




































In ternationa l
Scholars
Journa ls

 

African Journal of Agricultural Marketing ISSN 2375-1061 Vol. 6 (4), pp. 001-007, April, 2018. Available online at 
www.internationalscholarsjournals.org © International Scholars Journals 

 

Author(s)                                           Author(s) retain the copyright of this article. 
 
 

 

Full Length Research Paper 

 

Application of modified compromise weighted multi-
objective programming in Fadama farming in Dass 

Local Government Area of Bauchi State, Nigeria 

 
Sani, M. H.1*, Kushwaha, S.1, Abubakar, M. M.2 and Ayoola, G. B.3 

 
1
Agricultural Economics and Extension Programme, Abubakar Tafawa Balewa University, Bauchi, Nigeria. 

2
Animal Production Programme, School of Agriculture and Agricultural Technology, Abubakar Tafawa Balewa 

University, Bauchi, Nigeria. 
3
Department of Agricultural Economics, University of Agriculture, Makurdi, Benue State, Nigeria. 

 
Accepted 13 January, 2018 

 
The application of modified compromise weighted multi-objective programming to Fadama farming in Dass Local 
Government Area of Bauchi State was the main focus of the study. Samples of 106 Fadama vegetable cultivars were 
randomly selected from 12 Fadama user’s associations in the study area. The farm sizes were grouped and formed 
into three categories namely: below 1 ha, 1 to 2.99 ha and 3 to 4.99 ha farms, with sample size of 37, 39 and 30 
farmers, respectively. It was assumed that farming could be optimized using four specific objectives (maximization 
of income, and employment; minimization of fertilizer and ground water use). Modified compromise weighted multi-
objective programming technique was used to analyze the four objectives, which were optimized individually and 
combined. The results disclosed that the 3 to 4.99 ha farm size had the best maximum income level of N302,199.26 
(+28.11%) and employment of 1125 man days (+33.61%) and minimum level of fertilizer use of 182 kg (-8.08%) and 
ground water use of 3962 mm (-17.25%) at their respective existing farm levels compared to the other categories of 
farms. This implied that the farmers were characterized by preponderance of high level of adoption of agricultural 
technology, resulting from intensive cropping, leading to a high level of chemical fertilizer and increased use of 
ground water for irrigation which consequently led to reduction of ground water table in the study area. It was 
therefore recommended that the farmers in the study area should concentrate in the cultivation of the major Fadama 
crops like onion, tomato, pepper, okro, cabbage and lettuce instead of spreading out their resources to grow potato, 
carrot and garden-egg. 

 

Key words: Organic farming, irrigation, multi-objective programming, Fadama farming. 

 
INTRODUCTION 

 
In agriculture, several economic activities compete for 
common resources available, resulting in different level of 
returns and employment. The level of various economic 
activities is interdependent in respect to its returns, 
resource requirements and resource availability on the 
farm. The interdependence of decisions concerning the 
level of economic activities require the best suited 
methodology of multi-objective programming, since it has  
 
 
 
*Corresponding author. E-mail:drsanimoh@yahoo.com. Tel:  
+234(0)8069070184. 

 
 
 

 
the advantage of considering more than one farm 
objective simultaneously. The technique can be used to 
determine the level of various economic activities such as 
crop, and livestock that will make the most optimal use of 
land, labour, capital ground water and human resources. 
It is believed that agriculture in the form of settled 
cultivation of land began in Nigeria nearly thirty decades 
ago and because of the diversity of soil and climate, the 
country is endowed with rich flora and fauna. The choice 
of crops grown together was largely based on the 
domestic needs of farmers. During the colonial period, 
the demand of foreign markets influenced cropping 
pattern in Nigeria. 

file:///C:\Users\user\Documents\REPUBLICATION\AGRICULTURAL%20SCIENCES\AppData\Local\Temp\www.internationalscholarsjournals.org


 
 
 

 

Basically, the broad objective of the study was to 
analyze the application of modified compromise weighted 
multi-objective programming in Fadama farming in Dass 
Local Government Area of Bauchi State, Nigeria. The 
specific objectives of the study were to: 

 
1) Determine maximization of income and employment; 
and  
2) Minimization of fertilizer and ground water use over the 
existing farm level in the study area. 

