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© 2021 by the authors; licensee Asian Online Journal Publishing Group 
  

Asian Review of Environmental and Earth Sciences 
Vol. 8, No. 1, 10-17, 2021 

ISSN(E) 2313-8173 / ISSN(P) 2518-0134 
DOI: 10.20448/journal.506.2021.81.10.17 

© 2021 by the authors; licensee Asian Online Journal Publishing Group 

  
 

 

 
 
 
Analytic Hierarchy Process–Based Environmental Criteria Weight Assessment and 
Prioritization for Suitable Petroleum Refining Plant siting in Edo State, Nigeria  

 
Aweh D.S.1 
Igbokwe J. I.2 

Ejikeme, J.O.3  
( Corresponding Author)  

 
1Department of Surveying and Geoinformatics, Nnamdi Azikiwe University, Awka, Nigeria & Department of 
Surveying and Geoinformatics, Auchi Polytechnic, Auchi, Nigeria. 

 
2,3Department of Surveying and Geoinformatics, Nnamdi Azikiwe University, Awka, Nigeria. 

 
Abstract 

In this paper, Saaty’s Analytical Hierarchy Process (AHP) of Multi-Criteria Evaluation (MCE) 
technique was used to estimate the weights of some selected environmental criteria in the suitable 
siting of a Petroleum refining Plant. In doing this, fifteen (15) key environmental criteria, based 
on reviewed literature, specifications, and Environmental Impact Assessment Act (EIA) on the 
siting of petroleum refining plants were selected for this study, which includes Ground Water 
level, Proximity to major settlement, Proximity to Water bodies, Proximity to the Electricity 
transmission line, Land use / Land cover, Topography, Sensitive and Protected Areas proximity, 
Critically Polluted Areas (refuse dumpsites, landfill sites, etc.), Proximity to Existing Industrial 
areas, Major Transportation network, Flood zones, Proximity to crude oil supply (oil well), Wind 
speed, Large-scale Mines and Population density. The result from the calculated environmental 
criteria weights show proximities of Petroleum refinery to existing industrial areas; source of 
crude oil and Landuse/Landcover to have the highest influence value, followed by proximity to 
Water Body; Population Density; Groundwater Level; Major Settlement; Wind Speed; 
Transportation Network, Topography, while Sensitive/Protected Areas, Critically Polluted areas 
and Flood zones with the least influence value. The result of this AHP – based weight assessment 
will be used generally by Planners, Investors, Environmental Managers, and Oil and Gas experts 
as a general guide in the prioritization of criteria weights based on the influence of one criterion 
over the other in the suitability siting of petroleum refining plant. 

 
Keywords: Criteria weight, Site selection, AHP-BASED MCE, Petroleum refinery, Edo State. 

 
Citation | Aweh D.S., Igbokwe J. I., Ejikeme, J.O. (2021). Analytic 
Hierarchy Process–Based Environmental Criteria Weight 
Assessment and Prioritization for Suitable Petroleum Refining Plant 
siting in Edo State, Nigeria. Asian Review of Environmental and 
Earth Sciences, 8(1): 10-17. 
History:  
Received: 22 January 2021 
Revised: 26 February 2021 
Accepted: 18 March 2021 
Published: 20 April 2021 
Licensed: This work is licensed under a Creative Commons 

Attribution 3.0 License  
Publisher:  Asian Online Journal Publishing Group 
 

Acknowledgement: All authors contributed to the conception and design of 
the study. 
Funding: This study received no specific financial support. 
Competing Interests: The authors declare that they have no conflict of 
interests. 
Transparency: The authors confirm that the manuscript is an honest, 
accurate, and transparent account of the study was reported; that no vital 
features of the study have been omitted; and that any discrepancies from the 
study as planned have been explained. 
Ethical: This study follows all ethical practices during writing.   

 

 

Contents 
1. Introduction ...................................................................................................................................................................................... 11 
2. Materials and Methods ................................................................................................................................................................... 11 
3. Result and Analysis .......................................................................................................................................................................... 16 
4. Conclusion ......................................................................................................................................................................................... 17 
References .............................................................................................................................................................................................. 17 
 

 
 
 

 

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Contribution of this paper to the literature 
In this paper, Saaty’s Analytical Hierarchy Process (AHP) of Multi-Criteria Evaluation (MCE) technique 
was used to estimate the weights of some selected environmental criteria in the suitable siting of a 
Petroleum refining Plant. 

