Two essays on managing inventory and production systems with poisson demand

Abstract

Demand uncertainty usually increases the difficulty in managing inventory and production for system managers. Under a buy-and-sell environment, a desirable inventory replenishment policy, which achieves balanced trade-offs between inventory cost and order processing cost, can achieve a good system performance. Under a make-to-order environment, by contrast, no inventory is kept, and the production decisions play an important role in system control especially when the customers are delay-sensitive. In this thesis, we study optimization models under a buy-and-sell setting and a make-to-order setting with a Poisson demand process. It comprises two essays. The first essay focuses on the inventory control in a buy-and-sell environment. Specifically, we consider the long-run average profit maximization problem in a single-item inventory system under continuous review. We assume constant replenishment lead time and partial backlogging of unmet demand. The special case with complete backlogging, which is a classical problem, is revisited first. The original objective function is transformed into a new one, namely "effective profit." By exploring the optimal policy under this new objective function, we show that the (s, S) policy is optimal to the original problem and can be obtained by binary search algorithms. Furthermore, this new approach enables us to obtain near closed-form solutions and nice economic interpretations of the optimal reorder point, which are obtained for the first time in the literature. This new method is then extended to the general model with partial backlogging, and a well-performed heuristic is developed to determine the (s, S) policy and the average profit. The second essay focuses on the production control in a make-to-order environment. The two main features are fixed set-up cost and delay-sensitive customers. The latter is incorporated into the make-to-order system control for the first time. The production system is modeled as an M/M/1 queue with N-policy, where N is the waiting-customer-order threshold which triggers the production and is the control variable. Delay-sensitive customers make decisions on staying or leaving according to their expected waiting times, which depend on the information provided. Two information scenarios are considered, depending on whether the queue length of customer orders is observable or not. Customers' equilibrium strategies are obtained, which is a complement to the literature on queueing systems. The average cost function with strategic customers is obtained in closed form, which is either convex or piecewise convex in N when the waiting list of customer orders is not observable, but may not be convex when the waiting list is observable. The impact of strategic customer behavior on the average cost and the value of revealed information is demonstrated via numerical studies. We observe that if the customers are impatient, the system manager should be more cautious in making decisions on the choice of the threshold N and on whether revealing the information on the waiting list of customer orders.