Developing Multiobjective Equilibrium Optimization Method for Sustainable Uncertain Supply Chain Planning Problems

Abstract

This paper proposes a new multiobjective two-stage equilibrium optimization method for a supply chain planning problem with uncertain demand. To handle the ambiguity in the distribution of demand, the probability and possibility distributions are integrated to characterize the uncertain demand. As a result, the decision process in our equilibrium optimization problem is divided into two stages. In the first stage, decision variables should be taken before knowing the realizations of uncertain demand; while the second-stage decision variables must be taken after knowing the outcome of subjective uncertainty embedded in demand. On the basis of the proposed dynamic decision scheme, the objectives in the first-stage are constructed via credibilistic optimization methods. The objective and constraints in the second-stage are built via stochastic optimization methods. More specifically, three objectives in the first-stage are constructed based on the expected value operator and conditional value-at-risk of fuzzy variable, and the second-stage optimization model is built as a stochastic expected value model under a probabilistic constraint. When the random parameters follow normal distributions, the proposed equilibrium optimization model is equivalent to a triobjective two-stage credibilistic optimization model. To solve this model, we first employ a sequence of discrete possibility distributions to approximate continuous possibility distributions. Then, we design a new archive-guided multiobjective particle swarm optimization based on decomposition to solve the obtained approximate optimization model. Finally, numerical experiments via a light emitting diode industry problem are conducted to demonstrate the feasibility and effectiveness of the proposed optimization method and new heuristic algorithm.