AN ECONOMIC ORDER QUANTITY FOR A DETERIORATING ITEM WITH CONSIDERING LEAD TIME CRASHING COST AS A FUNCTION OF ORDER QUANTITY

In this paper, an economic order quantity (EOQ) model for a deteriorating item has been investigated. Considering a constant rate of deterioration, a portion of order is certainly decayed and thus is lost during lead time; that is what the firm receives is less than the order quantity. Thus purchase cost of these lost orders and also the related deterioration cost is imposed to the firm. On the other side, with a shorter lead time, less deterioration occurs. However an additional crashing cost must be paid for shortening the lead time. Thus, the objective function includes ordering cost, purchase cost, holding cost, decaying cost and crashing cost and the aim of this problem is to find the best trade-off between crashing cost, deterioration cost and also purchase cost of the decayed products; such that the total costs per unit of time is minimized. In the mentioned problem, lead time is considered as a decision variable and is assumed to have a number of components, each having a different crashing cost. Crashing cost depends both on the order quantity and the reduced lead time. Thus, a piecewise linear function of both the reduced lead time and the order quantity is used in our modelling. For solving the problem, the first derivations of variables have been taken and an algorithm is proposed. A numerical example has been solved and the related crashing cost and total cost has been shown. Finally, sensitivity analysis of key parameters has been performed. Based on these results, as deterioration rate of stock inventory increases, the model tries to decrease the order quantity in order to decrease the decayed items. As deterioration rate of on the way inventory increases, the model tries to prevent decaying costs from growing too much by crashing lead time. Thus, the model tries to increase the order quantity in order to prevent crashing cost from increasing too much. Also, total costs will increase as deterioration rates increases.