Optimal strategy for an integrated inventory system involving variable production and defective items under retailer partial trade credit policy

a r t i c l e i n f o Keywords: Supplier–retailer inventory system Trade credit Defective items Variable production This paper investigates an integrated inventory model with variable production rate and price-sensitive demand rate under two-level trade credit. The model considers two-level trade credit policy in which the retailer receives a full trade credit from its supplier, and offers partial trade credit to its customers. It is assumed that an arrival order lot may contain some defective items and the number of defective items is a random variable. This study attempts to offer a best policy for retail price, the replenishment cycle, and the number of shipment from the supplier to the retailer in one production run that aims at maximizing the joint expected total profit per unit time. An algorithm is designed to identify the optimum solution of the proposed model. Numerical examples are included to illustrate the algorithmic procedure and the effect of key parameters is studied to analyze the behavior of the model. Due to globalization of market and increased competition, organizations adopt trade credit policy to boost sales, promote market share, and reduce on-hand stock levels. As a result, trade credit financing plays an important role, as it can serve the source of business financing after bank or other financial institute, in business transactions. In commercial practice, the supplier usually offers a credit period to the retailer such that it allows the retailer to raise the flexibility in capital allocation. Accordingly, inventory models under trade credit have been studied extensively. Goyal [11] first derived an economic order quantity (EOQ) model under the conditions of permissible delay in payments. Aggarwal and Jaggi [2] then extended Goyal's model for deteriorating items. Jamal et al. [23] and Chang and Dye [5] extended Goyal [11] to the case for deterioration and allowable shortages. Teng [33] assumed that selling price is not equal to the purchasing price to modify Goyal [11]. Chung and Huang [10] extended Goyal [11] to consider the case that the units are replenished at a finite rate under permissible delay in payments. Since it is beyond the scope of this paper to discuss all contributions in detail we suggest to refer Soni et al. [30] for a comprehensive and up-to-date review on inventory models under trade credit. The common characteristic in the above mentioned articles is that the supplier offers a delayed payment period to …