A Minimum Variance Control Theory Perspective on Supply Chain Lead Time Uncertainty

Abstract

This paper addresses the lead time uncertainty problem in supply chain systems. In our previous paper [Xu et al. Ind. Eng. Chem. Res.2010,49,8644], we have investigated the impact of demand uncertainty on supply chains. Here we adopt a two-echelon supply chain model, which is basically the same as that used in the research of demand uncertainty. But the fixed lead time setting is replaced by a Markovian lead time model. Since the lead time varies with time, the dynamic characteristics of the supply chain model are different from that used in the demand uncertainty research. We make a comparison analysis of these differences from the view of dynamic systems. On the basis of the above analysis, we adopt two fundamental lemmas of the minimum variance control theory as the foundation for replenishment rules design and analysis. Then we derive formulas of the Order-up-to policy and the generalized Order-up-to policy with time-varying lead time. Moreover, we offer the variant forms of the above strategies when ...