

students of tertiary institutions in Kano State, Nigeria. International 



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8-14  

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Darwis, A., & Marzuki. (2023). Exploring artificial intelligence in 

academic essay: Higher education student’s perspective. International 

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https://doi.org/10.1016/j.ijedro.2023.100296  

Pratama, R.M.D. & Hastuti, D. J. (2024). The use of artificial intelligence to 

improve EFL students’ writing skill. English Learning and 

Innovation, 5(1),13-25. https://doi.org/10.22219/englie.v5i1.30212 

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Models in the post-pandemic era: ChatGPT and beyond. Journal of 

University Teaching & Learning Practice, 20(2), 3-16. 

https://doi.org/10.53761/1.20.02.07 

Spack, Q. & Burden, W. S. (2015) Language testing: A pragmatic approach. 

Barker & Barker.  

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Pemanfaatan Chat GPT dalam dunia pendidikan. Jurnal Ilmiah Flash, 

9(1), 25.    https://doi.org/10.32511/flash.v9i1.1069 

Risang, B. F. (2023). Integrating ChatGPT into EFL writing instruction: 

Benefits and challenges. International Journal of Education and 

Learning, 5(1), 44–55.  

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setting. Tamazak Publishers. 

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the academic writing of senior secondary school students in Nasarawa 

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Author Information: Dr. Mudassir Hassan is a lecturer 

in Department of English, Faculty of Humanities, The 

Nigeria Police Academy, Wudil, Kano, Nigeria. Email: 

mudakano1973@gmail.com 

 
 

 

 

 

Dr. Adebayo Abubakar Funsho is a lecturer in 

Department of Linguistics,   Faculty of Humanities, The 

Nigeria Police Academy, Wudil, Kano, Nigeria. 
 

 

 

 

 
 

APA 
 

Hassan, M. & Funsho, A. A. (2025). Exploring the Impact of 

Integrative Artificial Intelligence Tools on the Writing Proficiency 

of University Students in Kano State, Nigeria. Global Online 

Journal of Academic Research (GOJAR), 4(1), 91-104. 

https://klamidas.com/gojar-v4n1-2025-06/. [Google Scholar]  
 

MLA 
 

Hassan, Mudassir and Funsho, Adebayo Abubakar. “Exploring the 

Impact of Integrative Artificial Intelligence Tools on the Writing 

Proficiency of University Students in Kano State, Nigeria”. Global 

Online Journal of Academic Research (GOJAR), vol. 4, no. 1, 2025, 

pp. 91-104. https://klamidas.com/gojar-v4n1-2025-06/. [Google 

Scholar] 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



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Rethinking Motifs in Selected Children’s Literary 

Texts 

 

Blessing Ekpe Okpapi & Prof (Mrs) Enajite Ojaruega 

 

 

 

Abstract 

This study evaluates various motifs in selected children’s literary texts against the 

backdrop of exposing negative and anti-social conducts among children and 

members of the society. It also foregrounds the artistic merit in the use of various 

literary tropes by authors of children’s literature in enhancing their appeal to the 

audience. The primary texts for this study are James Ene Henshaw’s This is our 

Chance and Chinua Achebe’s Chike and the River. They are selected because they 

best exemplify the critical use of motifs in achieving the required message that this 

study is geared towards. The sociological approach to literature which concentrates 

on the extrinsic elements that examine the relationship between literature and society 

is applied to determine the artistic elements and motifs in the selected texts. The 

paper shows that the themes treated in children’s literatures are often those that 

children are concerned with at various stages of their life – such as heroism, 

adventure, risk, mischief, fantasy, love, overcoming restiveness, jealousy and so on. 

The paper, therefore, concludes that since heroism and adventure constitute the 

major fulcrum of Nigerian children’s literature, authors of children’s literature 

should choose a principal character who is going to be the hero or heroine in their 

works. Thus, the development of the story is the development of the hero/heroine 

until the end of the story where he/she overcomes the conflict.  

Keywords: children’s literature, motifs, thematic preoccupations, literary texts 

 

 

Introduction  

Children’s literature, which is often illustrated, consists of all literary 

creations for readers and listeners in their teenage or younger years. It is 

literature meant and intentionally written for children in elementary/primary 

schools as well as those in junior secondary schools to read and understand. 

The children, through their encounter with the texts, get involved with the 

events, setting, actions, intrigues, characters and ideas in the books. In other 

words, children literature offers the young ones the opportunity to explore 



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situations and feelings in literary texts they may have not yet encountered in 

real life.  

