Multiobjective Stochastic Linear Programming with Incomplete Information: A General Methodology

Abstract

Numerous multiobjective linear programming methods have been proposed in the last two decades for contexts where the parameters are deterministic. In many real situations, however, parameters of a stochastic nature arise and the analyst is, as a result, confronted with a stochastic multiobjective linear programming problem. Recently, some methods have been developed to deal with this kind of problems; in most of them, the decision maker is supposed to be placed in a risky situation, i.e. a situation where he can associate probability distributions to the stochastic parameters. In many cases, we believe that it would be more realistic to suppose that the decision maker is in a situation of partial uncertainty, i.e. a situation where he possesses only an incomplete information about the stochastic parameters; for example, he could be able to precise only the bounds of variation of the parameters and eventually, their central values. For such situations, we propose a general multiobjective stochastic linear programming methodology which includes many modes of transformation of the stochastic objectives and constraints in order to obtain an equivalent multiobjective deterministic linear programming problem. Finally, this deterministic equivalent program is solved by an interactive method derived from STEM. Our methodology will be illustrated through a didactical example.