 
1. Introduction 

The petroleum industry provides most of the needed fuel for everyday use for industrial, commercial, and 
domestic purposes. In fact, modern industrial civilization depends on petroleum and its products; the physical 
structure and way of life of the suburban communities that surround the great cities are the result of an ample and 
inexpensive supply of petroleum [1, 2]. In addition, the goals of developing countries - to exploit their natural 
resources and to supply foodstuffs for the burgeoning populations are based on the assumption of petroleum 
availability. Most of the world’s supply of petroleum comes from the Middle East, Nigeria, Angola, Libya, etc. [3-
6]. Despite this monumental projected importance of modular petroleum plants in remedying unemployment and 
economic issues, the adverse impact of these modular refineries on their immediate environment and beyond cannot 
be underemphasized. Therefore, stakeholders should be fully aware of these implications and should take necessary 
steps while setting up industries so as to minimize the possible adverse effects on environmental resources and 
quality of life, through careful selection and assessment of identified criteria [7]. 

The identification of a suitable site for Industrial Development is one of the critical issues in the process of 
planning, starting, expanding, or changing the location of industrial systems of all kinds [8]. One of the main 
objectives in industrial site selection is finding the most appropriate site with desired conditions defined by the 
selected criteria. In a site selection process, the analyst strives to determine the optimum location that would 
satisfy specified conditions which is a direct determinant of the influence level (weight) of the selected criteria. The 
most frequently raised problem in MCE is how to establish weights for a set of activities according to importance 
Mohamed, et al. [9]. Saaty [10] has shown that this weighting of activities in MCE can be dealt with using a 
theory of measurement in a hierarchical structure. The analytic hierarchy process (AHP) is a comprehensive, 
logical, and structural framework, which allows improving the understanding of complex decisions by 
decomposing the problem in a hierarchical structure. The incorporation of all relevant decision criteria and their 
pairwise comparison allows the decision-maker to determine the trade-offs among objectives. Such multi-criteria 
decision problems are typical for industrial site selection. 

The AHP allows decision-makers to model a complex problem in a hierarchical structure showing the 
relationship of the goal, objectives (criteria), sub-objectives, and alternatives [9]. Uncertainties and other 
influencing factors can also be included. It does not only supports decision makers by enabling them to structure 
complexity and exercise judgment, but also allows them to incorporate both objective and subjective considerations 
in the decision process [10]. 
 

2. Materials and Methods 
2.1. Study Area 

The area selected for this study, Edo state is in the South-South geopolitical zones of Nigeria. Edo is a state in 
southern Nigeria. It was created on 27th August 1991 when the former Bendel State (now Edo and Delta) was 
separated into these two states. Edo state is located between latitudes 7°18'8.61"N to 5°52'48.77"N of the equator 
and longitudes 6°36'59.29"E to 5°12'58.38"E of the Greenwich meridian, with a surface area of approximately 
19,603 km2. Its capital is Benin City. With a population of 3,218,332 million people (2006 Census). It is bounded in 
the north and east by Kogi State, in the south by Delta State, and in the west by Ondo State. Economically, Edo 
state is more of a commercial and agricultural driven state. The majority of its population are either farmers or 
traders. There are various solid mineral deposits within the state such as; industrial clay, silica, lignite, kaolin, tar 
sand, decorative rocks, limestone, etc. still waiting to be properly used to their full potential. Edo state also has 
deposits of crude oil and this makes it one of the petroleum-producing states in Nigeria. Figure 1, is the Map of 
Nigeria showing the study area (Edo state) and the satellite image of Edo state. 
 

2.2. Research Instrument 
A total of one hundred (100) experts which consist of Planners, Oil and Gas Engineers, and 

Geomaticians/Environmentalists within Edo state were proposed via a simple random sampling system. However, 
since the population is finite, it becomes imperative to apply a statistical model in determining the sample size. 
Thus, Yamane [11] formula was employed, at an acceptable level of probability of whose confidence level is set at 
0.05 as displayed in Equation 1. 
Thus; 

n = 
𝑁

1+𝑁(𝑒)2           (1) 

Where; 
n = Sample size 
e = level of significance (e = 0.05) 
N = Population size (N= 100) 
1 = Constant 
Applying the above formula, population size was computed as follows: 

n = 
100

1+100 (0.05)2
 

n = 
100

1+100 (0.0025)
= 

100

1.25
  = 80 

 

 
 



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2.3. Selection of Criteria  
Based on reviewed pieces of literature and guidelines from relevant authorities, in this case, Department of 

Petroleum Resources, Nigerian National Petroleum Company, and Environmental Impact Assessment Act (EIA) 
on the siting of petroleum refining plants, the following fifteen (15) criteria (factors/constraints) were identified 
and considered in this research. Table 1 shows the criteria (factors/constraints) and the applied codes.     
 