       Although critics of children’s literature believe that the characteristics of 

children’s literature are its short length, limited characters, action, 

condensation of plot and incident, linear story-line and simple language style, 

the most important and endearing aspect of children’s literature is its photo 

illustrations. Children’s literature is important because it provides pupils with 

opportunities to respond to literature. It makes them appreciate their own 

cultural heritage as well as those of others. It helps develop emotional 

intelligence and creativity. It nurtures growth and development of their 

personality and social skills; and it transmits important literature and themes 

from one generation to the next.  

       Various forms of children’s literature abound. They range from 

biographies, children’s poetry, children’s stories, fables, fairy tales, fantasy, 

to science fiction, among others. These various forms are well propagated in 

books, VCDs and animated film stations. Since one of the functions of 

children’s literature is to promote morality in children, children’s books 

usually feature well-illustrated pictures relevant to the text to broaden the 

children’s knowledge and sensitize them on current socio-political and 

scientific issues. In this regard, books with themes of greed, dishonesty, 

injustice, hunger, industry and heroism are well illustrated to portray negative 

and positive traits that the children should imbibe or discard. The graphic 

illustrations play a great role in books intended for young readers – texts 

some critics refer to as “Beginner’s Books”, especially when they are written 

for pre-literate children between ages 0-5. These illustrated pictures remain in 

the memory of the children for a long time. According to Lesnik-Oberstein 

(1994, p.6), “even after children attain sufficient levels of literacy to enjoy the 

story without illustrations, they continue to appreciate the occasional 

drawings found in chapter books”.  

       Nigerian children’s literature are fictional narratives that treat various 

themes that revolve around heroism, adventure, bravery as well as others that 

are meant for the edification of the young ones. However, Acholonu (2012, 

p.23) raises concern about the overriding exploitation of the themes of crime 

and violence in some so-called children’s books with the portraiture of young 

children involved in criminal acts. This, to Acholonu, is inappropriate 

because it makes a child or the reader of these texts, relive the harrowing 

experiences that the protagonist goes through. In essence, themes of violence 

and crime in children’s literature should be toned down. To this end, 

Acholonu, in discussing the use of motifs, primarily focuses on language and 

its appropriateness, while recommending positive themes, such as heroism, 

the use of images and various literary devices that enhance the message and 

aesthetic quality of children’s books. 

       Furthermore, while some of the existing scholarship on Nigerian 



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Children’s literature have contributed to the understanding of moral aspects 

of children’s literature, little studies have been done in the area of heroism 

and the artistry inherent in creative works that constitute Nigerian children’s 

literature, which is what this essay sets out to investigate. In order to achieve 

this, the paper focuses on James Ene Henshaw’s This is Our Chance and 

Chinua Achebe’s Chike and the River. The choice of these texts derives from 

the fact that they best exemplify the themes of heroism, bravery, adventure, 

etc. which constitute the pedagogical fulcrum of this paper. 
 

Diverse Themes in Achebe’s Chike and the River and Henshaw’s This is 

our Chance 

Multiple themes are explored in the two texts selected for investigation in this 

essay. They include the themes of heroism/bravery, love, and adventure. 

Other favoured themes are jealousy and hatred. These themes are significant 

because they express the general experience of children in relation to the 

environment and human society. Children’s literature, therefore, comments 

on both the positive and negative aspects of society, with the aim of 

orientating the children to learn from the experiences of persons portrayed in 

the stories.  

       The theme of heroism is a favoured one in the genre of children’s 

literature in Africa. According to Dandatti Abdulkadir (1981, p.31), the term 

‘hero’ in Africa is used to describe “courage and endurance man exhibits in 

his struggle for survival, or in his pursuit of honour”. He states further that 

“these actions involve great risk and are considered heroic by the conventions 

and values of his community”. With specific reference to children’s literature 

which thrives on the children’s quest for adventure, the thematic orientation 

foregrounds elements of valour and bravery. The children in their quest to 

achieve certain goals encounter various ordeals (physical, supernatural and 

metaphysical) which are also reflected in the texts. These themes are utilized 

by writers of children’s literature in ways that make their books interesting. 

       Chinua Achebe’s Chike and the River, for instance, explores the themes 

of heroism/bravery. In the text, Chike, as an 11-year old child, had never left 

his village, Umuofia. Then, one day, his mother told him that he would be 

going to Onitsha to live with his uncle. This gives him a sense of joy as he 

had earlier received from his uncle’s servant, Michael, highlights of the good 

things that he is sure to encounter in Onitsha. “He was tired of living in a 

bush village and wanted to see a big city” (p.1). With this mindset, Chike is 

poised for adventure in this new city. At the point of departure, we find the 

young Chike hesitant to leave home. However, Chike embarks on his 

adventure into the city, where he soon finds out that the city may indeed 

glitter, but it is not all gold. Firstly, the child-hero is exposed to the values of 

the village before embracing the city and all its challenges. But Chike soon 



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makes friends and is forced to mature quickly in an intimidating metropolis 

where all manner of dangers lurks.  

