Optimizing the ordering policy in a supply chain

This study analyzes an inventory management problem within a supply chain. An enterprise whose stock is replenished by outside suppliers faces random demands for one of its products. The objective is to minimize the expected total cost for the enterprise, which includes the holding and shortage costs. The enterprise must choose the suppliers to whom the orders are sent while minimizing the costs. If the enterprise sends all the orders to the same supplier during the planning period, the supplier who has the maximum service rate must be chosen. In the case of choosing possibly different suppliers for different orders, the supplying system is modelled as an open queuing network and explicit expressions are obtained for the average total cost as a function of the decision variables. Numerical results measure the advantage for the producer to use different suppliers instead of a single one.