Optimal reorder point inventory models with variable lead time and backorder discount considerations

Lead time reduction has been one of the major factors in the successful implementation of the popular just-in-time inventory system. In many practical situations, this controllable lead time can be decomposed into several components, each having a crashing cost for the reduced lead time and the associated crashing expenses contain a fixed cost and a variable cost per unit product. If an item is out of stock in an inventory system in which shortage is allowed, the supplier may offer a negotiable price discount to the loyal, patient and captive customers to compensate for the inconvenience of backordering. This paper studies the integrated inventory systems with the objective of simultaneously optimizing the order quantity, lead time, backordering and reorder point. There are two inventory models proposed in the paper, one with normally distributed demand, and another with generally distributed demand. Numerical examples are included to illustrate the procedures of the algorithms.