An Integrated Supplier-Buyer Inventory Model with Conditionally Free Shipment under Permissible Delay in Payments

It is well known that production, distribution, marketing, inventory control, and financing all/each have a positive impact on the performance of a supply chain. Despite the growing interest in the development of integrated inventory models, the interactions between these elements of a supply chain may not be efficiently included, resulting in a restricted supply chain model presentation. To incorporate this phenomenon, a mathematical model that tackles the interdependent relationships between these aforementioned elements is developed in this paper. This study considers the determination of the optimal pricing, ordering, and delivery policies of a profit-maximizing supply chain system, faced with (1) unit wholesale price of the supplier is set based on unit production cost, (2) unit production cost is taken as a function of demand rate and production rate, (3) the supplier's production rate is adjusted according to market demand, (4) market demand depends upon buyer's selling price, (5) a free freight is offered if the buyer's order exceeds a certain minimum requirement, and (6) a constant credit period is offered by the supplier to stimulate the demand of the buyer. Algorithm for computing the optimal policies is derived. The sensitivity of the optimal results with respect to those parameters which directly influence the production and transportation costs is also examined.