A Decomposition Based Minimax Regret Approach for Inverse Multiple Criteria Sorting Problem

Abstract

Multiple criteria sorting problem aims to assign objects evaluated on multiple criteria to ordered classes. In inverse multiple criteria sorting problem, the class assignments of objects are known and the decision maker can manipulate the scores of objects on criteria by implementing actions. Selected actions enable the improvement of objects' final classification. As the decision maker chooses to implement more actions, better classifications may be obtained. The contribution of this paper is under two-folds. First, we decompose inverse multiple criteria sorting problem into two phases, where phase one is a pre-process that computes the minimum cost required for each feasible object-class pair considering the underlying sorting model. Phase two interacts with the decision maker to analyze the classification and budget related trade-offs, through an assignment model generated with the outputs of phase one. The second contribution is using a modified version of a regret-based approach available in the literature. This modification includes a tighter formulation of the regret model, and an interactive solution approach using a mixed integer program for computing the minimax regret value rather than a branch-and-bound approach. We present an example instance to illustrate the developed ideas and conduct computational tests on randomly generated instances. The simultaneous use of the decomposition approach, tighter formulation and the interactive algorithm reduces the computation time significantly.