 

 
Figure-1. Map of Nigeria showing the study area (Edo state) and the satellite image of Edo State. 

 



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Table-1. Criteria (factors / constraints) and Codes Used. 

S/n Criterion ( Input) Factors/ Constraints  Code 

1 Water bodies proximity  Factor MWB 
2 Electricity transmission line proximity Factor ETL 
3 Land use / Land cover Factor LULC 
4 Topography Factor TOPO 
5 Sensitive and protected areas proximity Constraint  SPA 
6 Critically Polluted areas (refuse dump sites, landfill sites etc.) Constraint CPA 

7 Proximity to Existing Industrial areas Factor EIA 
8 Transportation network Factor MTN 
9 Flood zones Constraint  FZ 
10 Raw material supply (Crude oil) Factor  SRM 
11 Wind speed Factor WS 
12 Large-scale Mines  Constraint  LSM 
13 Population density  Factor PD 
14 Proximity to major settlement Constraint MS 
15 Ground Water level Constraint GWL 

 
2.4. Pairwise Comparisons 

The pairwise comparisons method was developed by Saaty [10] in the context of the Analytical Hierarchy 
Process (AHP). This method of criteria weight assessment involves pairwise comparisons to create a ratio matrix. 
As input, it takes the pairwise comparisons of the parameters in numerical form (i.e. on a scale of 1 to 9) and 
produces their relative weights as output. One (1) on the scale means that the two factors are equally important and 
9 means that the one factor is absolutely more important than the other as shown in Table 2. If a factor is less 
important than another then this is indicated by reciprocals of the 1 to 9 values (i.e.1/2 to 1/9). 
 

Table-2.  Preferences made on 1-9 Scale. 

Numeric Rating (Judgment value) AHP Scale of Importance for comparison pair  

9 Extreme importance  

8 Very strong to extremely  
7 Very strong importance  
6 Strongly to very strong  
5 Strong importance  
4 Moderately to strong  
3 Moderate importance  
2 Equally to moderately  
1 Equal importance  

 Source: Saaty [10]. 

 

2.4.1. Pairwise Comparison Matrix Formation 
The pairwise matrix (Table 3) was formed using the judgment value of comparison as the matrix elements and 

following the basic formation rules as established by Saaty [10] and Mohamed, et al. [9]. For example, the 
judgment value of MWB (LHS) against ETL (RHS) is “6”, therefore, the matrix element in a cell, second roll, the 
third column (2, 3) is “6”; the judgment value of FZ (LHS) against TOPO (RHS) is “3” therefore, the matrix 
element in a cell, tenth roll, fifth column (10, 5) is “3”; (i.e. 1/3), etc. 
 

Table-3. Pair-wise comparison matrix of the study. 

 MWB ETL LULC TOPO SPA CPA EIA MTN FZ SRM WS LSM PD MS GWL 

MWB 1.00 6.00 0.25 3.00 7.00 5.00 0.25 5.00 7.00 0.33 4.00 6.00 1.00 4.00 1.00 
ETL 0.17 1.00 0.11 0.33 1.00 2.00 0.11 0.50 2.00 0.11 0.33 1.00 0.17 0.50 0.17 

LULC 4.00 9.00 1.00 6.00 9.00 8.00 1.00 7.00 9.00 1.00 6.00 8.00 3.00 7.00 3.00 
TOPO 0.33 3.00 0.17 1.00 3.00 2.00 0.17 1.00 3.00 0.17 1.00 3.00 0.33 2.00 0.33 
SPA 0.14 1.00 0.11 0.33 1.00 1.00 0.11 0.25 1.00 0.11 0.25 1.00 0.17 0.50 0.17 
CPA 0.20 0.50 0.13 0.50 1.00 1.00 0.11 0.33 1.00 0.11 0.33 1.00 0.20 0.33 0.20 
EIA 4.00 9.00 1.00 6.00 9.00 9.00 1.00 6.00 9.00 1.00 6.00 9.00 4.00 6.00 4.00 

