A note on the use of goal programming for the multiplicative AHP

The main aim of this paper is to identify the opportunities of utilizing goal programming (GP) in the multiplicative analytic hierarchy process (MAHP). It starts with the issue of weight derivation from judgemental matrices. The use of GP for the weight derivation problem is not new, but GP is viewed in this paper from the perspective of augmenting the capabilities of the widely used row geometric mean method (RGMM) of the 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 those of the 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 interval judgements and missing judgements, which cannot be readily solved by the RGMM. The proposed technique provides extensive scope for utilizing the vast literature on non-linear programming, say, for conducting sensitivity analysis. It also has the potential to be useful to more complicated issues of the MAHP, such as group decision making and interlevel dependence, hitherto little explored areas of the MAHP.