The classification problem can succinctly be stated as follows: correctly classify an entity i to one of k groups or classes on the basis of measurements taken from the entity on m different attributes (ai1,...,aim). Typical examples of classification problems in business include: (1)the case where a bank loan officer wishes to correctly classify a new loan applicant into the categories of good or poor credit risk; (2)a marketing manager who wishes to predict a customer as either an adopter or a nonadopter of a newly introduced product; and (3)a financial officer who wishes to predict the likely failure of new ventures on the basis of information obtained from the business. Recently, mathematical programming (MP) formulations, in particular the l1-norm linear program, have emerged as powerful approaches to solve this type of classification problem. This paper extends existing MP formulations to address two relevant and important issues that arise in classification analysis: (1)how to deal with unequal costs of misclassification across groups, and (2)how to take into account the number of misclassified cases, as well as the total distance of the misclassified cases from the cutting hyperplane(s) which establish the classification rule. Using convenient properties of the MP formulation, this paper presents a multicriteria approach which directly and simultaneously addresses these issues, providing insights into the problem (such as tradeoffs between the different measures of classificatory performance, and unequal costs of misclassification) which cannot be gained by applying previous methods.