MTN 0.20 2.00 0.14 1.00 4.00 3.00 0.17 1.00 3.00 0.17 1.00 3.00 0.50 1.00 0.50 
FZ 0.14 0.50 0.11 0.33 1.00 1.00 0.11 0.33 1.00 0.11 0.25 1.00 0.20 0.33 0.20 

SRM 3.00 9.00 1.00 6.00 9.00 9.00 1.00 6.00 9.00 1.00 5.00 9.00 4.00 6.00 4.00 
WS 0.25 3.00 0.17 1.00 4.00 3.00 0.17 1.00 4.00 0.20 1.00 4.00 0.50 1.00 1.00 

LSM 0.17 1.00 0.13 0.33 1.00 1.00 0.11 0.33 1.00 0.11 0.25 1.00 0.17 0.25 0.25 
PD 1.00 6.00 0.33 3.00 6.00 5.00 0.25 2.00 5.00 0.25 2.00 6.00 1.00 2.00 2.00 
MS 0.25 2.00 0.14 0.50 2.00 3.00 0.17 1.00 3.00 0.17 1.00 4.00 0.50 1.00 1.00 

GWL 1.00 6.00 0.33 3.00 6.00 5.00 0.25 2.00 5.00 0.25 1.00 4.00 0.50 1.00 1.00 
Total 15.85 59.00 5.12 32.33 64.00 58.00 4.97 33.75 63.00 5.09 29.42 61.00 16.23 32.92 18.82 

Basic Rule: If the criterion in the column is preferred to the criteria in the row, then, the inverse of the judgment value is given, otherwise, the actual 
judgment value. 
Note: The numbers represent expert judgment values of the importance of one factors in relation to other factors in the suitable siting of a modular 
refinery. 

 

2.5. Demonstration of Satty’s Ranking Scale for Judgment Values  

 



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By this judgment value, it means that siting the refinery in close proximity to major water bodies (MWB) is 
strongly important than its proximity to electricity transmission line (ELT). 

 
By this judgment value, it means that topography (slope) is moderately important than proximity to flood zone 
(FZ). 

 
By this judgment value, Population density is slightly more important than Major Settlement. 
 

2.6. Computation of the Criterion Weights  
This involves the following operations;  

(a) Formation of normalized pairwise comparison matrix. 
(b) Formation of the prioritization weight matrix. 
 

2.6.1. Normalized Pairwise Comparison Matrix Formation 
The normalized pairwise comparison matrix was formed from the Pairwise Comparison Matrix in Table 4. 

Here, the elements of the normalized matrix were formed by dividing the elements of each column by their sum 
total. For instance, the first element of the first column of the normalized matrix is computed thus; 1/15.85 = 0.06. 
Where 1 is the first element of the first column of the pairwise comparison matrix and 15.85 is the sum total of its 
column. 
 

Table-4. Normalized pairwise comparison matrix.  
MWB ETL LULC TOPO SPA CPA EIA MTN FZ SRM WS LSM PD MS GWL 

