| The focus of this thesis is on two fundamental issues in inventory management and control, when to place an order and how much to order. Decisions involving these two issues become complicated when demand is uncertain, and the need to trade off various costs is considered. We study three topics in detail and focus on the structural results, in particular on the structures of optimal policies.; First, we consider a periodic review, single product, single location, finite horizon stochastic inventory model with lost sales and zero lead times. At the beginning of each period the inventory manager decides how many units to purchase at a fixed plus variable ordering cost. During the period, the inventory manager has the discretion of rejecting demands even if there is sufficient on-hand inventory. This allows him/her to keep inventory for future periods. At the end of each period, the inventory manager has the option of placing emergency orders, at a fixed plus variable cost, to satisfy shortages at the end of each period. The objective is to maximize the expected profit which is equal to the expected revenue from sales minus the expected holding and ordering costs. Under mild conditions on the cost structure, we show that (s, S) policies remain optimal in this setting. In addition, we show that a base-stock policy is optimal when both the regular and the emergency setup costs are zero. We also show that emergency orders are never placed if the emergency variable cost is higher than the selling price, and that emergency orders are placed only when the number of units short exceeds a threshold level. Extensive numerical studies are conducted to gain managerial insights and to learn how the optimal policy and the value function behave as the planning horizon grows.; In studying stochastic dynamic programming models, very often one important and interesting topic is the infinite horizon problem. We study the discretionary sale and emergency order infinite horizon problem under both discounted and average cost criteria. Our objective is same as that of the finite horizon problem, i.e., to maximize the total expected profit which is equal to the expected revenue from sales minus the expected holding and ordering costs under both discounted cost criterion and average cost criterion. We prove that the (s, S) policies are optimal for both criteria. In addition, we show that a myopic policy is optimal when both the regular and the emergency setup costs are zero under the discounted cost criterion.; Our third topic is a production/inventory problem with finite capacity. In many production/inventory systems, not only is the production/inventory capacity finite, but the systems are also subject to random production yields that are influenced by factors such as breakdowns, repairs, maintenance, learning, and the introduction of new technologies. The influence of these factors on random yields can be effectively modeled by a Markov chain driven process. We study a single-item, single-location, periodic-review model with finite capacity and Markov modulated demand and supply processes. When demand and supply processes are driven by two independent, discrete-time, finite-state, time-homogeneous Markov chains, we show that a modified, state-dependent, inflated base-stock policy is optimal for both the finite and infinite horizon planning problems. We also show that the finite-horizon solution converges to the infinite-horizon solution. |
