Note on the Use of Goal Programming for Multiplicative AHP

摘要

The main aim of this paper is to identify the opportunities of utilizing goalprogramming (GP) for use in the Multiplicative Analytic Hierarchy Process (MAHP). It starts with the issue of weight derivation from judgemental matrices. Use of GP for the weight derivation problem is not new, but GP is viewed in this paper with the perspective of augmenting the capabilities of the widely used row geometric means method (RGMM) of Logarithmic Least Squares Technique (LLST). Different possible approaches using GP are discussed. It is shown that the formulation of the GP problem can be easily modified to provide the same weights as that of LLST. While this proposed GP technique is not superior to the RGMM in terms of computational ease or speed, it is quite useful in solving certain other problems of the MAHP, such as the interval judgements or missing judgements, which cannot be readily solved by the RGMM. The proposed technique provides extensive scope for utilizing the vast literature on nonlinear programming, say, for conducting sensitivity analysis. It also has the potential to be useful to more complicated issues of MAHP, such as group decision making and the inter-level dependency, hitherto little explored areas of MAHP. (Copyright (c) 1995 by Faculty of Technical Mathematics, Delft, The Netherlands.)