Policies for a single-vendor multi-buyer system with finite production rate

We deal with a multi-echelon inventory system in which one vendor supplies an item to multiple buyers. The vendor produces the item at a finite rate and customer demand occurs at each buyer at a constant rate. There is a holding cost per unit stored per unit time at the vendor and at each buyer. Each time a production is carried out the vendor incurs a setup cost. Moreover, placing an order at a buyer entails a fixed ordering cost. Shortages are not allowed. The goal is to determine the order quantities at the buyers and the production and shipment schedule at the vendor in order to minimize the average total cost per unit time. We formulate the problem in terms of integer-ratio policies and we develop a heuristic procedure. We also show how the problem should be addressed in case of independence among the vendor and the buyers. Both solution procedures are illustrated with a numerical example. Finally, we present the results of a numerical study which illustrates the performance of the heuristic for computing integer-ratio policies. Additionally, we compare the integer-ratio policies with the decentralized policies, and a sensitivity analysis of parameters is also reported.