An Economic Order Quantity Model with Completely Backordering and Nondecreasing Demand under Two-Level Trade Credit

In the traditional inventory system, it was implicitly assumed that the buyer pays to the seller as soon as he receives the items. In today’s competitive industry, however, the seller usually offers the buyer a delay period to settle the account of the goods. Not only the seller but also the buyer may apply trade credit as a strategic tool to stimulate his customers’ demands. This paper investigates the effects of the latter policy, two-level trade credit, on a retailer’s optimal ordering decisions within the economic order quantity framework and allowable shortages. Unlike most of the previous studies, the demand function of the customers is considered to increase with time. The objective of the retailer’s inventory model is to maximize the profit. The replenishment decisions optimally are obtained using genetic algorithm. Two special cases of the proposed model are discussed and the impacts of parameters on the decision variables are finally investigated. Numerical examples demonstrate the profitability of the developed two-level supply chain with backorder. 1. Introduction Since the introduction of the classical economic order quantity (EOQ) model by Harris [1], many researchers have extended it in several ways. One of the discussed issues in this area is including delay in payment, as an incentive system, in the EOQ or economic production quantity (EPQ) models [2]. According to Piasecki [3] and Molamohamadi et al. [4], different types of delay in payment can be classified as pay as sold, pay as sold during a predefined period, pay after a predefined period, and pay at the next consignment order. In the first type of delay in payment, so-called consignment inventory, the buyer defers paying for the items till they are sold to the customers. The second type refers to the case that the buyer pays off as soon as he sells the items to the customers during a predefined period. At the end of this period, he can either pay for the remaining items in his stock or return the unsold items to the vendor. According to the third type of delay in payment, which is known as trade credit in the literature, the buyer must pay to the vendor at the end of a predetermined period. During the credit period, the buyer sells the items to his customers and accumulates revenue and earns interest. After this period, however, he would be charged a higher interest if the payment is not settled. Based on the fourth type, the payment for each order would be settled at the time of the next replenishment order. Therefore, there is one replenishment cycle delay for each received