Essays on Inventory Management, Capacity Management, and Resource-sharing Systems

Book excerpt: This dissertation consists of three essays, each focusing on one of the following three important topics in operations management: inventory management, capacity management, and management of resource-sharing systems. These topics are each summarized below. In the first essay, we investigate the following integrality question for inventory control on distribution systems: Given integral demands, does an integral optimal policy exist? We show that integrality holds under deterministic demand, but fails to hold under stochastic demand. In distribution systems with stochastic demand, we identify three factors that influence the gap between integral and real optimal policies: shipping cost variation across time, holding cost difference across stages, and economies of scale. We then obtain a tight worst-case bound for the gap, which captures the impact of all these factors. In the second essay, we investigate the computational complexity of determining the capacity of a process, a fundamental concept in Operations Management. We show that it is hard to calculate process capacity exactly and, furthermore, also hard to efficiently approximate it to within a reasonable factor; e.g., within any constant factor. These results are based on a novel characterization, which we establish, of process capacity that relates it to the fractional chromatic number of an associated graph. We also show that capacity can be efficiently computed for processes for which the collaboration graph is a perfect graph. The third essay addresses an important problem in resource-sharing systems. We study the minimum-scrip rule in such a system: whenever a service request arises, among those who volunteer and are able to provide service, the one with the least number of scrips (also known as coupons) is selected to provide service. Under mild assumptions, we show that everybody in the system being always willing to provide service is a Nash Equilibrium under the minimum-scrip rule. This suggests that the minimum scrip rule can lead to a high level of social welfare.