Optimization of Multi-objective Stochastic Linear Programming Problem in Fuzzy Environment: An Iterative-Interactive Optimization Process

In this article, we consider Multi-Objective Stochastic Linear Programming Problem (MOSLPP) and present a general iterative-interactive optimization process (IIOP) for determining preferable Pareto optimal solution in fuzzy environment. Sakawa et al. originally presented an interactive method to optimize MOSLPP in fuzzy environment. They considered the expectation of each fuzzy objective function of MOSLPP to simultaneously attain respective goal. Accordingly, they had set initial reference membership level as unity for all cases. However, we observe in existing methods that expectations of conflicting objective functions cannot simultaneously attain respective goals in fuzzy environment. In addition, we cannot effectively specify any objective function as main objective function that has highest priority of the decision maker, in fuzzy environment in several other multi-objective optimization methods. Here in proposed IIOP, decision maker can set an objective function as main objective function. Next, we employ trade-off ratios among membership functions of expectations of objective functions in fuzzy environment to elicit corresponding reference membership levels and thereby determine preferable Pareto optimal solution to MOSLPP in fuzzy environment. We illustrate proposed IIOP through numerical application of a multi-objective supply chain management model along with numerical examples. We present managerial insights by performing sensitivity analysis of key parameters of this model. Finally, we draw conclusions.