       Rather than destroy his innocent disposition, the events help in propelling 

him towards an intriguing adventure that is set ahead of him. For instance, his 

first challenge which eventually constitutes the conflict in the story revolves 

around his quest to cross the River Niger through ferry to Asaba. This 

ambition made him to pass through various ordeals especially his curiosity to 

survive among his new classmates and friends in Onitsha. His brave quest to 

cross the River Niger to Asaba is to show to his friends that he has achieved a 

feat which in the estimation of his friends is the hallmark of a city boy. As the 

writer puts it, “Anyhow, Chike was happy about one thing. He could now talk 

like the rest of his companions” (p.56). It should be well stated here that 

Chike’s adventure to cross the River Niger constitutes an act of heroism, a 

feat he must achieve in order to be accepted into the fold of his companions. 

   

       During the journey Chike felt as proud as Mungo Park when he 

finally reached the Niger. Here at last was the great River Niger. 

Chike stuck out his chest as though he owned the river, and drew a 

deep breath. The air smelt clean and fresh (p.54).  

As a proud hero, he added this feat to his name as part of his achievement as a 

young boy. The writer says –  

It was all like a dream. Chike wondered whether it was actually 

happening. ‘So this is me’, he thought. ‘Chike Anene, alias Chiks the 

Boy, of Umuofia, Mbaino District, Onitsha Province, Eastern Nigeria, 

Nigeria, West Africa, Africa, World, Universe.’ This was how he 

wrote his name (p.53). 

       Chike’s bravery is also manifested when he exposes the night-watchman 

and the thieves who stole from a shop in the market. Chike is brave despite 

the man’s aggression towards him. He refuses to be cowed in the face of 

intimidation by the night watchman who threatened to harm him should he 

expose him. As a little boy, he is alone in a strange land. His safety is at stake. 

Should anything happen to him, he will be alone at the mercy of fate. But as a 

brave boy, he needs to show that he has fully imbibed all the morals he 

received from his mother – especially the one that says, truth is golden and 

falsehood leads to disgrace. At the end, he becomes a hero in the process of 

the recovery of the stolen goods. This is why Bowra (1952) tells us that 

heroic literature “may be concerned with any action in which a man stakes his 

life on his ideal of what he ought to be” (p.48). Chike stands his ground and is 

able to convince the people that the night-watchman was part of the people 

that stole from the shop. The narrator explains it thus: 

As Chike told his story the night-watchman began to shake. He 



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covered his face with his hands to hide his tears. Chike became a hero. 

One big man in the crowd lifted him up and placed him on his 

shoulders. The others applauded. They said they had never seen such 

bravery from such a little boy… Everywhere people spoke of Chike’s 

adventure. His photograph appeared in the local newspapers and his 

name was mentioned on the radio. Then after the three thieves and the 

night-watchman had been tried and imprisoned Chike got a letter from 

the manager of the shop. He announced that the company which 

owned the shop had decided to award a scholarship to Chike which 

would take him right through secondary school (p.66). 

 Here, Chike’s bravery is recreated as an example for the young reader to 

emulate. Achebe re-imagines this role for the child-hero in a manner that 

Chike’s success will necessarily encourage other young children to stand for 

the truth at all time and emulate him under similar circumstances. The letter 

of commendation and award of scholarship from the manager of the shop is a 

pointer to societal acceptation of his bravery and good deeds. By this, Chike 

becomes a source of inspiration to all young children who aspire to become 

great in life. 

The theme of adventure in Achebe’s Chike and the River provides excitement 

for young readers because they can share in the experiences of Chike who is 

also young. Chike’s journey from his village Umuofia and his ambition to 

cross the River Niger give the text an exhilarating appeal that excites the 

young reader; this is because of the accidental adventure that follows after 

Chike missed the return boat. In his desperation, Chike strays by accident into 

a gang of armed robbers and then he is caught up in the rapidly unfolding 

events. The passage goes thus: 

When the lorry stopped the man at the back climbed out. Chike 

opened his eyes but it was pitch dark. The three men were now talking 

in whispers. Then the driver reversed the lorry. For a while there was 

silence. Chike prayed that the men would move away for even one 

minute so that he could get down and hide. But they did not move. 

