Examining optimal criterion weights in mixed integer programming approaches to the multiple-group classification problem

Several mixed integer programming approaches to the multiple-group statistical classification problem are examined. Many papers have investigated conditions under which a degenerate solution occurs in linear programming approaches to the two-group discriminant problem. Very little research has been conducted in the multiple-group case. This paper investigates conditions under which a degenerate solution can occur in mixed integer programming approaches to the multiple-group classification problem. A multiple-group ‘minimize the sum of deviations’ model is presented. This model is similar in structure to the general single function classification model. Also, a two-goal approach to the multiple-group classification problem is discussed.