 

Howell (2001) reported that irrigated agriculture is an 
important component of total agriculture worldwide and 
covers a wide range of agricultural products such as 
vegetable, fruits and cereals. The author further stated 
that most agriculture in the Middle East countries rely on 
irrigation, for example, irrigated agriculture in Iraq, Saudi 
Arabia and Iran is expected to account for 92, 82 and 
73%, respectively. The Sub-Saharan Africa is expected to 
use less than 5% of crop land (Calzadilla et al., 2010). 
FAO (2002) also revealed that it is expected that the 
developing countries as a whole, are to increase their 
irrigated land from 202 million ha in 1997 to 1999; to 242 
million ha by 2030.  

According to Douglas (1985), agriculture is the primary 
instrument for feeding the world through a combination of 
more resources and greater efficiency. Agriculture is also 
considered as an ecological phenomenon and an 
institution that impact on the social organization and 
culture of rural life. The Brundtland Report defined 
sustainable farming as a system that meets the demands 
of the peasants without compromising the ability of the 
future generations to meet their own demands. This 
involves eradication of hunger through sustainable food 
security. Edward (1987) defined sustainable agriculture 
as integrated systems, which are less dependent on high 
input of energy and systematic chemicals and more 
dependent on intensive management than conventional 
monoculture systems. These systems maintain an 
increased net income for the farmer, ecologically 
desirable and protective of the environment. It was 
concluded that sustainable agriculture should be able to 
in the long run enhance environmental quality and 
resource base on which agriculture depends, provided for 
basic human food and fibre needs that is economically 
viable and enhance the quality of life for farmers and 
society as a whole.  

In a study conducted by Tahar (2010), it was concluded 
that increasing demand for food production worldwide, in 
regions where water is scarce, the improvement of 
agricultural water production became an urgent need. As 
irrigated agriculture remains virtually important as a 
means of food production, enhancing water use efficiency 
is one of the main approaches to make better use of 
water. Many options to improve water use efficiency in 
Fadama farming are available and the target is to 
produce yield with possible minimum amount of water. 

 
 
 
 

 

The author further opined that in order to assure water 
use efficiency in irrigated agriculture, farmers should be 
able to increase the economic crop production per unit of 
water in water scarce environment. The effective use by 
the crop of a limiting water supply can be achieved by 
manipulating crop penology or by using agronomic 
techniques and farm practices that are sustainable to the 
extent of improving water use efficiency. Spencer (1985) 
explained that the emphasis of sustainable agriculture is 
on design and management procedures that work with 
natural processes to conserve the resources, minimize 
waste and environmental damages, while maintaining or 
improving farm profitability. Sustainable farming system 
also aimed at ensuring the well being of rural 
communities to produce food that are nutritious and 
uncontaminated, that might harm human and livestock 
health (Warren, 1991).  

In the words of Duffy (1990), sustainable agriculture is 
one of many terms used to describe alternative ways to 
evaluate an agricultural production system and other 
terms used are alternative low input and regenerative 
agriculture. The common link in these efforts is the desire 
to find profitable ways to produce environmental 
problems associated with current production practices. 
Sustainable agriculture therefore, is simply using the 
most appropriate agricultural production practices given 
the land, labour, capital and management available to the 
farmer. Lack of sustainability may be indicated by 
declining productivity but equally an experience suggest 
that collapse may occur without warning. Kushwaha et al. 
(1989) emphasized that sustainable agriculture is an 
integrated system of plants and animal production 
practices, having a site-specific applications that will over 
the long term satisfy human feeds, and fibre needs, 
enhance environmental quality and the natural resource, 
based upon which the agricultural economy depends; 
make the most efficient use of non-renewable resources 
and on-farm resources and integrate, where appropriate, 
natural biological cycles and control, sustain the 
economic viability of farm operations, and enhance the 
quality of life for farmers and society as a whole. 
Mamman (1997) opined that the concept of sustainable 
agricultural development embodies a believe that people 
should be able to alter and improve their lives, in 
accordance with criteria which take account of the needs 
of others and which protect the planet and future 
generations. In a way, sustainable agricultural develop-
ment seeks to respond to five broad requirements: 

 

1) Integration of conservation and development; 
2) Satisfaction of basic human needs, 
3) Achievement of equity and social justice,  
4) Provision of social self-determination and cultural 
diversity and, 
5) Maintenance of ecological integrity. 
 