Instead, a fourth man came and joined them. From what they said 

Chike understood that this fourth person was the night-watchman. … 

Then he told the driver, whose name was Ignatius, to move out the 

benches from the back of the lorry. Chike was half-dead. He heard the 

man let down the tail-board. But he did not come in. instead he 

returned to the front of the lorry to get a flash light. In the twinkling of 

an eye Chike slipped out and began to walk away. He had no idea 

where he was going. It was too dark to see. But he continued walking 

as quietly as a cat. Unfortunately, his foot kicked against a tin and 

made a noise. The driver shouted: ‘Who dat?’ Chike turned sharply to 

his left and ran. His eyes were now used to the darkness and he could 

see vaguely. He saw something like a door and walked in (p. 61-62) 



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 The above episode underscores the scary nature of the accidental 

adventure that the child-hero goes through in his quest to survive in a strange 

land. The use of suspense and introduction of actions that make the curious 

reader to pray on behalf of Chike that he should not be caught adumbrates the 

artistic significance of the text. However, the child-hero survives the scary 

incidents through a dint of luck and the strength of his character and when the 

situation affords itself for him to display his bravery, he seizes it and becomes 

the hero that exposes the armed gang. This episode of Chike’s adventure thus 

provides the opportunity for revealing his inner strengths and weaknesses. 

Chike therefore comes up at the end of the story wiser than before. 

 What endears Achebe’s Chike and the River to the young reader is that it 

serves as a mirror of life for young children. Chike, the child-hero for 

instance, moves from naïveté and ignorance to self-knowledge and self-

discovery. Life for the young child is like a series of well-planned events all 

geared towards his personal development and growth. But he succeeds 

through determination and constant hard work – in spite of temptations to go 

astray. Chike stuck to the lessons he learnt from home and from his mother. 

He is honest, truthful, courageous, and polite and these are qualities that earn 

him the success at the end of the story. It is significant to note that although 

Chike is attracted by good life, wealth, and material acquisitions, the ultimate 

success that Achebe allows him to achieve is the prize that gives him great 

self-confidence and pride which is the scholarship he wins to go to school to 

receive a good education, the reward for exposing and turning in the 

criminals. This is thus the new imagination that the story encapsulates. 

 Like in Achebe’s Chike and the River, the theme of heroism and bravery 

are also explored in James Ene Henshaw’s This is our Chance. At the 

beginning of the story, we encounter Princess Kudaro at crossroads with the 

customs and traditions of Koloro kingdom. As the plot develops, it becomes 

clear that she is poised to change the rigid system of things placed on the 

people of Koloro by their now anachronistic customs and traditions. The only 

way opened to her is to defiantly elope with the Prince of Udura (an enemy 

kingdom) whom she had met in her school in the city. The Princess is 

conscious of the consequences of her action, but as it is typical with all heroic 

literature where the hero cares less for his/her safety, she runs out of the 

palace to unite with her lover. Her action pits her kingdom against Udura. 

War alarms are sounded and both kingdoms square up for a showdown.  

 As the intrigues continue, Bambula, her private teacher, who is another 

youth, is fingered as the one who radicalised her into taking such a step. 

Bambula is taken to prison, awaiting his death. Also, the Prince of Udura is 



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arrested and imprisoned in Koloro kingdom. However, the conflict is 

amicably resolved when news comes from the kingdom of Udura that the 

princess had performed a heroic act by saving the life of one of the sons of 

Chief Mboli, the king of Udura. Of great significance is the act of bravery and 

heroism displayed by the young lovers in the play. Both Princess Kudaro and 

Prince Ndamu defy the age-long animosity between their kingdoms to get 

married in order to unite the kingdoms.  

 When the young Prince Ndamu is brought before Chief Damba, he 

displays critical features of a hero – fearlessness, composure and wits as 

revealed thus:  

Damba: (walking around him, and examining him disdainfully.) 

Young man, you interest me, I have two questions for you.  

Firstly, are you the young man called Vitamins? Secondly, 

where is my daughter? 

 

Ndamu: (with princely dignity.) My name is Ndamu, Prince of  

the village of Udura. It is true that your daughter and I  

tried to get away. Search parties were after us, one from  

this village and another from my own. I, therefore, tried  

to hide her under a bush, but before I could find a suitable 

hiding-place for myself, I was caught by your men. Oh 

I wish I knew what had happened to her: sweet, kind, 

gentle, obedient Kudaro. Oh…. (p.23). 

 

From the above conversation, the reader is exposed to the fact that King 

Damba’s knowledge is at variance with contemporary realities. He is hooked 

on the past, hence he mistakes Prince Ndamu with the notion of vitamin 

which his daughter’s home teacher had espoused in his several discussions 

with him. However, further interrogation opens a cultural dimension to the 

discourse - elopement is alien to African culture. But in the play, Henshaw 

uses position as tool towards solving identified problems in the society. These 

problems are from all indications still the problems of our time. That is, 

cultural enmity which according to the author must be changed, even if it 

means total disregard for the old and obsolete cultural principles.  

