Mixed Integer Linear Programming in Credit Scoring System

Each prospective client is obliged to fulfill a questionnaire based on which a credit score is calculated. The score reflects a quality of the client: the higher score, the better client. One of the management goals is to divide all clients into a few groups according to their scores. These groups should be kind of intrinsically homogenous (the clients within one group have approximately coincident probability of default) and mutually heterogeneous (the clients from different groups have significantly different probability of default). Historical records provide an estimate of the probability of default for every single score. The aim is to calculate the critical score values that split the clients into the homogeneous groups. This model leads to a min-max linear programming problem that can be transformed into a mixed integer linear programming (MILP) problem. In general, solving MILP problems even with hundreds of variables is hard, computationally exhaustive. Although a corresponding exact model has an excessive number of integer variables, some further derivations can significantly reduce the number of variables and tighten the set of feasible solutions. These derivations can be performed due to the special structure of the MILP problem. With these modifications we achieved a considerable reduction in the computation time.