Jyrki Wallenius

Some Tests of an Interactive Programming Method for Multicriterion Optimization and an Attempt at Implementation

This paper describes an attempt to apply in practice and test a multiple criteria method recently developed by the authors. The test was conducted in a large company on a corporate planning problem involving multiple objectives. Two simplified linear programming models assuming a linear utility function of objectives were developed. Managers experienced in making the kind of judgements required participated in the experiment and individually used the method to solve the problem. The results of the test are described, and the main features of the models and the computational system to implement the method are discussed.

Observations Regarding Choice Behaviour in Interactive Multiple Criteria Decision-Making Environments: An Experimental Investigation

Many interactive procedures have been developed for solving optimization problems having multiple criteria. In such procedures, an exploration over the feasible or efficient region is conducted for locating the most preferred solution. As Steuer (1986) notes, interactive procedures are characterized by phases of decision-making alternating with phases of computation. Generally a pattern is established that we keep repeating until termination. At each iteration, a solution, or group of solutions, is generated for a decision-maker’s (DM’s) examination. Based on the examination, the DM inputs information to the solution procedure in the form of tradeoffs, pairwise comparisons, aspiration levels, etc. The responses are used to generate a presumably, improved solution, and so forth.

V I G — A Visual and Dynamic Decision Support System for Multiple Objective Linear Programming

In this paper we describe the principles of VIG (Visual Interactive Goal Programming), a Multiple Criteria Decision Support System, recently developed by Korhonen. PARETO RACE is a corner-stone of this system, which is designed to support both the modelling and solving of a multiple objective linear programming problem. The interface is based on one main menu, spreadsheets, and interactive use of computer graphics. VIG provides the decision-maker with the possibility to approach his/her decision problem by using an “evolutionary approach”. This means that the decision-maker does not have to specify the model precisely prior to solving the problem. In fact, the model evolves progressively. We also discuss several applications of VIG to practical problems.

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 faculty colleagues. In presenting this update, we make every effort to accurately attribute (and reference) each piece of research to the appropriate person(s). Though we have tried not to omit any references or acknowledgments, or both, we apologize in advance for any inadvertant omissions.

Multiple Criteria Decision Analysis

This historical note is based on a plenary talk ‘A History of Early Developments in Multiple Criteria Decision Making’, presented by Stanley Zionts at the 21st International Conference on Multiple Criteria Decision Making held in Jyvaskyla, Finland, June 2011. It draws heavily on our book, Multiple Criteria Decision Making: From Early History to the 21st Century, published by World Scientific, Singapore, 2011 (Copyright

A METHODOLOGY FOR SOLVING THE MULTIPLE CRITERIA MACROECONOMIC POLICY PROBLEM

In this paper we review the results of our research on using interactive multiple criteria optimization methods for solving macroeconomic policy problems in Finland. An existing econometric model describing the interrelationships between different variables and sectors of the economy is used. In addition, the current status of the implementation work is reported and some possibilities for future research are discussed.

A Method for Identifying Redundant Constraints and Extraneous Variables in Linear Programming

This paper presents a method for identifying redundant constraints and extraneous variables in linear programming problems. The method has evolved from the method of Zionts (1965) (see also Thompson, Tonge and Zionts (1966)) which identified redundant constraints and extraneous variables either prior to or during the solution of linear programming problems. In earlier work (Zionts and Wallenius (1976)) we had to solve a problem that is closely related to identifying all redundant constraints and extraneous variables in a linear programming problem. In Zionts and Wallenius (1980) we show that the method can solve five related problems, one of these problems being the redundant constraint problem. This paper develops the method fully for identifying redundant constraints and extraneous variables.

Principles for Solving Sequential Multiple Criteria Decision Problems

In this paper a sequential multiple criteria decision problem is studied. The problem arises, when a decision maker is unable to consider all possible decision alternatives simultaneously. If the decision maker evaluates only a subset of all decisions from among which he chooses the most preferred alternative, it is not necessarily globally best. In this context an interesting question is, how good the most preferred alternative is and what the chances are of finding a better solution by considering additional alternatives. The principles of a an approach based on probability theory to solving this problem are described and illustrated with numerical examples.

An Interactive Bargaining Procedure for Solving the Multiple Criteria Problem with Discrete Alternatives

In a typical decision-making situation a group of decision-makers seeks to identify a compromise solution from among a set of explicitly defined alternatives. In this paper we describe a framework for a negotiation process and propose a procedure which attempts to facilitate the negotiations by structuring the problem in an appropriate way. The basic idea of the negotiation process is to identify the individual optimal alternatives and to encourage the group members to make concessions until a compromise solution will be found. Our procedure attempts to aid the group in identifying the compromise solution by using mathematical tools to define certain stages of the negotiation process which benefit from the use of an interactive computer system. Such stages consist of identifying the optimal alternative for each group member, identifying the possible compromise solutions, structuring the concession making process by informing the group whose turn it is to make concessions and finding the smallest concession for her/him, and finally dealing with various exceptional situations such as resolving deadlock. We present two approaches: the first uses approximations to describe individual and group utility functions and the second is an ad hoc procedure. We have implemented the second procedure and are in the process of implementing the first procedure on the Burroughs 6700 time-sharing system. Some numerical tests have been performed and the procedure seems to function well.

Decision-Making with Multiple Objectives—Some Analytic Approaches

Publisher Summary In almost every management situation, several criteria are involved in making decisions. Plant location problems, for example, are solved as a function of site cost, labor availability, cost of raw materials, transportation facilities, and other criteria. Simply maximizing one objective may not be appropriate. For example, profit maximization may be important but not if excessive deterioration in employee morale is a by-product. One way of handling more than one objective is to consider all but one objective as a constraint. Thus, for a plant location problem, one may choose the minimum cost site having adequate labor availability, costs of raw materials, and transportation facilities. Analytic problem solving where one objective is to be maximized subject to constraints has been possible for some time using quantitative techniques. There has been an increasing awareness of the need for analytically handling more than one objective. Numerous methods have been developed to solve such problems and the methods vary considerably in their approach and ease of use. This chapter presents a guided tour of a selected group of methods that are practice-oriented and describes some applications of these methods.