Of significant import is the cultural perspective that the playwright tries to 

advocate with the boldness of Prince Ndamu in defending his attempt to elope 

with the king’s daughter. Herein lies new imagination in the text – 

multiculturalism can make people of diverse cultures to live together as one 

as well as intermarry without any hindrance. This concept is given voice in 

the manner in which the playwright articulates the intrigues in the play where 

the Princess’s life is necessarily hanging in the balance should the king 

continue to defend traditional values against the new imagination which is 



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constitutive of cultural change and assimilation. 

Similar display of bravery and heroism is shown in the action of Ayi, 

Kudaro’s young maid who defies the status of the king and questions the 

place of tradition over humanity. She tells the king bluntly that:  

Ayi: But, Sir, where would principles be without men to observe 

them? And where would men be without human heart beating within 

them? (p.30) 

When it becomes obvious that the elders of Koloro kingdom will not yield to 

the voice of reason, as exemplified by the children, Ayi confesses to the king 

thus:  

Ayi: (interrupting). Damba, Sir, I have lived here with you to learn. 

But all I knew was from your good wife. I beg you, permit me to leave 

this village. Where I will go I do not know. No matter what happens I 

shall always treasure the memory of your wife and her last words – 

“tell Damba, for the children’s sake, for the women’s sake, let there be 

no war…” (p,32). 

The young maid, Ayi, is brave in telling the truth to the leaders of Koloro 

kingdom. To the children, therefore, time has changed and it has come to the 

point when their education has exposed them to the reality of things. They 

can no longer cope with primitive customs and traditions that reduce their 

humanity. In the restoration of the Koloro kingdom from the path of self-

destruction, it is the actions of the children that represent the voice of reason 

and triumph over those of the elders who are brash, divisive and insensitive to 

reality. The elders dwell in the past and make custom and tradition a fortress 

that retards their progress. This is why Betiang believes that Henshaw’s plays, 

written somehow in the Shavian tradition of the problem play, were and are 

an ‘invitation to action’ towards solving these identified problems in the 

society. (p.123). According to Fanon, a writer from a colonized culture who 

writes for his people “ought to use the past with the intention of opening the 

future, as an invitation to action and a basis for hope” (p.187). The children 

become the basis of hope in the society. 

What the author has done with the theme of love in this play is to capture the 

invasion of love bred in the comfort of Western education against the African 

traditional love arrangement. He exposes the battle facing every dare-to-break 

conventional rule in the pursuit of a new culture that encourages humanity 

and freedom of choice.  As he puts it himself in the preface to the play, there 

is “the need to preserve good traditions, and at the same time to graft upon 

them,where appropriate, the best from other countries” (p.5). At the end of 

the play, education and modernity win against tradition and ethnocentrism. 



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For instance, Chief Damba submits to the caprices of the children and accepts 

the fact that modernity has triumphed over mundane sentiments. He says: 

“But is this the price of education that our children should dislike what their 

fathers love, and place high values on what we loathe. Perhaps it is the will of 

our Fathers’ spirits that it must be (p.31). Peter P. Ekeh (1989, p.8-12) 

articulates this phenomenon as a conflict between the demand of the 

‘primordial culture’ and that of the ‘civic culture’.  The primordial culture, 

according to him, is kin-group specific and built around the ‘notional’ and 

‘substantive’ concepts of ethnic groups. This type of culture is pre-colonial 

and based on tribe and carries the tribal ethos and controls. The civic culture, 

on the other hand, is a colonial contact culture which contains social 

formations, ideas, values and institutions that arise from the Nigerian nation 

state. Civic culture is, therefore, Western, modern and urban based. 

The Use of Various Literary Motifs in Achebe’s Chike and the River and 

Henshaw’s This is our Chance 

In the articulation of the themes of heroism/bravery in Henshaw’s This is our 

Chance and Achebe’s Chike and the River, the writers adopt various motifs 

and styles with which they address contemporary issues which constitute 

thematic fulcrum of this essay. These motifs are examined to bring out the 

salient indices of bravery, fantasy, mischief, love, and others in the works. As 

has been noted above, the themes prevalent in many of the children’s 

literature relate to events in the cultural, political and economic milieu of the 

children. The formation of the right characters, narrative techniques, and 

appropriate themes in children’s literature is thus the primary concern of the 

writers of children’s works. 

