Ranking aggregation of preferences with common set of weights using goal programming method

Abstract

In aggregation of preferences system, each decision maker (DM) selects a subset of the alternative and places them in a ranked order. The key issue of the aggregation preference is how to determine the weights associated with different ranking places. To avoid the subjectivity in determining the weights, data envelopment analysis (DEA) is used in Cook and Kress to determine the most favorable weights for each alternative. With respect to DEA-based models, two main criticisms appear in the literature: multiple top-ties and overly diverse weights. DEA models use assignments of the same aggregate value (equal to unity) to evaluate multiple alternatives as efficient. There is no criterion to discriminate among these alternatives in order to construct a ranking of alternatives. furthermore, overly diverse weights can appear, given that each alternative can have its own vector of weights (i.e., the one that maximizes its aggregate value). Thus, the efficiencies of different alternatives obtained by different sets of weights may be unable to be compared and ranked on the same basis In order to solve these two problems above, In order to rank all the alternatives on the same scale, In this paper we proposed an improvement to Kornbluth’s approach by introducing an multiple objective linear programming (MOLP) approach for generating a common set of weights in the DEA framework. In order to solve the MOLP model we use a goal programming (GP) model. solving the GP model gives us a common set of weights and then the efficiency scores of candidate can be obtained by using these common weights and finally we can rank all alternative.