MWB 0.06 0.10 0.05 0.09 0.11 0.09 0.05 0.15 0.11 0.07 0.14 0.10 0.06 0.12 0.05 
ETL 0.01 0.02 0.02 0.01 0.02 0.03 0.02 0.01 0.03 0.02 0.01 0.02 0.01 0.02 0.01 
LULC 0.25 0.15 0.20 0.19 0.14 0.14 0.20 0.21 0.14 0.20 0.20 0.13 0.18 0.21 0.16 
TOPO 0.02 0.05 0.03 0.03 0.05 0.03 0.03 0.03 0.05 0.03 0.03 0.05 0.02 0.06 0.02 
SPA 0.01 0.02 0.02 0.01 0.02 0.02 0.02 0.01 0.02 0.02 0.01 0.02 0.01 0.02 0.01 
CPA 0.01 0.01 0.02 0.02 0.02 0.02 0.02 0.01 0.02 0.02 0.01 0.02 0.01 0.01 0.01 
EIA 0.25 0.15 0.20 0.19 0.14 0.16 0.20 0.18 0.14 0.20 0.20 0.15 0.25 0.18 0.21 
MTN 0.01 0.03 0.03 0.03 0.06 0.05 0.03 0.03 0.05 0.03 0.03 0.05 0.03 0.03 0.03 
PFZ 0.01 0.01 0.02 0.01 0.02 0.02 0.02 0.01 0.02 0.02 0.01 0.02 0.01 0.01 0.01 
SRM 0.19 0.15 0.20 0.19 0.14 0.16 0.20 0.18 0.14 0.20 0.17 0.15 0.25 0.18 0.21 
WS 0.02 0.05 0.03 0.03 0.06 0.05 0.03 0.03 0.06 0.04 0.03 0.07 0.03 0.03 0.05 
LSM 0.01 0.02 0.02 0.01 0.02 0.02 0.02 0.01 0.02 0.02 0.01 0.02 0.01 0.01 0.01 
PD 0.06 0.10 0.07 0.09 0.09 0.09 0.05 0.06 0.08 0.05 0.07 0.10 0.06 0.06 0.11 
PMS 0.02 0.03 0.03 0.02 0.03 0.05 0.03 0.03 0.05 0.03 0.03 0.07 0.03 0.03 0.05 
GWL 0.06 0.10 0.07 0.09 0.09 0.09 0.05 0.06 0.08 0.05 0.03 0.07 0.03 0.03 0.05 
Total 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 

  

2.6.2. Prioritization Weight Matrix Formation 
In computing the element of this matrix, the normalized sum of each row is divided by the total number of its 

criteria. The obtained values (average) provides the relative weights of the criteria being compared as described in 
the studies by Permadi [12] and Odell [4]. For instance, the criteria weight of Major Water Bodies (MWB) in this 
can be obtained thus; 
0.06 + 0.10 + 0.05 + 0.09 + 0.11 + 0.09 + 0.05 + 0.15 + 0.11 + 0.07 + 0.14 + 0.10 + 0.06 + 0.12 + 0.05 (sum of the 
elements in first row) = 1.35 
Total number of criteria in first row = 15 
Therefore, the weight of Major Water bodies (MWB) = 1.35/15 = 0.09 
Weight of the criteria in percentage = 0.09 x 100 = 9% 
 

2.6.3. Consistency Ratio Check 
In checking the reliability of the respondent’s judgments, the consistency ratio (CR) for the judgment values 

provided by the consulted experts were calculated. According to Saaty [10] if this ratio is found to be less than 
10% (CR< 0.1) then the respondent judgment is consistent if otherwise (i.e. CR> 0.1) then the expert or 
respondent judgment is not consistent. Calculating the consistency ratio of a judgment involves the following 
operations: Formation of the weight as factor matrix by introducing the weights of the criteria as the first row of 
the matrix of comparison. Calculation of the weighted column and weighted sum (consistency vector) by 
multiplying matrix of comparisons by the vector of priorities (corresponding weights) to get a new column vector. 

Calculation of the Average Value of the Consistency Vector by dividing the first component of a new column 
vector (first element of the weighted sum matrix) by the first component of priorities vector (first element of the 
weight matrix), the second component of new column vector by the second component of priorities vector, and so 

on. Calculation of the consistency index by adding up all the elements of the consistency vector (λ max) and 

applying the mathematical expression CI = (λ-n) / (n-1) where n is the total number of criteria under consideration 
(in this case 15) Finally, estimating the consistency ratio via the mathematical expression CR = CI/RI according to 
Saaty [10] where CI is the consistency index and RI the random index (as given by Saaty [10]). Table 5 below is a 



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Matrix whose comparison factors are the considered factors on one side and their respective derived weights on the 
other. With this matrix, the consistency vector was estimated. 
 

Table-5. Prioritization weight matrix. 

