An interactive multiple objective linear programming method based on piecewise-linear additive value functions

Abstract

S. Zionts and J. Wallenius (1976) have discussed how their method for interactive multiple-objective linear programming can be extended to handle pseudoconcave utility functions. They do not, however, specify how an implied interactive search over faces of the simplex is to be done. E. Jacquet-Lagreze and J. Siskos (1982) have introduced the idea of approximating a utility function by a piecewise-linear additive form, i.e. a separable programming approach. It is shown how these two concepts can be brought together in an interactive method for multiple-objective linear programming that avoids the unspecified search of Zionts and Wallenius but is nevertheless able to approximate the true preferred solution when the utility function is concave. This method is applied to two hypothetical problems, and its performance is compared with that of the Zionts-Wallenius procedure. The major advantage of the proposed method is that it uses a single procedure, requiring only pairwise preference statements from the decision-maker.