Production and distribution policy in a two-stage stochastic push-pull supply chain

We consider a model of a two-stage push-pull production-distribution supply chain. The orders arrive at the final stage according to a Poisson process. Two separate operations, which take place at different locations with exponential service times, are required to convert the raw materials into finished goods. When the first operation is completed the intermediate inventory is held at the first stage and then transported to the second stage where the items are produced to order. The objective is to minimize the average sum of the production, transportation, and holding costs. We consider the optimal policy for a version of this model. Our experimental analysis demonstrates that this optimal policy is counter-intuitive. We develop a heuristic based on a deterministic version of this model, and computationally test the heuristic.