An Interactive Multiple Objective Linear Programming Method for a Class of Underlying Nonlinear Utility Functions

TLDR

The method extends a prior approach published in this journal (Zionts & Wallenius, 1976). The paper develops an interactive multiple‑objective linear programming method for unknown pseudo‑concave utility functions. The authors present an interactive programming algorithm for solving multiple‑criteria problems, detailing its theory, implementation options, and practical experience across several versions. The revised method resolves technical problems from earlier versions and incorporates practical implementation insights. Published in Management Science, vol.

Abstract

This paper develops a method for interactive multiple objective linear programming assuming an unknown pseudo concave utility function satisfying certain general properties. The method is an extension of our earlier method published in this journal (Zionts, S., Wallenius, J. 1976. An interactive programming method for solving the multiple criteria problem. Management Sci. 22 (6) 652–663.). Various technical problems present in predecessor versions have been resolved. In addition to presenting the supporting theory and algorithm, we discuss certain options in implementation and summarize our practical experience with several versions of the method.