A New Linear Programming Method for Weights Generation and Group Decision Making in the Analytic Hierarchy Process

This paper proposes a new linear programming method entitled by LP-GW-AHP for weights generation in analytic hierarchy process (AHP) which employs concepts from data envelopment analysis. We propose four specially constructed linear programming (LP) models which are used to derive weight vector from a pair-wise comparison matrix or a group of them. We can use both interval and relative importance weights for each decision maker in LP-GW-AHP. In this method, solving only one LP model is enough for local weights derivation from pair-wise comparison matrices. Five numerical examples are examined to illustrate the potential applications of the LP-GW-AHP method. We show that not only derived weights of the new method have slight differences than Saaty’s eigenvector weights but sometimes they are better than eigenvector method weights in the fitting performance index as well. LP-GW-AHP is compared with a method which has been recently proposed for the weights derivation in the group AHP and it becomes obvious that LP-GW-AHP provides better weights. The simple additive weighting method is utilized to aggregate local weights without the need to normalize them.