 In Chike and the River, for instance, Achebe exhibits the same simple 

style that is famous in his adult novels. He shows through the adventures of 

Chike that despite the use of a single character around whom the activities 

revolve he could still deepen our insight and illustrate deeper levels of human 

nature. For example, at the beginning of the novel, the writer presents a vivid 

and graphic description of Chike’s mood when he hears the news of his going 

to Onitsha to stay with his uncle; the author also contrasts the village setting 

with that of Onitsha. The story goes thus: 

 

Chike was now eleven years old, and he had never left his village. 

Then one day his mother told him that he would be going to Onitsha 

in the new year to live with his uncle who was a clerk in one of the 

firms there. At first Chike was full of joy. He was tired of living in a 

bush village and wanted to see a big city. He had heard many 

wonderful stories about Onitsha. His uncle’s servant, Michael, had 

told him that there was a water tap in the very compound where they 

lived. Chike said this was impossible but Michael had sworn to its 



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truth by wetting his first finger on his tongue and pointing it to the 

sky. Chike was too thrilled for words. So he would no longer wake up 

early in the morning to go to the stream. The trouble with their village 

stream was that the way to it was very rough and stony, and 

sometimes children fell and brake their water-pots. In Onitsha Chike 

would be free from all these worries. Also he would live in a house 

with an iron roof instead of his mother’s poor hut of mud and thatch. 

It all sounded so wonderful. (p. 1-2). 

 The narrative above appeals to boys and girls because the author 

manages to localize the story in an identifiable environment through the use 

of familiar activities. This narrative motif endears the story to the young 

children. Besides, the young reader can see the contrasting pictures of the 

rural and urban environments. The former lacks modern amenities, good 

water supply, electricity, and modern infrastructure, but it is safe and serene 

and had the human touch and human face. The urban centre, on the other 

hand, has physical structures and amenities, but life in them is relatively 

unsafe. There are frequent drug abuse and fraud. But the beauty of the work is 

that Achebe is careful to show through the experiences and actions of the 

child-hero in the text that if a child holds on to his or her good upbringing he 

can survive in any environment. 

 Chike and the River is an adventure story. However, the plot revolves 

around Chike’s ambition to cross the River Niger in a boat. It is this desire 

that nearly makes him deviate from his good upbringing as he tries to get 

money through a magician known as Prof. Chardus who swindles him 

thereby depriving him of his three kobo. Chike is so desperate to sail across 

the river that he begs his uncle for some money but the man looked so stern 

that he had to run from him. Nevertheless, his wish is fulfilled when he goes 

to the riverside to wash cars for people and is rewarded with one naira. 

 The adventure takes a different turn when Chike fulfills his ambition and 

he is enamoured by Asaba that he forgets to return to the riverside to catch the 

last boat to Onitsha. The author contrives the story interestingly to include a 

patriotic act by Chike who sleeps in a lorry that is used for robbery. Chike 

helps the police in tracking down the three thieves thereby exposing a thief 

known as Peter Nwana the miserly trader. This final act is the crux of the 

didactic message in the novel. The author uses the message as a motif to teach 

the simple lesson that all good acts are rewarded. By making Chike famous 

through his brave act, the author is encouraging other boys and girls to 

emulate him. This is the didactic aspect of the novel that is invaluable.  

         However, within the story, Achebe also discusses issues relating to the 

moral consciousness of children. He indicates this motif in the novel through 

Chike’s abhorrence to filthy environment. In the house in which Chike lives 

there are two latrines for about fifty people, one for adults and the other for 

children. Both are filthy but the children’s own is worse. It swarms with flies 



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bigger than any Chike had ever seen at Umuofia. They revolt him, and so he 

learns that a big town is not always better than a village. The juxtaposition of 

Onitsha, the town and Umuofia, a village is used to inform the reader that a 

village has certain virtues that can be absent in a town. Achebe is thus 

changing the erroneous concept that a town is filled with only the good things 

of life. 

 In the same manner, the novelist tells the story of Ezekiel, the spoilt 

child, in order to illustrate a different behaviour from that of Chike which 

must be condemned by all good children. This juxtaposition of the two 

characters is important. Ezekiel is an only son but due to over-pampering he 

“was developing into a lawless imp.” (p.15). Ezekiel formulates a plan in 

school through which he writes to some pen-friend boys in England asking 

for money and promising to send them leopard skins. Ezekiel has no plan to 

send them the leopard’s skin because he simply wants their money. His act 

encourages other boys to send similar letters too. The bad boys are punished 

when the headmaster discovers their criminal acts. 

