A Decision Aid Approach for Optimisation Problems Involving Several Economic Functions

Many concrete real life problems ranging from economic and business to industrial and engineering may be cast into a multi-objective optimisation framework. The redundancy of existing methods for solving this kind of problems susceptible to inconsistencies, coupled with the necessity for checking inherent assumptions before using a given method, make it hard for a nonspecialist to choose a method that fits well the situation at hand. Moreover, using blindly a method as proponents of the hammer principle (when you only have a hammer, you want everything in your hand to be a nail) is an awkward approach at best and a caricatural one at worst. This brings challenges to the design of a tool able to help a Decision Maker faced with these kinds of problems. The help should be at two levels. First the tool should be able to choose an appropriate multi-objective programming technique and second it should single out a satisfying solution using the chosen technique. The choice of a method should be made according to the structure of the problem and to the Decision Maker’s judgment value. This paper is an attempt to satisfy that need. We present a Decision Aid Approach that embeds a sample of good multi-objective programming techniques. The system is able to assist the Decision Maker in the above mentioned two tasks.

Chance-Constrained Approaches for Multiobjective Stochastic Linear Programming Problems

Multiple objective stochastic linear programming is a relevant topic. As a matter of fact, many practical problems ranging from portfolio selection to water resource management may be cast into this framework. Severe limitations on objectivity are encountered in this field because of the simultaneous presence of randomness and conflicting goals. In such a turbulent environment, the mainstay of rational choice cannot hold and it is virtually impossible to provide a truly scientific foundation for an optimal decision. In this paper, we resort to the bounded rationality principle to introduce satisfying solution for multiobjective stochastic linear programming problems. These solutions that are based on the chance-constrained paradigm are characterized under the assumption of normality of involved random variables. Ways for singling out such solutions are also discussed and a numerical example provided for the sake of illustration.

A Kaleodoscopic View of Fuzzy Stochastic Optimization*

The last three decades have witnessed development of optimization under fuzziness and randomness also called Fuzzy Stochastic Optimization. The main objective of this new field is the need for basing many human decisions on information which is both fuzzily imprecise and probabilistically uncertain. Consistency indexes providing a union nexus between possibilities and probabilities of uncertain events exist in the literature. Nevertheless, there are no reliable transformations between them. This calls for new paradigms for coping with mathematical models involving both fuzziness and randomness. Fuzzy Stochastic Optimization (FSO) is an attempt to fulfill this need. In this paper, we present a panoramic view of Fuzzy Stochastic Optimization emphasizing the methodological aspects. The merits of existing methods are also briefly discussed along with some related theoretical aspects.