OPTIMAL AND APPROXIMATE POLICIES FOR PERIODIC REVIEW INVENTORY SYSTEMS: THE CASE OF ORDER CROSSOVER AND MULTIPLE SUPPLY OPTIONS

This dissertation explores two main topics within the area of periodic review inventory systems. These are: (1) periodic review inventory systems under order crossover and (2) periodic review inventory systems with multiple supply options. The main focus in this dissertation is investigating optimal and approximate policies and comparing the cost performance of these policies to other sub-optimal order up-to form of base-stock policies. A majority of the work done till date in the area of inventory systems modeling and analysis has ignored or circumvented the issue of order crossover. Order crossover occurs whenever replenishment orders do not arrive in the same sequence in which they were placed. It is observed that of late there are a number of factors which make order crossover more likely than in the past. By ignoring order crossover, the traditional single cycle approach used to model inventory systems and set inventory policies overstates shortages. First we consider a model with a single supply source/option and formulate the order crossover problem as a Markov Decision Process and investigate the optimal policy. Through computational experiments, we show that considering order crossover in setting the inventory policy results in a potential reduction in inventory levels and inventory costs due to a lowering of the order-up-to level, if the inventory policy is an order-up-to-level form of policy. We also propose approximate policies and demonstrate through simulation that these policies perform substantially better than, or at least perform as well as, the sub-optimal order-up-to base-stock form of policies and are easier to compute and implement as compared to the optimal policy.Further, we extend the order crossover problem to include two supply sources/ options having stochastic supply lead times. The supply options are characterized by a faster source (mode) of supply which is usually more expensive and a slower source (mode) of supply which is comparatively more economical. Under such a scenario, the decision maker is faced with the task of making a choice between the two supply (mode) options or using a combination of both these supply (mode) options. We investigate the optimal and near-optimal inventory policies under such scenarios and compute the performance of these policies under various demand lead-time distributions. Through numerical experiments, we show that for a vast majority of problem instances, not considering the use of the fast supply option can result in sub-optimal policies and significant additional costs as high as 21-23 percent, even when the cost of using the fast supply option is ten times more than the cost of using the slow supply option. Even when the cost of using the fast supply option is substantially higher, (twenty times more expensive), a significant portion of the orders are placed using this option, especially when stock-out costs are high