An integrated production-distribution model for a deteriorating inventory item

We develop an integrated production-distribution model for a deteriorating item in a two-echelon supply chain. The supplier's production batch size is restricted to an integer multiple of the discrete delivery lot quantity to the buyer. Exact cost functions for the supplier, the buyer and the entire supply chain are developed. These lead to the determination of individual optimal policies, as well as the optimal policy for the overall, integrated supply chain. We outline a procedure for determining the optimal supply chain decisions with the objective of minimizing the total system cost. Our approach is illustrated through a numerical example.