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

and Applied Analysis 3 Table 1: Comparison between the papers discussing integrated inventory model with a trade credit. Author s Demand rate Production rate Production/purchase cost Freight rate Wholesale price Abad and Jaggi 39 Retail price sensitive Constant Constant — Constant Jaber and Osman 40 Constant — — — Constant Yang and Wee 41 Retail price sensitive — Constant — Constant Sheen and Tsao 42 Retail price sensitive — Constant Quantity discounts are offered Constant Chen and Kang 43 Constant — — — Constant Su et al. 44 Customer’s credit period sensitive Constant Constant — Constant Ouyang et al. 45 Retail price sensitive Adjust with demand rate Constant Quantity discounts are offered Constant Ho et al. 46 Retail price sensitive Adjust with demand rate Constant — Constant This paper Price sensitive Adjust with demand rate Production and demand sensitive Conditionally free shipment Production cost related “—” denotes the factor is not considered in the model. Tsao 42 explored how channel coordination can be achieved using trade credit. Chen and Kang 43 developed integrated models for determining the optimal replenishment time interval and replenishment frequency. Su et al. 44 considered a seller-buyer channel in which the end demand is credit period sensitive. Recently, Ouyang et al. 45 and Ho et al. 46 considered an optimal replenishment and order policy with a credit term when the demand is price sensitive and the production is rate sensitive demand. In this study, to analyze pricing, ordering, delivery, and trade credit with comprehensive considerations of operation, marketing, and financing among channel members, a supplier-buyer inventory model is developed. We assume the supplier’s unit selling price is based on his/her unit production cost which is decided by the market demand and production rates. And the production rate is adjusted with a price-sensitive market demand. In such circumstances the unit wholesale price, reflecting the costs of the product, imposed by the seller on the buyer, does influence the end demand for the product. In addition, the supplier offers to pay freight charges if an order quantity meets or exceeds a certainminimum requirement. Furthermore, a fixed trade credit period is offered by the supplier. In this paper, we maximize the total profit of the whole supply chain i.e., treating the supply chain as a single level profit centre . An algorithm is developed to determine the optimal ordering, shipping, and pricing policy. Numerical examples with relevant data are devoted to find the optimal policies of the developed model. Sensitivity analysis for main parameters is also conducted. The major difference between our model and other related models is shown in Table 1. 4 Abstract and Applied Analysis Customers Buyer Supplier IA(Q)(h +wQ) $c(D,R) = c0D−βRγ Transportation cost per order