Inventory Control and Demand Distribution Characterization
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This thesis studies three problems related to inventory control. The first problem is motivated by the need to eliminate the bullwhip effect in a supply chain. An important source of this effect is the inventory control policy, which is originally designed to smooth production in response to demand variation along the supply chain arising from the customers. To address this issue, we propose an estimation method based on the control variate technique. A byproduct of this approach is a stabilizing inventory control policy. We evaluate the effectiveness of the proposed method using the models from the literature. Generally, the derivation of the inventory policies requires the knowledge of the specific demand distribution. Unfortunately, in several cases the demand is not observable in a direct way. The second problem is motivated by a practical application where only partial demand information is observable. Towards this end we derive estimators of the first two moments of the (daily) demand by means of the renewal theoretical concepts. We also propose a regression-based approximation to improve the quality of the estimators. A series of numerical studies are carried out to evaluate the accuracy and precision of the estimators and to investigate the impact of the estimation on the optimality of the inventory policies. The last part of this dissertation studies a periodic-review inventory system with regular and emergency orders. Emergency orders, characterized by shorter lead-time, higher ordering cost and higher setup cost, are placed when the inventory level becomes critically low. Based on our assumptions, we formulate a dynamic programming model and prove the optimality of state-dependent sS type polices for both emergency and regular orders. We also derive analytic properties of the optimal policies. We gain some managerial insights into the optimal policies and cost performance from numerical studies.