Integer programming formulations of statistical classification problems

A series of approaches is presented to formulate statistical classification problems using integer programming. The formulations attempt to maximize the number of observations that can be properly classified and utilize single function, multiple function and hierarchical multiple function approaches to the problems. The formulations are tested using standard software on a sample problem and new approaches are compared to those of other authors. As the solution of such problems gives rise to various awkward features in an integer programming framework, it is demonstrated that new approaches to formulation will not be completely successful in avoiding the difficulties of existing methods, but demonstrate certain gains.