Li Tan and Shenghan Xu. In Proceedings of the 2012 annual meeting of annual meeting of Production and Operation Management Society. Chicago, IL. April, 2012.

The strategy of simultaneously splitting replenishment orders among serveral suppliers, also known as order splitting, has been widely used to improve the performance of supply chains under uncertainty. An important metric of stochastic performance of supply chain is its level of safety stock. In this research we propose a formal analysis technique that can algorithmically analyze the impact of oder splitting on safety stock. The formal analysis technique is based on probabilistic model checking technique developed in Computer Science for analyzing large-scale dynamic systems. To facilitate formal analysis, we develop formal stochastic models based on Markov Decision Processes (MDPs) for supply chains under uncertainty. Using the new analysis technique and formal models, we are able to validate the benefit of order splitting on safety stock, and more importantly, identify the key factors that affect such benefits.