Multiple Objectives in Mathematical Programming

Abstract

The abstraction from a real situation to a model suitable for mathematical programming often raises the dilemma of multiple objective functions, and of the arbitrary roles of objective functions and restrictions. This dilemma is resolved by formulating a more general model of the total objective function. This formulation includes (1) defining a subobjective space, (2) defining a set of mutually exclusive regions in subobjective space, (3) defining an individual objective function for each such region, (4) indicating an order of preference for the regions. Examples are given for the problems of optimal product mix and military aircraft design.