Computational procedure of optimal inventory model involving controllable backorder rate and variable lead time with defective units

This paper investigates the backorder rate inventory problem with defective units. In practice, the uncertainties of customer’s demand and backorder rate are inherent; hence, backorder rate and customer’s demand are not constant. In this study, we assume that the backorder rate is dependent on the amount of shortages and backorder price discounts, and the lead time demand follows a mixture of distributions. Here, we derive the mixture inventory system, and construct the algorithm procedure to optimize the order quantity, backorder price discount and lead time. Numerical examples are also included to illustrate the results.