Optimal manufacturer's cost sharing ratio, shipping policy and production rate – A two-echelon supply chain

We analyze an integrated inventory supply chain and seek the optimal production lot, optimal production rate, and optimal (integer) number of shipments per production lot. An increasing need for higher operational efficiency, as well as growing competition among multiple products for a limited storage capacity, is driving retailers to require more frequent shipping. This imposes pressure on suppliers to share the shipping cost with retailers. The sharing ratio of the shipment cost has not previously been considered within the context of an integrated supply chain. Therefore, we contribute to the literature by investigating this entirely new parameter, assuming that the shipment cost is shared between a manufacturer and a retailer. We also consider a distributed supply chain in which each party optimizes its own cost. We analyze the problem of finding the optimal sharing ratio of the shipment cost for such a supply chain and show that there exists a specific choice of shipment cost-sharing ratio (set by the manufacturer) that results in total costs similar to those obtained in the integrated inventory model. We develop deterministic models that provides basic insights into the investigated problem. Through mathematical analysis of a nested-designs model, we provide intermediate results (which are of interest in their own right) as well as optimal analytical solutions. We show, through numerical examples, that in the scenario where each party optimizes its own cost, the manufacturer's shipment cost is a central control variable in the sense that it affects the costs of both parties.