Criteria Code Row total of the Normalized Matrix Average Weight (%) Criteria Name 

MWB 1.35 0.09 9.00 Major WaterBody 
ETL 0.26 0.02 2.00 Electricity Transmission Line 

LULC 2.70 0.18 18.0 Landuse/Landcover 
TOPO 0.54 0.04 4.00 Topography (Slope) 
SPA 0.22 0.01 1.00 Sensitive/Protected Areas 
CPA 0.22 0.01 1.00 Critically Polluted Areas 
EIA 2.79 0.19 19.0 Existing Industrial Areas 

MTN 0.53 0.04 4.00 Major Transportation Network 
PFZ 0.21 0.01 1.00 Proximity to Flood Zones 
SRM 2.70 0.18 18.0 Source of Raw Materials 
WS 0.62 0.04 4.00 Wind Speed 

LSM 0.22 0.01 1.00 Large Scale Mines 
PD 1.14 0.08 8.00 Population Density 

PMS 0.53 0.04 4.00 Proximity to Major Settlements 
GWL 0.95 0.06 6.00 Groundwater Level 
Total 15.00 1.00 100.00  

 
Table-6. The weights as factor matrix. 

Code MWB ETL LULC TOPO SPA CPA EIA MTN PFZ SRM WS LSM PD PMS GWL 

weights 0.09 0.02 0.18 0.04 0.01 0.01 0.19 0.04 0.01 0.18 0.04 0.01 0.08 0.04 0.06 
MWB 1.00 6.00 0.25 3.00 7.00 5.00 0.25 5.00 7.00 0.33 4.00 6.00 1.00 4.00 1.00 
ETL 0.02 1.00 0.11 0.33 1.00 2.00 0.11 0.50 2.00 0.11 0.33 1.00 0.17 0.50 0.17 

LULC 4.00 9.00 1.00 6.00 9.00 8.00 1.00 7.00 9.00 1.00 6.00 8.00 3.00 7.00 3.00 
TOPO 0.33 3.00 0.17 1.00 3.00 2.00 0.17 1.00 3.00 0.17 1.00 3.00 0.33 2.00 0.33 
SPA 0.14 1.00 0.11 0.33 1.00 1.00 0.11 0.25 1.00 0.11 0.25 1.00 0.17 0.50 0.17 

CPA 0.20 0.50 0.13 0.50 1.00 1.00 0.11 0.33 1.00 0.11 0.33 1.00 0.20 0.33 0.20 
EIA 4.00 9.00 1.00 6.00 9.00 9.00 1.00 6.00 9.00 1.00 6.00 9.00 4.00 6.00 4.00 

MTN 0.20 2.00 0.14 1.00 4.00 3.00 0.17 1.00 3.00 0.17 1.00 3.00 0.50 1.00 0.50 
PFZ 0.14 0.50 0.11 0.33 1.00 1.00 0.11 0.33 1.00 0.11 0.25 1.00 0.20 0.33 0.20 
SRM 3.00 9.00 1.00 6.00 9.00 9.00 1.00 6.00 9.00 1.00 5.00 9.00 4.00 6.00 4.00 
WS 0.25 3.00 0.17 1.00 4.00 3.00 0.17 1.00 4.00 0.20 1.00 4.00 0.50 1.00 1.00 

LSM 0.17 1.00 0.13 0.33 1.00 1.00 0.11 0.33 1.00 0.11 0.25 1.00 0.17 0.25 0.25 
PD 1.00 6.00 0.33 3.00 6.00 5.00 0.25 2.00 5.00 0.25 2.00 6.00 1.00 2.00 2.00 

PMS 0.25 2.00 0.14 0.50 2.00 3.00 0.17 1.00 3.00 0.17 1.00 4.00 0.50 1.00 1.00 
GWL 1.00 6.00 0.33 3.00 6.00 5.00 0.25 2.00 5.00 0.25 1.00 4.00 0.50 1.00 1.00 

TOTAL 15.85 59.00 5.12 32.33 64.00 58.00 4.97 33.75 63.00 5.09 29.42 61.00 16.23 32.92 18.82 

 

2.6.4. Calculation of Weighted Column and Weighted Sum (Consistency Vector) 
The following steps were observed in calculating the consistency vector: 

a. A matrix showing the judgment comparisons and derived weights was started. 
b. Using the priorities (weight) as factors for each column as shown in Table 6 above, the values in each column of 
the comparison matrix were multiplied by their corresponding criterion weight in that column.  
E.g. 0.09 x 1 = 0.09, 0.09 x 0.02 = 0.018; 0.09 x 4 = 0.36 …………….. 0.09 x 1 = 0.09 
c. Adding up all the values in each row (weighted sum) e.g. for row 1: (0.09 + 0.11 + 0.05 + 0.11 + 0.10 + 0.08 + 
0.05 + 0.18 + 0.10 + 0.06 + 0.17 + 0.09 + 0.08 + 0.14 + 0.06) = 1.44. Table 7 shows the obtained Weighted 
Column and Consistency Sum Matrix. Table 8  shows the result of the consistency vector. This consistency vector 
is calculated thus: Divide each of the weighted sums by their corresponding weighted value. 
 