According  to Reganold et al. (1990), an economically 



 
 
 

 

viable farming system, which reduces the use of off-farm 
inputs such as chemicals, produces adequate food of 
high quality and are environmentally safe, could reduce 
production cost and make farm more ecologically sound. 
In this regard, the author further emphasized soil building 
practices, natural pest control, crop and livestock 
diversity. Manos (1991) observed that the farms 
especially those which included livestock enterprises are 
often faced with multi-objectives such as the 
maximization of total costs, minimization of feed costs 
and that such problems can be solved by developing a  
multi-objective programming model which can incorporate 
more than one goal. The aim of this study therefore, is to 
show how multi-objectives can be manipulated in farm 
planning. Kushwaha (1992) pointed out that if two or 
more objective functions generate the same set of 
activities with respect to its optimization through single 
objective linear programming function, then, there are no 
conflicts among the objectives in mind.  

In such a situation, there is no use of multi-objective 
programming. However, conflicting nature of various 
economic activities with respect to farm resources is very 
common. The author concluded that a common set of 
activities, which would optimize the multiple objectives at 
a go, is developed and should be regarded as the most 
optimal. Sankhayan et al. (1988) developed optimum 
cropping plans for a typical farm with multiple objectives 
using combined planning. The limitations of traditional 
linear programming technique are too obvious as a 
decision-maker on a farm firm is seldom, confronted with 
a single objective. But in reality, multi-objectives are a 
rule in farm planning. With the help of multi-objective 
programming approach, the authors had developed ten 
alternative farm plans assigning different weights to the 
objective functions and found that in terms of unit of gross 
margins generated by plans the multi-objective 
programming (MOP) results were very close to existing 
farm plans. However, the cropping pattern in these plans 
is somewhat variant. Ciuchi and Penaechi (1990) 
examined one of the multi-criteria decision making 
methods that can be used for farm management, that is, 
weighted goal programming. After briefly describing the 
methods, some ways in which it can be applied to the 
farm was illustrated, taking into consideration different 
hypothesis about entrepreneurs’ behaviors. The method 
appears useful as regards the possibilities offered to 
overcoming some of the limits of the single-criteria model. 
However, it is unsatisfactory, in that it was necessarily 
used to consider all the objectives.  

Das and Haimes (1979) presented a multi-objective 
planning framework for a River Basin that considered 
both point and non-point source pollutants. The need for 
an integrated approach to pollution abatement originating 
from these two sources was discussed in the light of the 
public law 92 to 500. The need for including multi-
objective functions in non-commensurable formats and 
units were also discussed. Two broad-based planning 

  
  

 
 

 

objectives considered are economic development and 
environmental quality. The environmental quality model 
include, the following multi-objectives: soil erosion, 
phosphorus and biological oxygen demanding load in the 
streams. Non-inferior solution and trade-off among the 
objectives are examined for several alternative-planning 
scenarios using the surrogate worth trade-off (swt) 
method.  

The study recognizes the fact that agriculture is still in 
bad shape in Nigeria in general and the study area in 
particular thereby causing the growth of output to lag 
seriously behind the geometrically population growth and 
the nation that is becoming progressively incapable of 
feeding itself and supplying agro-allied industries the 
needed agricultural raw materials. The study was 
therefore carried out in the study area in view of this 
situation, and considering the interdependent nature of 
various competing farm economic activities which made 
farmers nowadays to maximize farm objectives thereby 
causing uncertainty of net returns, variation in expected 
yields due to random weather changes and the 
unpredictable nature of farm produce prices. 
 

 
MATERIALS AND METHODS 
 
The study area 

 
Keeping in mind the need for sustainable Fadama farming, the 
study was carried out in Dass Local Government Area of Bauchi 
State. The State is located between Latitudes 90° 30’N and 12° 
30’N of the equator and Longitudes 8° 42’E and 11° 50’E of the 
Greenwich Meridian. Dass Local Government Area of Bauchi State 
is one of the paramount regions in the state regarding Fadama 
irrigated crop production. The farmers practiced both rained and dry 
season cropping. Fadama land irrigation in the study area was 
widely practiced and cultivated compared to other regions of the 
state. The Fadama farmers in the study area were mostly small and 
marginal land holdings.  