 Most of the activities in this novel are structured to reflect the importance 

of good behaviours. The manner in which Chike fords a river when he travels 

with his mates to convey the luggage of a missionary to Okikpe gives him 

confidence. Achebe uses that incident to stress that most obstacles that seem 

insurmountable could yield to brave confident children. This incident is 

juxtaposed with the incident of some boys who take brain pills to enable them 

pass examinations. These boys lack confidence in themselves and they break 

down before the day of examinations thereby losing even the little knowledge 

they would have been able to produce on the examination day.  

 The most important aspect of Achebe’s didacticism in Chike and the 

River is the illustration that a town possesses several influences that could 

turn a child from his or her good upbringing. He therefore points out some of 

these problem areas thereby aiding the children in understanding what is good 

and also helping parents in ensuring that their children are not influenced by 

bad boys and girls. 

 Furthermore, the various literary motifs used by Achebe in the novel 

make it rewarding for children. There are familiar folksongs, idioms and code 

mixing, humourous anecdotes, games that children play for entertainment and 

amusement, children’s pranks and slangs, children’s fantasies and day-

dreaming, children’s nicknames for each other, and children’s perceptions of 

the adult world, which they discuss among themselves in their peculiar types 

of dialogue. For example, Chike’s classmate, Samuel, who is a good 

footballer gives himself a nick name, S.M.O.G in place of his full name. The 

novelist puts it thus: 

 

S.M.O.G. was Samuel’s nickname which he gave himself. His full 

name was Samuel Maduka Obi: so his initials were S.M.O. Then one 



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day he saw that if he added a ‘G’ to his initials he would become 

S.M.O.G, He immediately did so. In Onitsha the letters S.M.O.G. 

were said to bring good luck because they stood for Save Me O God 

(p. 4). 

 Similarly, Chike is called ‘ChiksThe Boy’ by his peers. When he 

eventually crosses the River Niger, in excitement Chike rills out his full name 

and includes his nickname thus: 

It was all like a dream. Chike wondered whether it was actually 

happening. ‘So this is me,’ he thought. ‘ChikeAnene, alias Chiks the 

Boy, of Umuofia, Mbaino District, Onitsha Province, Eastern Nigeria, 

Nigeria, West Africa, Africa, World, Universe.’ This was how he 

wrote his name (p. 53). 

 The use of idioms, slangs and humourous anecdotes are evident in the 

headmaster’s statement in front of the assembly when he scolded Ezekiel and 

his friends who sent letters to other children in England requesting gifts from 

them. Such idioms and slangs like scallywag and nincompoops were strange 

to the children and they laughed. The event is well captured thus: 

‘That is what these nincompoops here have done to you.’ There was 

laughter again at nincompoops, another strange word (p. 15). 

 Folksongs in the novel are used to express happiness and excitement in 

the children. Chike becomes excited when he makes the money to take the 

ferry boat to Asaba, however, he becomes impatient when the boat seems to 

take long time in coming. He resorts to singing to keep himself happy. This 

interesting scenario is captured by the narrator, thus: 

Chike’s dream had come true; at last he could go to Asaba. He jumped 

up and down several times and sang ‘One more river to cross’. It was 

one of the songs he had learnt at the C.M.S. Central School, Umuofia 

(p. 51). 

 All these literary motifs and aesthetic devices are used to reinforce the 

authenticity of the story and the reality of the children’s world created in the 

text.  

 In This is Our Chance, Henshaw uses the medium of dramatic literature 

to foreground the role of children as a stabilising feature in any society. Here 

the author juxtaposes the modern vision and ideas of the children about the 

ever-changing society against archaic traditional disposition of the adults. The 

children represent modern civilization which they have acquired through 

western education while the adults foreground the tenets of retardation 

dictated by customs and traditions and abhor good neighbourliness. The 

morals that the author passes across to the society is that exposure through 



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education will open society to freedom and progress. 

       Through the characters of the young children: Princess Kudaro, Prince 

Ndamu and Ayi, the reader is brought into the world of the powerful versus 

the weak. With clear and simple words, Henshaw takes the reader through 

children’s travail in the hands of the adults who take pleasure in upholding 

the ancient customs and traditions which are unknown to the children. Here, 

the author pits Ayi who represents those ideals of the children against Damba 

and Ajugo who oppose them. This idea is aesthetically recreated: 

Ayi: How would you like your daughter killed and your dead? 

Damba: Don’t trifle with my wife. 

Ayi: I trifle not, but I must speak my mind. For long I have seen her 

serve and love you as never a woman has. I have seen her organise the 

women of this village in their farms and in their homes. I have seen 

her trying to do everything to make you, and the village, worthy of 

her. And yet as she lies dying, tortured by all that your stubbornness 

has brought to her, you sit here and talk of principles, of Customs and 

Traditions, and listen to the advice of a man who has no feelings at all. 

