Integrated lot sizing and safety stock placement in a network of production facilities

In a network of production facilities, safety stock placement is determined at the network level to hedge against uncertainty in demand, while considering the production cycle time (PCT) of each stage as an exogenous parameter. The lot sizing policy at each stage affects setup time, capacity, and is a major determinant of queuing behavior and PCT. This paper integrates strategic safety stock placement and tactical lot sizing, which are typically optimized independently. We model the integrated problem to minimize system-wide production and inventory costs subject to meeting service-level requirements of external customers. We establish bounds for optimal lot sizes and extend existing safety stock placement dynamic programming algorithm to solve the integrated problem. Based on numerical experiments, we assess the value of integrating the two decisions and find that integration leads to smaller lot sizes, shorter lead times, and favors pooling of safety stocks. The setup cost, setup time, and the added value at a production stage are the most significant factors in determining the amount of savings generated through integration. In addition, simulation studies show that integration reduces PCT variability and decreases the fraction of delayed items.