Inventory Model with Fixed and Variable Lead Time Crashing Costs and Controllable Backorder Rate.

In most studies dealing with inventory problems, lead time is treated as fixed. However, in several practical situations, the lead time can be reduced at an added cost, which is called a "crashing cost". By shortening the lead time, we can lower the safety stock, save inventory space, reduce the stock-out loss, and improve the customer service level. In fact, there are some studies that consider lead time reduction. Pan et al. (2002) proposed the crashing cost, which is assumed to be a function of both the order quantity and the reduced lead time. Ouyang et al. (2001) and Lee (2005) proposed the backorder rate, which is assumed to be dependent on the amount of shortages. There are no inventory models that consider both crashing cost in the Pan et al. (2002) and backorder rate in the Lee (2005). In this paper, we present an inventory model in which the order quantity, reorder point, and lead time are regarded as decision variables. The crashing cost is represented as a function of both the reduced lead time and the order quantity, and the backorder rate is assumed to be dependent on the amount of shortages. We develop an algorithm to find near optimal solutions and give numerical examples to demonstrate the effectiveness of our proposed model. Furthermore, a sensitivity analysis is also conducted to identify situations where shortening lead time is valuable. [ABSTRACT FROM AUTHOR]