A coordinated production and shipment model in a supply chain

In this study, we consider the coordination of transportation and production policies between a single supplier and a single retailer in a deterministic inventory system. In this supply chain, the customers are willing to wait at the expense of a waiting cost. Accordingly, the retailer does not hold inventory but accumulates the customer orders and satisfies them at a later time. The supplier produces the items, holds the inventory and ships the products to the retailer to satisfy the external demand. We investigate both a coordinated production/transportation model and a decentralized model. In the decentralized model, the retailer manages his own system and sends orders to the supplier, while the supplier determines her own production process and the amount to produce in an inventory replenishment cycle according to the order quantity of the retailer. However, in the coordinated model, the supplier makes all the decisions, so that she determines the length of the replenishment and transportation cycles as well as the shipment quantities to the retailer. We determine the structure of the optimal replenishment and transportation cycles in both coordinated and decentralized models and the corresponding costs. Our computational results compare the optimal costs under the coordinated and decentralized models. We also numerically investigate the effects of several parameters on the optimal solutions.