According to NBS (2006), the study area has a total population 
figure of 280,468 people. It has wet and dry seasons with wet 
season spanning from April to October and dry season 
commencing in November to March. The inhabitants are mostly 
farmers. A sample size of 106 Fadama farmers categorized into 37, 
39 and 30 for farmers operating below 1 ha, 1 to 2.99 ha, and 3 to 
4.99 ha, respectively were selected using multi-strata random 
sampling technique for this study. The data were analyzed using 
Modified Compromise Weighted Multi-objective Programming, 
taking into consideration irrigated crops such as onion, tomato, 
pepper, okro, carrot, cabbage potato and garden-egg. 
 

 
Model specification 

 
The adoption index (Kushwaha and Sani, 1998) of individual farmer 
was developed as follows: 
 

m 
FYMAj 

 
AHj 

 
PAj 

 
FAj 

 
IAj 

 
CAj 

 
 

AI  =  ∑[ + + + + ] X   

      
 

j - 1 FYMRj  CAj  PRj  FRj  IRjGCA 
 

        (1) 
 



 
 
 

 
where, j = 1,2,3...m, and m= total number of major crops; A = 
Adoption index of farmers; FYMAj = Amount of FYM applied per unit 

of area in jth crop; FYMRj = Amount of FYM recommended for 

application per unit of area of jth crop; AHj = Area under HYV of jth 

crop; CAj = Cropped area (HYV + Local) of jth crop; FAj = Amount 

of fertilizer (N+P+K) applied per unit of area of jth crop; FRj = 

Amount of fertilizer recommended per unit of area for jth crop; PAj = 
Amount of pesticide applied as plant protection chemicals 
(weedicide, pesticide, insecticide) per unit of area in jth crop; PRj = 

Amount of pesticide recommended for jth crop; IAj = Number of 

irrigation applied to jth crop; IRj = Number of irrigation 
recommended for jth crop; GCA = Gross cropped area.  

The compromise weighted multi-objective programming approach 
used was expressed mathematically as follows: 

 
 
 

 

 
 

I cmax > 0 ∀ n 

I lm ax > 0  ∀  m 

E M AX > 0 ∀  o 

K M IN >  0  ∀  p 

 
 
 

 
 
 

 

(7) 
 

 

(8) 
 

 

(9) 
 

 
(10) 

  

M A X . I c (x) 
 
where, (11), (12), (13) and (14) revealed the limitation of the 
application. The results from new compromise multi-objective 
programming can then be shown as:  

 

O p tim ize Z (x) = 
 
 

 

 

Subject to: 

 
M A X . I l (x) 
 

M  ax . E (x) 
 

M IN . K (x) 

 
 
 

s
  Ic (x) 

∑ 
<

  Icmax  
(2) 

n=1 Icmax 
 

 

 (11)    
 

 

  ≤       
t
   Il (x)   

 

               

        

∑ <  Ilmax  

         
 

[ aij ] [ x j ] = [bi ] 
    m=1 Ilmax  

(12)           
 

  ≥      (3) 
u
  E(x) < M 

 

         

∑ 
   

   

i = 1, 2, . . . , n 

  E ax 
 

x j ≥   0 ∀ij 
o=1EMax  

(13)             
 

j = 1, 2, . . . , m 
      

 

         
 

        (4) v
  K(x) 

  
 

          K  

Where, n = number of constraints; m = number of decision variable; 
∑ < 

 

    

MIN 
 

k=1KMIN 
 

Ic  = objective function optimum  Gross  Income  for all  crops;  IL  =   
 

objective function of optimum Gross Income for all livestock rearing;  (14)       
 

E = objective function of optimum family labour in man days; K =       
 

objective  function  of  optimum  energy  conservation  in  both  crop Taking the aforestated  into consideration,  the individual  objective 
 

production as well as livestock production in Megajoul (M J); aij  = functions can be specified as thus explained. 
 

matrix of the constraint coefficients; xj  = decision variables vector;       
 

and bi = constraint level vector.           
 

All objectives  in  Equation  2 were optimized  (maximized  and Objective function I (maximization of income)  

minimized) individually and obtained as: 
  

 

        
  

 

MAX. Ic  (x) = Icmax . 

