Multiobjective Two-level Simple Recourse Programming Problems with Discrete-type LR Fuzzy Random Variables

Abstract

In this paper, we focus on multiobjective two-level simple recourse programming problems with discrete-type LR fuzzy random variables, in which each of the decision makers called the leader and the follower optimizes his/her multiple objective functions independently, shortages and excesses arising from the violation of the constraints with discrete-type LR fuzzy random variables are penalized, and the sum of the objective function and the expectation of the amount of the penalties is minimized. To deal with such problems, we introduce a new solution concept called an estimated Pareto Stackelberg solution for the leader. To obtain a candidate of a satisfactory solution for the leader from among an estimated Pareto Stackelberg solution set, using the Kuhn-Tucker approach and the transformation technique for complementarity conditions, an original problem is transformed into a mixed integer programming problem. Then, we propose an interactive algorithm to obtain a satisfactory solution of the leader from among an estimated Pareto Stackelberg solution set. A numerical example illustrates the proposed algorithm for a multiobjective two-level fuzzy random simple recourse programming problem under the hypothetical leader.