(looking at AJUGO).(p.30) 

Through clarity of expression, Henshaw projects the nuances of the characters 

in the text. Through the use of language, the text lends itself to the theme of 

oppression. From the beginning of the text to almost the end, the language use 

expresses the tension between the forces of retardation typified by the adults 

and progress represented by the children. The simple but emphatic statement 

by Kudaro that she plans to run away and get married to Ndamu already gives 

the reader and the story a sense of wonder as to what comes next. It brings 

some presence to the text itself. The statement raises many other questions 

and makes the reader interested in paying more attention to the text. As the 

plot develops, the thematic preoccupation continues to be unraveled. 

Throughout this period, the tone of the language is high.  

       The play, therefore, creates a frame to express the oppression of children 

characters. Kudaro, Ayi and other children in Koloro Kingdom who are 

victimized by the insensitivity of adults yearn for freedom. Kudaro expresses 

her inner feelings to Ayi thus: 

 

Kudaro: (lowering her voice). Ayi, my girl, I have a secret for you, it 

is not that I do not like my home, but I have a handsome young man in 

the town where I used to go to school (Then she smiles as she speaks.) 

He promised to marry me. But how can he marry me when I am 

locked up in this village? (She almost weeps.) (p. 12) 

The children are pictured constantly in one form of discomfort. The children 

are not given the carefree and naïve characteristics usually associated with 



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children. Rather, the children are portrayed as emotionally and physically 

strong, though disturbed. Through various literary motifs, the text lends itself 

to an aesthetic ideal.  

Conclusion  

The aim of this essay is to demonstrate that the aesthetic goal of the creators 

of children’s literature is to compose stories that appeal to young adults 

through the themes treated and literary motifs used. The analysis establishes 

the fact that children’s literature thematises issues of heroism, bravery, 

adventure, jealousy and triumphs whose appeal derives essentially from the 

alluring use of various motifs. Thus, the peculiar use of language in the 

selected texts and other literary motifs are artistic tropes used by writers to 

make children’s literature in Nigeria aesthetically appealing to the reader.  

 

References  

Abdulkadir, D. (1981) “Oral Composition: A Historical Appraisal” Oral 

Poetry in Nigeria.Uchegbulam N. Abalogu. et al (eds). Lagos: Nigeria 

Magazine. 

Achebe, C.(1966).Chike and the River. Cambridge: Cambridge University 

Press 

Acholonu, C.O. (2012). “The Female Writer as a Goddess” Nokoko Journal. 

No. p.20-48 

Betiang, Liwhu (2012). “A Critical Survey of Cultural Perspectives in the 

Drama of James Ene Henshaw, 1924-2003” LWATI: A Journal of 

Contemporary Research, 9(1), 120-133.  

Bowra, C.M. (1966). Heroic Poetry. London: Macmillan. 

Ekeh, Peter P. (1989). “The Scope of Culture in Nigeria”. In Peter P. Ekeh 

and Garba Ashiwaju, eds. Nigeria since Independence: The First 25 

Years (Culture). VII. Ibadan: Heinemann,1–17. 

Fanon, Frantz (1981). The Wretched of the Earth. Harmondsworth: Penguin. 

HenshawEne James (1956).This is our Chanceand other Plays. London: 

University of London Press Ltd. 

Lesnik-Oberstein, Karin (1994). Children’s Literature: Criticism and the 

Fictional Child. Oxford: Clarendon Press. 

 



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Author Information: Blessing Ekpe Okpapi is of the 

Department of English and Literary Studies, Delta State 

University, Abraka, Nigeria. Email: blessingekp@gmail. 

com 
 

 

 

 

Prof (Mrs) Enajite Ojaruega is of the Department of 

English and Literary Studies, Delta State University, 

Abraka, Nigeria. Email: ojaruega@delsu.edu.ng 

 

 

 

 

 
 

APA 

 

Okpapi, B. E. & Ojaruega, E. (2025). Rethinking Motifs in Selected 

Children’s Literary Texts. Global Online Journal of Academic 

Research (GOJAR), 4(1), 104-118. https://klamidas.com/gojar-v4n1-

2025-07/.  

 

MLA 

 

Okpapi, Blessing Ekpe and Ojaruega, Enajite. “Rethinking Motifs in 

Selected Children’s Literary Texts”. Global Online Journal of 

Academic Research (GOJAR), vol. 4, no. 1, 2025, pp. 104-118. 

https://klamidas.com/gojar-v4n1-2025-07/.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