MAX. IL  (x) = ILmax . 
Max. E(x) = MAX 

   E 

MIN. K(x) = KMIN . 

  
n m 

MAX  Z1 = ∑Co Xo  + ∑Cl Xl 

o = 1 l = 1 (15) 

 

where, Z1 =Total annual returns (Income) over variable costs in 

Naira; Co =Annual returns over variable costs per unit of Oth crop  

(5) activity; Xo =Level of Oth crop activity; CL =Annual returns over variable 

costs per unit of Lth livestock activity; Xl = Level of Lth Livestock. 
 

 
s  t  u  v Objective function II (maximization of employment) 

 

MAX. W(x)  =   ∑ I c  (x) 
 + ∑ I l  (x) 

 + ∑ E(x) - ∑ K(x) 
 

  
 

      
 

n = 1  Icmax  m = 1  Ilmax  o = 1 E M ax  p = 1 KMIN n m 
 

           (6) MAX   Z 2    =∑Y o X o +  ∑Y l X l 
 

             
 

 

Subject to the constraint (7) and (8): 
o = 1

 
l = 1

 
(16)

 

The common set of x decision variables was determined from the 
following combined objective functions: 



 
 

 

 

Table 1. Maximization and minimization of the variables over the existing level on sampled farmers operating below 1 ha.  

 

 
Particulars 

Existing Max. of Max. of Min. of Min. of ground Multi-objective 
 

 

level income employment fertilizer use water use programming (MOP) 
 

  
 

 Income (=N) 33,999.57 49,980 (+47.00) 37,060(+9.00) 30,259.62 (-11.00) 30,259.62 (-11.00) 48,960 (+44.00) 
 

 Employment (man days) 389 424 (+9.00) 455 (+16.97) 342.00 (-12.08) 342.00 (-12.08) 447 (+14.19) 
 

 Fertilizer use (kg) 68.73 85 (+23.67) 87 (+26.58) 56 (-18.52) 58 (-15.61) 60 (-12.70) 
 

 Ground water use (mm) 522 930 (+78.16) 910(+74.33) 510 (-2.30) 490 (-6.13) 500 (-4.21) 
 

 

Figures in parentheses shows the percentage of each variable over existing farm level. Source: Updated field survey data, 2009. 
 

 

 

where, Z2 =Total employment in days on different farm sizes, Yo = 

Requirement of labour working days per unit for Oth crop activity,YL 
=Requirement of labour working days per unit of Lth Livestock 

activity, XL= Level of Lth Livestock activity. 
 

 

Objective function III (minimization of fertilizer use) 
 

n 

MIN Z 3 = ∑ F o  X o  

o = 1 (17) 
 

where, Z3 =Total annual requirement of fertilizer in kg, Fo = 

Fertilizer applied per unit of Oth crop activity in kg, Xo = Level of Oth 
crop activity. 

 

 

 

 

 

are  the  maximum  level of income, 
 
employment, the minimum level of fertilizer and ground water use, 
respectively. 
 

From the aforestated, the common objective function to obtain 
the most optimal solution is constructed as: 

 

  k  k  k  k 
 

  ∑C j X j  ∑Y j X j  ∑F j X j  ∑Gj X j 
 

MAX   Z
*
 = 

j = 1 
+ 

j = 1 
- 

j = 1 
- 

j = 1 
 

     

W1 W2 W3 W4 
 

     
 

        (23) 
 

 

 

RESULTS AND DISCUSSION 

 

       Table  1  disclosed  the  results  of  the  level  of  annual 
 

Objective function IV (minimization of ground water use) 
income,  employment,  fertilizer  and ground  water  on 

 

sampled  farmers  operating  below 1  ha.  The  result         
 

 n      indicated  that  conflicts  exist  among objectives,  that  is, 
 

         

MIN   Z 4     = ∑Go X o 
    optimization of one objective has negative effect on the 

 

    
rest  objectives.  If  the  annual  income  and  employment  

 
o = 1 

   
(18)  

    
was maximized alone one by one, the increment in the  

       
 

where,  Z4   =Total  requirement  of  ground  water  annually,  Go income  was found  to  be  47.00%  over  existing  level  of 
 

income. But the employment, fertilizer, and ground water 
 

=Requirement  of  ground water  per  unit  of Oth crop activity, Xo  = 
 

Level of Oth crop activity.     use has to be increased by 9.00, 23.67 and 78.16% over 
 

From   the   earlier   stated   four   objectives   of   income   and existing level, respectively. The minimization of fertilizer 
 

employment maximization and minimization of fertilizer and ground use  envisaged decline in fertilizer use  by 18.52%  over  

water use, the single objective linear programming could be derived  

existing  level.  Income  and  employment  level  has  also  

as:       
 

      

increased  by  11.00  and  12.08%  over  existing  level, 
 

       
 

  k     respectively. Similarly, the minimization of ground water 
 

M AX .  Z 1 = ∑C j X j  =   W 1 use  indicated  the  decline  in  the  ground  water  use  by 
 

  j = 1    
(19) 

4.21%, while the fertilizer use and income have declined 
 

     

by  11.00  and  15.16%  over  existing  level,  respectively. 
 

