0000000000429926
AUTHOR
Stanley Zionts
Solving the Discrete Multiple Criteria Problem using Convex Cones
An interactive method employing pairwise comparisons of attainable solutions is developed for solving the discrete, deterministic multiple criteria problem assuming a single decision maker who has an implicit quasi-concave increasing utility (or value) function. The method chooses an arbitrary set of positive multipliers to generate a proxy composite linear objective function which is then maximized over the set of solutions. The maximizing solution is compared with several solutions using pairwise judgments asked of the decision maker. Responses are used to eliminate alternatives using convex cones based on expressed preferences, and then a new set of weights is found that satisfies the i…
An interactive approach to multiple criteria optimization with multiple decision-makers
In this article we propose a formal man-machine interactive approach to multiple criteria optimization with multiple decision makers. The approach is based on some of our earlier research findings in multiple criteria decision making. A discrete decision space is assumed. The same framework may readily be used for multiple criteria mathematical programming problems. To test the approach two experiments were conducted using undergraduate Business School students as subjects in Finland and in the United States. The context was, respectively, a high-level Finnish labor-management problem and the management-union collective bargaining game developed at the Krannert Graduate School of Management…
An Interactive Multiple Objective Linear Programming Method for a Class of Underlying Nonlinear Utility Functions
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.
Recent Developments in our Approach to Multiple-Criteria Decision Making
Approximately ten years ago we began a study of multiple criteria decision making at the European Insti tute for Advanced Studies in Management in Brussels. The project started as a way of finding a multiple objective linear programming method that would work better than those tested by Wallenius (1975). We did a substantial amount of work on the problem and came up with such a method (Zionts and Wallenius, 1976). Wallenius’ (1975) thesis, one of the first outputs of that project, comprises a rather significant piece of research in the multiple criteria area. Since that time our work has continued. We have worked together on a great deal of it; some of it has involved students and other fac…