Inverse multiple criteria sorting problem

Multiple criteria sorting problem is to assign objects evaluated with multiple criteria to one of the predefined ordered classes. In this study, we consider the inverse multiple criteria sorting problem (IMCSP), in which it is possible to perform actions which have an impact of objects evaluations, hence on the objects classification. IMCSP aims at determining which action(s) to implement so as to provide guaranties on objects classification. Each action has a corresponding cost and impact on the evaluations of objects on each criterion. In this paper we study IMCSP for three different sorting methods: linear, UTADIS and MR-Sort. We consider two levels of information; (i) the sorting method parameters are known explicitly (simple version), and (ii) assignment examples restrict the set of compatible parameters (robust version). We study two types of problems; first, finding the least costly set of actions that guarantees the objects assignment to desired classes, and second, improving the assignment of objects under a limited budget. For each case, we develop a resolution method based on mathematical programming models. Extensive computational experiments on randomly generated instances show the performance and applicability of the approach.