      
 

       
 

  
k     This result implies that income and employment cannot 

 

      

be  increased  more  than  47.00  and  9.00%  over  the 
 

MAX .  Z 2 = ∑Y j X 
2
 

  

= W 2 
 

j  existing  level,  respectively.  The  fertilizer  and  ground 
 

  j = 1    
(20) water  use  cannot  be  increased  more  than  18.52  and  

      
 

  k     6.13%  respectively  over  the  existing  level.  Kushwaha 
 

      

(1992) confirmed this when he emphasized that because 
 

M IN .  Z 3 = ∑F j X 
3
 
 

= W 3 
 

j of the conflicting nature of several objectives, the multi- 
 

  j = 1    (21) objective  programming  technique  was  modified  in  the  

      
 

  
k 

    form  of  compromise  weighted  multi-objective  program- 
 

      

ming  technique.  David  et  al.  (2009)  also  agreed  with 
 

M IN .  Z 4 = ∑G j X 
4
 

 

= W 4 
 

j these  findings  stating  that  even  though  small-scale 
 

  j =  1    (22) vegetable Fadama agriculture is  profitable,  farmers  can 
 

where  W 1,  W2,  W3,  and  W4 



 
 
 

 
Table 2. Maximization and minimization of the variables over the existing level on sampled farmers operating on 2 to 3.99 ha.   
 
 

Particulars 
Existing Max. of Max. of Min. of Min. of ground Multi-objective 

 

 

level income employment fertilizer use water use programming (MOP)  

  
 

 Income (=N) 73,437.97 113,829(+55) 82,985 (+13) 85922 (+17) 88,860(+21) 109,723(+49) 
 

 Employment (man days) 995 1106 (+11) 1204 (+21) 1134 (+14) 1119(+13) 1184 (+19) 
 

 Fertilizer use (kg) 104.35 132.52 (+27) 96.00 (-8) 87.65(-16) 92.87 (-11) 91.25 (-12.5) 
 

 Ground water use(mm) 2106 1993 (-5.36) 1903(-9.73) 1569(-25.48) 1407 (-33.19) 1481 (-29.67) 
 

 
Figures in parentheses shows the percentage of each variable over existing farm level. Source: Updated field survey data, 2009. 
 
 

 
Table 3. Maximization and minimization of the variables over the existing level on sampled farmers operating 3 to 4.99 ha.   

 

Particulars 
Existing Max. of Max. of Min. of fertilizer Min. of ground Multi-objective 

 

level income employment use water use programming (MOP) 
 

 
 

Income (N) 235,890.45 310,125.18(+32.0) 298,849.61 (+26.69) 208,692.27 (-11.53)200,789.96 (-14.88) 302,199.26(+28.11) 
 

Employment (Man days) 842 1108(+31.59) 1153 (+36.94) 752 (-10.69) 712 (-15.44) 1125 (+33.61) 
 

Fertilizer Use (kg) 19.8 213(+7.58) 221 (+11.62) 179 (-9.60) 186 (-6.06) 182 (-8.08) 
 

Ground Water use (mm) 4788 5228(+9.19) 4557 (-4.82) 4240 (-11.45) 3851 (-19.57) 3962 (-17.25) 
 

 
Figures in parentheses shows the percentage of each variable over existing farm level. Source: Updated field survey data, 2009. 

 
 

 

obtain high profit through rational resource inputs 
adjustment and re-allocation. Table 2 shows the 
maximization of income, employment and fertilizer and 
ground water use of sampled farmers in the study area 
operating on 1 to 2.99 ha. It reveals again that conflict 
existed between income and employment, income and 
fertilizer use, income and ground water use.  

