Stochastic vendor managed replenishment with demand dependent shipment

We investigate optimal properties of the replenishment policy for a two-echelon outsourcing system in which a company outsources production of certain products and supplies raw material required to produce those products for its outsourcing partner. The model presented has three distinct features. First, the company is a single decision maker facing replenishment decisions and whose objective is to minimize total system costs. Second, replenishment decisions are made dynamically based on the system status such as demand, production, and delivery processes. Third, a shipment is activated only when N new demands are realized after the replenishment decision. The model is formulated as a Markov decision problem. Using dynamic programming, we show that the optimal replenishment policy has a monotonic threshold structure under a single order quantity. Numerical investigation suggests that the optimality of monotonicity might be preserved even with multiple order quantities. We present a simple procedure that numerically finds optimal shipment rule and replenishment quantity.