Robust optimization of supply chain network design in fuzzy decision system

This paper presents a new robust optimization method for supply chain network design problem by employing variable possibility distributions. Due to the variability of market conditions and demands, there exist some impreciseness and ambiguousness in developing procurement and distribution plans. The proposed optimization method incorporates the uncertainties encountered in the manufacturing industry. The main motivation for building this optimization model is to make tools available for producers to develop robust supply chain network design. The modeling approach selected is a fuzzy value-at-risk (VaR) optimization model, in which the uncertain demands and transportation costs are characterized by variable possibility distributions. The variable possibility distributions are obtained by using the method of possibility critical value reduction to the secondary possibility distributions of uncertain demands and costs. We also discuss the equivalent parametric representation of credibility constraints and VaR objective function. Furthermore, we take the advantage of structural characteristics of the equivalent optimization model to design a parameter-based domain decomposition method. Using the proposed method, the original optimization problem is decomposed to two equivalent mixed-integer parametric programming sub-models so that we can solve the original optimization problem indirectly by solving its sub-models. Finally, we present an application example about a food processing company with four suppliers, five plants, five distribution centers and five customer zones. We formulate our application example as parametric optimization models and conduct our numerical experiments in the cases when the input data (demands and costs) are deterministic, have fixed possibility distributions and have variable possibility distributions. Experimental results show that our parametric optimization method can provide an effective and flexible way for decision makers to design a supply chain network.