Ordering Cost Reduction in Inventory Model with Defective Items and Backorder Price Discount

In the real market, as unsatisfied demands occur, the longer the length of lead time is, the smaller the proportion of backorder would be. In order to make up for the inconvenience and even the losses of royal and patient customers, the supplier may offer a backorder price discount to secure orders during the shortage period. Also, ordering policies determined by conventional inventory models may be inappropriate for the situation in which an arrival lot contains some defective items. To compensate for the inconvenience of backordering and to secure orders, the supplier may offer a price discount on the stockout item. The purpose of this study is to explore a coordinated inventory model including defective arrivals by allowing the backorder price discount and ordering cost as decision variables. There are two inventory models proposed in this paper, one with normally distributed demand and another with distribution free demand. A computer code using the software Matlab 7.0 is developed to find the optimal solution and present numerical examples to illustrate the models. The results in the numerical examples indicate that the savings of the total cost are realized through ordering cost reduction and backorder price discount. 1. Introduction In real life, the occurrence of shortage in an inventory system is phenomenon. Under the most market behaviors, we can often observe that many products of famous brands or fashionable goods such as certain brand gum shoes, hi-fi equipment, and clothes may lead to a situation in which customers may prefer to wait for backorders while shortages occur. Besides the product, the image of selling shop is one of the potential factors that will motivate the customers intention of backorders. To establish the good image and enhance customers’ loyalty, the selling shop could invest in upgrading the servicing facilities, maintaining the high quality of selling products and spending money on advertisement. Other endeavors, such as mailing the greeting card and providing free gift, can also be done to establish a good relationship with their customers. We note that such type of activities is not certainly free. Naturally, an extra-added cost must be spent for these efforts. Further it is expected to have a result to reduce the shortage cost of lost-sales and the total expected annual cost. Under the situation, for a vendor, how to control an appropriate length of lead time to determine a target value of backorder rate so as to minimize the relevant inventory cost and increase the competitive edge in business is worth discussing.