Table-7. Obtained weighted column and consistency sum matrix. 

MWB ETL LULC TOPO SPA CPA EIA MTN PFZ SRM WS LSM PD PMS GWL Weightedsum 

0.09 0.11 0.05 0.11 0.10 0.08 0.05 0.18 0.10 0.06 0.17 0.09 0.08 0.14 0.06 1.44 

0.01 0.02 0.02 0.01 0.01 0.03 0.02 0.02 0.03 0.02 0.01 0.01 0.01 0.02 0.01 0.27 
0.36 0.16 0.18 0.22 0.13 0.12 0.19 0.25 0.13 0.18 0.25 0.12 0.23 0.25 0.19 2.94 

0.03 0.05 0.03 0.04 0.04 0.03 0.03 0.04 0.04 0.03 0.04 0.04 0.03 0.07 0.02 0.56 
0.01 0.02 0.02 0.01 0.01 0.02 0.02 0.01 0.01 0.02 0.01 0.01 0.01 0.02 0.01 0.22 
0.02 0.01 0.02 0.02 0.01 0.02 0.02 0.01 0.01 0.02 0.01 0.01 0.02 0.01 0.01 0.23 
0.36 0.16 0.18 0.22 0.13 0.14 0.19 0.21 0.13 0.18 0.25 0.13 0.30 0.21 0.25 3.04 
0.02 0.04 0.03 0.04 0.06 0.05 0.03 0.04 0.04 0.03 0.04 0.04 0.04 0.04 0.03 0.55 
0.01 0.01 0.02 0.01 0.01 0.02 0.02 0.01 0.01 0.02 0.01 0.01 0.02 0.01 0.01 0.21 
0.27 0.16 0.18 0.22 0.13 0.14 0.19 0.21 0.13 0.18 0.21 0.13 0.30 0.21 0.25 2.91 
0.02 0.05 0.03 0.04 0.06 0.05 0.03 0.04 0.06 0.04 0.04 0.06 0.04 0.04 0.06 0.64 
0.01 0.02 0.02 0.01 0.01 0.02 0.02 0.01 0.01 0.02 0.01 0.01 0.01 0.01 0.02 0.23 
0.09 0.10 0.06 0.11 0.09 0.08 0.05 0.07 0.07 0.04 0.08 0.09 0.08 0.07 0.13 1.20 
0.02 0.04 0.03 0.02 0.03 0.05 0.03 0.04 0.04 0.03 0.04 0.06 0.04 0.04 0.06 0.55 
0.09 0.10 0.06 0.11 0.09 0.08 0.05 0.07 0.07 0.04 0.04 0.06 0.04 0.04 0.06 1.00 

 
 
 
 



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Table-8. The consistency vector. 

Weighted sum Consistency vector 

1.44 / 0.089 16.18 
0.27 / 0.018 15.00 
2.94 / 0.180 16.33 
0.56 / 0.036 15.55 
0.22 / 0.015 14.62 
0.23 / 0.015 15.33 
3.04 / 0.186 16.34 
0.55 / 0.036 15.28 
0.21 / 0.014 15.00 
2.91 / 0.179 16.26 
0.64 / 0.042 15.24 
0.23 / 0.015 15.33 
1.20 / 0.076 15.97 
0.55 / 0.036 15.28 
1.00 / 0.064 15.63 

 
2.6.5. Calculation of the Consistency Index  

Where n = total number of considered factors which in this case is 15, and (λ max) the summation of the 

elements of the consistency vector, CI (consistency index) can be calculated by the formula; CI = {(λ-n) / (n-1)} 
[10] 

Therefore, λ max = (16.18 + 15.00 + 16.33 + 15.55 + 14.67 + 15.33 + 16.34 + 15.28 + 15.00 + 16.26 + 15.24 + 15.33 
+ 15.79 + 15.28 + 15.63) / 15 = (233.205 / 15) = 15.547 

CI = (λ-n) / (n-1) 
CI = (15.547 – 15) / (15 – 1) = 0.0366. 

