An Analytic Hierarchy Process (AHP) Approach to Port Selection Decisions – Empirical Evidence from Nigerian Ports

Abstract

This study presents the findings of a survey to determine the service characteristics that shippers consider important when selecting a port and the way these characteristics are prioritised according to their importance. Seven criteria for the port selection decision and four ports were identified, and the decision problem was structured into a three-level hierarchy using the Analytic Hierarchy Process. The findings suggest that shippers place high emphasis on efficiency, frequency of ship visits and adequate infrastructure, while quick response to port users' needs was insignificant to them. Results from the study are of interest to Port managers because they provide essential information on the key factors that come into the decision process of port users, thus, identifying the strengths and weaknesses of the ports.

Appendices

Appendix I

INPUT MATRIX

When employing the AHP methodology, the input data for the decision problem consists of matrices of pairwise comparisons of elements of one level that contribute to achieving the objectives of the immediate preceding level. Thus, the Level 2 attributes are compared pairwise with one another, in relation to their importance to the Level 1 objective. If there are n attributes in Level 2 of the hierarchy, a total of n(n−1)/2 comparisons are required. This results in a n × n matrix. Similarly, the Level 3 attributes are pairwise compared with one another, in relation to their preference with regard to each of the n m × m matrices.

For this study, the input matrix of the respondents' judgments would look like the following:

The matrix shows that attribute 1 is α times more important than attribute 2 and is k times more important than attribute 7. the matrix has the property that its principal diagonal elements are all unity because when compared with itself, each elements has equal importance. The lower triangle elements of the matrix are the reciprocal of upper triangle elements. Thus, pairwise comparisons are collected for only half of the matrix elements.

Appendix II

THE EIGENVALUE METHOD

The eigenvalue method of the AHP takes in as inputs the pairwise comparisons of the respondents and judgements and produces the relative weights of the elements at each level of the decision hierarchy. Following Zahedi (1986), if the evaluator could know the actual relative weights of n elements (at one level of the hierarchy with respect to the level above), the matrix of the pairwise comparisons would be

In this case, the relative weights could be obtained from each of the n rows of matrix A. In other words, matrix A has rank 1 and the following holds:

Where W is the vector of actual relative weights and n is the number of elements. In matrix algebra, n and W are called the eigenvalue and the right eigenvector of A respectively.

The AHP posits that the evaluator does not know W and therefore, is not able to produce the pairwise relative weights of matrix A accurately. Thus, the observed matrix A contains inconsistencies. The estimation of W, denoted by Ŵ could be obtained from

where  is the observed matrix of pairwise comparisons, λ _max is the largest eigenvalue of Â, and is its right eigenvector.

Saaty (1980) has shown that λ _max can be considered an estimation of n and that λ _max is always greater than or equal to n. Furthermore, when the observed values of  are consistent, the value of computed λ _max is very close to n. this property allows the construction of the consistency index (C.I) as

and the construction of the consistency ratio (C.R) as

where ACI is the average index of randomly generated weights. The computational algorithm is available in Expert Choice Software.

In summary, the eigenvalue method in the AHP is one of the widely used methods for estimating the relative weights of W from the matrix of pairwise comparisons.