A methodological comparison between standard and two-stage mixed integer approaches for discriminant analysis

A standard mixed integer programming (MIP) approach is compared with a two-stage MIP approach. A computational difference between the two DA (discriminant analysis) approaches is that the former uses a single MIP model to solve various classification problems and the latter uses two MIP models that classify all observations into one of two groups or an overlap at the first stage and then reclassify the overlapped observations at the second stage. In this study, the two MIP approaches are methodologically compared and then applied to a published data set related to Japanese banks. These classification performances are assessed by four hit rates. Based upon the comparison, it is confirmed that the two-stage approach performs at least as well as the standard approach.