Essays in stochastic inventory management
Student thesis: Doctoral Thesis
Related Research Unit(s)
This thesis consists of three essays. The first essay is on optimal production, pricing and substitution policies in continuous review production-inventory systems. We consider the optimal production, pricing, and substitution policies of a continuous-review production-inventory system with two products: a high-end product and a low-end product. Each product has its associated customer stream; however, the demands for the low-end product may be satisfied by the high-end product. The demand rates for the two products are price-dependent. A control policy specifies when to produce for each product, when to use the high-end product as substitute to satisfy low-end demand, and how to set the optimal prices. We formulate the problem as a Markov decision process and characterize the structure of the optimal control policy. We show that a base-stock production policy is optimal, but the optimal base-stock level for each product depends on the inventory level of the other product and it features a monotonic property. We also show that the optimal substitution policy is an echelon rationing policy. We find that the optimal prices can be either decreasing or increasing in the inventory levels, depending on the forms of demand functions. Furthermore, we use numerical experiments to investigate the impact of different system characteristics on the benefits of substitution and dynamic pricing. Finally, we investigate when the dynamic pricing strategy and the substitution strategy are complementary or supplementary. The second essay is on optimal policies for nested assemble-to-order (ATO) systems. We investigate the optimal allocation and ordering policy for a nested assemble-to-order inventory system. In such a system, the central decision is how to fulfill demands of different products based on the inventory levels of different components. Under our setting, we first show that a priority allocation policy is optimal such that it is always optimal to first fulfill the demand of the product with a higher backordering cost. We then show the optimal allocation policy can be described by either a static rationing level policy or an iterated static rationing level policy with state-independent rationing levels for all products. In addition, we find that that for stationary data, a simple base-stock policy is optimal for each component. The third essay is on inventory control with all-units discounts. All-units discounts refer to the retail contracts whereby sellers get a discount for every unit from a supplier if the purchase amount is above or equal to a quantity threshold. However, in general the optimal procurement strategy under all-units discounts for a seller could be complicated due to the structure of the ordering costs. By assuming log-concave demand and appropriate cost parameters, for the lost-sales inventory problem with all-units discounts we show that the objective functions are quasiconvex and a generalized jump base-stock policy is optimal. In addition, for general cost parameters, we characterize the structure of the optimal policy except for a bounded interval. We also numerically show that the generalized jump base-stock policy is robust to general cost parameters (with the performance gap less than 1%). Finally, we extend our results to the case of quantity discounts with batch ordering and systems with capacity limits.
- Inventory control, Statistical methods, Stochastic control theory