However, the compromise solution obtained through 
optimization of combined objective functions reveals that 
income has increased by 49.00% which is less than its 
individual optimization level, that is 55.00% but definitely 
higher than its levels and the rest of the three objectives. 
The employment has increased by 19.00%. This is less 
than individual optimization, that is, 21.00%; the amount 
of fertilizer use annually declined by 12.50% which is 
higher than its individual minimization rate (16.00%) but 
certainly lesser than its declining rate under the rest three 
objectives. Similarly, the amount of ground water use has 
decreased by 29.27% which is larger than its individual 
minimization rate (33.19%) but certainly lesser than its 
increasing rate under maximization of income and 
employment objective and lesser than declining rate 
under minimization of fertilizer use by multi-objective. 
These results disagreed with Ani (1999) revealing that 
despite various agricultural programmes such as 
Community Based-Agricultural and Rural Development 
Projects (CBARDP), National Programme for Food 
Security (NPFS), Operation Feed the Nation (OFN) and 
Green Revolution (GR), rural home household uses farm 
resources generally below the profit maximization level 
because of their low capital base signifying that there is 
the need for resource adjustment by farmers in order to 

 
 
 

 

obtain maximum profit.  
Table 3 revealed the level of income, employment and 

fertilizer and ground water use of sampled farmers 
operating on 3 to 4.99 ha farm size. The result indicated 
that income alone was maximized by 32.00% while 
employment, fertilizer and ground water use by 31.75, 
7.58 and 9.19%, respectively, over the existing level. The 
maximization of employment alone shows the increase in 
employment by 36.91%. Ndanitsa et al. (2010) confirmed 
this, recommending that since the gross margin of 
vegetable production was higher and profitable, 
especially for tomato enterprise, its production should be 
intensified by smallholder farmers and school leavers 
should be encouraged and motivated into it, especially 
now that the ‘white collar jobs’ are almost becoming 
extinct in the Nigerian labour market. On the other hand, 
income and fertilizer use increased by 26.69 and 11.62%, 
respectively, while the use of ground water decreased by 
4.82% over the existing level. The minimization of 
fertilizer use has declined the fertilizer use by 6.06% 
income, and employment levels and ground water use 
also decreased by 11.53, 10.72 and 11.45%, respectively 
over the existing level. Similarly, the minimization of 
ground water use has declined by 19.57%, income, 
employment and fertilizer use by 14.88, 15.46 and 6.06%, 
respectively over the existing level. The findings of this 
result indicate a significant level of conflicts among all the 
four objectives. These disclosures are in line with Tahar 
(2010) that irrigated agriculture remains virtually 
important as a means of food production, enhancing 
water use efficiency is one of the main approaches to 
make better use of water. 



 
 
 

 

CONCLUSION AND POLICY IMPLICATIONS 

 

From the study, it was realized that conflicts existed 
among the four specific objective functions. Therefore, 
the solution obtained through the multi-objective 
programming technique was selected as the best 
compromising optimal solution for sustainable Fadama 
farming. As a result of the conflicting nature of several 
objectives, the multi-objective technique was modified in 
the form of compromise weighted multi-objective 
programming technique, to generate the best fit 
compromise optimal solution for decision making to 
obtain alternate sustainable Fadama farming. The 
technique is therefore, free from subjective weights as 
well as multi-dimensional aggregation. It was therefore 
recommended that these categories of farmers should 
have multiple farm objectives in order to complement 
each other and improve the farming operations and well 
being of the farmer and the study area in general. 
 

 
REFERENCES 
 
Ani AO (1999). Analysis of the Performance of Rural Farmers in the 

Fadama Users Association (FUA) Programme in the Northern Zone 
of Bauchi State. Nig. J. Trop. Agric., 1: 36-40.  

Calzadilla A, Rehdanz RS, Tol J (2010). The economic impact of more 
sustainable water use in agriculture: A computable general 
equilibrium analysis. J. Hydrol., 384: 292-305.  

Ciuchi P, Pennaechi F (1990). A farm planning problem with multiple 
objectives. Rivista Di Economia Agraria, 45(2): 295-332.  

Douglas GK (1985). When is agriculture sustainable? Sustainable 
Integrated Farming Systems, East Lansing, Michigan State University 
Press, p. 368.  

David HD, Abdulrrahman S, Sani RM, Kushwaha S, Nasiru M (2009). 
Resource Use Efficiency in Irrigated Crop Production by Fadama 
Users in Bauchi State, Nigeria: Implication for Food Security and 
Poverty Alleviation. In: Sustainable Agricultural Growth to Meet 
National Economic Development Goal edited by I. Muhammed, U. B. 
Kyiogwom, W . A. Hassan, A. L. Ala, A. Singh and S. D. Dogondaji. 

