Optimal stationary policies in a 3-stage serial production-distribution logistic chain facing constant and continuous demand

In this paper, we study a 3-stage production-distribution system that faces constant and continuous demand. The system is made up of three storing sites: a production facility, a warehouse and a retailer. This system was constructed to study the need for coordinating distribution and production in the decision of lot-sizes. Hence, the production capacity is limited. Our objective is to compute lot-sizes that leads to the lowest possible cost in such a system. We consider stationary inventory management policies. In such a policy, a fixed lot-size is supplied from one stage to the next with a constant time interval. We introduce the concept of multiple policies and give a solution to find the best one. We then prove that multiple policies are guaranteed to cost less than 1.51% more than the best stationary policy. We improve this guarantee to 0.51% by adding some simple but non-multiple policies to our candidate policies.