In calculating the constituency value, which is a ratio of consistency index to the random index, the 
mathematical expression; CR = CI/RI according to Saaty [10] was used. Random index (RI) is the inconsistency 
index of a randomly generated pair-wise comparison matrix of order 1 to 15 obtained by approximating random 
indices. See Table 9. 
 

Table-9. Random Inconsistency Indices (CI) 

n 1 2 3 4 5 6 7 8 9 1 11 12 13 14 15 16 
RI 0 0.00 0.52 0.89 1.11 1.25 1.35 1.40 1.45 1.49 1.52 1.54 1.56 1.58 1.59 1.73 

 
Where n = order of matrix 
When the order of a comparison matrix is n > 15, the average values of the random index CI  may be roughly 
calculated using  Podvezko [13] formula as displayed in Equation 2: 

𝐶𝑙 =
1.98 (𝑛−2)

𝑛
                               (2) 

Where n = number of criteria under consideration. 
Consequently, the consistency ratio, in this case is CR = CI / RI. 
CR in this case is; 0.0366 / 1.59 = 0.023 
 

3. Result and Analysis 
Table 5 shows the Computed Average Criteria Weight for Consistent Respondents which revealed 

the influence level of the individual criteria considered for this study. The result from the calculated environmental 
criteria weights show that proximity of Petroleum refinery to existing industrial areas; source of crude oil and 
Landuse/Landcover to have the highest influence value, followed by proximity to Water Body; Population Density; 
Groundwater Level; Major Settlement; Wind Speed; Transportation Network, Topography, while 
Sensitive/Protected Areas, Critically Polluted areas, and Flood zones with the least influence value. The result of 
this AHP – based weight assessment would play a key role in any decision-making process involving the siting of a 
petroleum refining plant. It is anticipated that the results of this assessment can be used generally by Planners, 
Investors, Environmental Managers, and Oil and Gas experts as a general guide in the prioritization of criteria 
weights based on the influence of one criterion over the other in the suitability siting of petroleum refining 
plant. The result of this AHP – based weight assessment will play a key role in any decision-making process 
involving the siting of a petroleum refining plant. It is anticipated that the results of this assessment can be used 
generally by Planners, Investors, Environmental Managers and Oil and Gas experts as a general guide in the 
prioritization of criteria weights based on the influence of one criterion over the other in the suitability siting of 
petroleum refining plant. The findings agreed with the several studies [11, 13]. 

As a check on the reliability of respondents’ judgments, the Consistency Ratio (CR) for the judgment values 
was calculated. This Consistency Ratio value was found to be 0.023, which is less than 0.1. According to Saaty [10] 
if this ratio is found to be less than 10% (CR< 0.1) then the respondent judgment is consistent, if otherwise (i.e. 
CR> 0.1) then the judgment is not consistent. By the result of this study, it means that there is a reasonable level of 
consistency in the comparison of the criteria by the respondent of this very outcome and that the computed weights 
are within the acceptable limit. If the reverse was the case (CR > 0.1) it means that the weights obtained are 
inconsistent and the judgment values need to be checked for logical correctness. 75% (60) of the total number of 
respondents were consistent in their judgment and the remaining 25% (14) were inconsistent. These 
inconsistencies in judgment by the responders may be a lack of logical knowledge of the Pairwise Comparison. 
 



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4. Conclusion 
Investors are constantly faced with tough decisions on the location of facilities that will yield the highest 

returns on low environmental impact. To optimize the benefits and constraints of particular land uses in a certain 
area, a planner needs to have a good knowledge of the influence of one criterion over the other. The Analytic 
Hierarchy Process (AHP) has been proved by literature and existing projects to produce reliable and consistent 
results since it provides an alternative for a check and the fact that it can deal with inconsistent judgments and 
provides a measure of the inconsistency of the judgment makes the methodology a better solution that can help 
deal with the complex problems of a suitable site a selection like the one of this research (modular petroleum 
refining plant siting), which involves the consideration of multi-criteria/alternatives simultaneously. It is 
anticipated that the results of this assessment can be used generally by Planners, Investors, Environmental 
Managers, and Oil and Gas experts as a general guide during criteria weighting and prioritization based on the 
influence of one criterion over the other in the suitability siting of petroleum refining plant. 
 

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