Proceedings of the 23
rd

 Annual Conference of the Farm Management 
Association of Nigeria (FAMAN) at Usmanu Danfodiyo University, 

Faculty of Agriculture, Sokoto, Sokoto State, Nigeria, 14
th

 – 17
th

 
December.  

Das P, Haimes YY (1979). Multi-objective optimization in water quality 
and land management. Water Resour. Res., 15(6): 1313-1322.  

Duffy M (1990). Economic consideration in sustainable agriculture for a 
Mid Western Farmer. Report of Rodale Conservation Project 
(Kutztown), pp. 1-32.  

Edward CA (1987). The concept of integrated systems in low input 
sustainable agriculture. Am. J. Altern. Agric., 2(4): 148-152.  

FAO  –  Food  and  Agricultural Organization (2002). World  Agriculture: 
Towards 2015/2030. Summary Report, Rome. 

  
 
 
 

 
Howell TA (2001). Enhancing water use efficiency in irrigated 

agriculture. Agron. J., 93: 281-289.  
Kushwaha S, Sen C, Gupta SBL (1989). A farming without conventional 

energy. A paper from periodicals of international conference on 
information and systems, Zhejiang University, China, pp. 1451-1454.  

kushwaha S (1992). Sustainable economic agriculture. Kisan World, 
19(6): 14. 

Kushwaha S, Sani MH (1998). Socio-economic analysis of adoption 
efficiency: Case study of Dass Local Government Area of Bauchi 
State, Nigeria. Kano J. Arts Soc. Sci. (KAJASS), 1(1): 1-5.  

Mamman M (1997). Making development work for people, New 
Nigerian Newspaper, Friday October 10, p. 18.  

Manos BD (1991). Farm planning with multi-objectives: An Application 
of Compromise Programming in Greece. Agric. Mediterr., 121(3): 
223-238.  

NBS (2008). National Bureau of Statistics of Nigeria. Annual Abstract of 
Statistics, p. 22.  

Ndanitsa MA, Omotesho OA, Adewumi MO, Umar IS, Olaleye RS, 
Mohammed US, Sadiqs RK, Abubakar SB (2010). Cost-Returns 
Analysis of Vegetable Production (Tomato Enterprise) in Mokwa 
Local Government Area of Niger State, Nigeria. In: Commercial 
Agriculture, Banking Reform and Economic Downturn: Setting a New 
Agenda for Agricultural Development in Nigeria edited by J. N. 
Nmadu, M. A. Ojo, U. S. Mohammed, K. M. Baba, F. D. Ibrahim and 

E. S. Yisa. Proceedings of 11
th

 Annual National Conference of 
National Association of Agricultural Economists (NAAE), held at New 
Lecture Theatre, School of Agriculture and Agricultural Technology, 

Federal University of Technology, Gidan Kwano, Minna, 30
th

 

November – 3
rd

 December.  
Reganold JP, Robert IP, Parr JF (1990). Sustainable agriculture in the 

USA: An overview. In: Sustainable Agricultural Resource 
Management edited by S. H. Anderson, S.B.L. Gupta and S. Sen. 
Proceedings of the International symposium on Natural Resource 
Management for Sustainable Agriculture held at the International 
Agricultural Research Centers (ICRISAT), India, 11-12 December, 
444-456.  

Spencer DSC (1985). A research strategy to develop appropriate 
agricultural technologies for small farm development in Sub- Saharan 
Africa. Appropriate technologies for farmers in semi-arid West Africa. 
West Lafeyette in Purdue University, p. 401.  

Sankhayan S, Rao MSRM, Chettarajan S (1992). Impact and Constraint 
analysis of Watershed resource conservation cum production 
management in Alfisols of Karnataka. Agricultural Situation in India, 
46(11): 799-806.  

Taha B (2010). Improvement of Water Use Efficiency in Irrigated 
Agriculture: A Review. J. Agron., 9(1): 1-8.  

Warren DM (1991). Indigenous knowledge for agricultural and rural 
development, West African farming systems. Oxford University, 
Press, p. 236. 

WCED - World Commission on Environment and Development, (1987). 
Our common future: the Brundtland Report, Oxford University Press, 
Oxford, England. 


