| This thesis models a two-stage supply chain where the upstream stage (stage 2) always meets demand from the downstream stage (stage 1). Demand is stochastic; hence, shortages will occasionally occur at stage 2. Stage 2 must fill these shortages by expediting, using overtime production and/or premium freight shipments. We derive optimal inventory control policies under decentralized, centralized, and coordinated control and perform numerical analysis to compare the results.; Under decentralized control, stage I ignores stage 2 and follows a simple base-stock policy; stage 2 also follows a simple base-stock policy if there is no setup cost for regular production. When we include this setup cost at stage 2, two decisions must be made: how much to produce during regular production and how much to produce during overtime production. We show that the optimal regular production policy is an (s, S) policy and that the optimal overtime production policy depends on the cost parameters.; Under centralized control, the two stages work together to minimize system costs. By substituting system variables for stage 2 variables and relaxing some constraints, we show that the optimal policy at stage 1 has two order-up-to levels and depends on the available system inventory. We also show that the optimal policy for the system is a base-stock policy and the optimal policy for stage 2 is to ensure the system base-stock level is achieved.; To coordinate the two stages, we develop two contracts. Both contracts depend on a two-tiered wholesale cost and a linear transfer payment. Contract A achieves system optimality, but requires the two stages to share cost information. Without sharing cost information, Contract B achieves near-optimality for the system (optimality for the average cost case). Under both contracts, an appropriate transfer payment may be negotiated that benefits both stages.; We perform numerical analysis to compare the supply chain under different forms of control. We show that centralized control may affect significant savings over decentralized control, particularly if the demand variation, holding costs, or expediting costs are high. We also show that Contract B yields nearly optimal results, particularly if the discount factor is close to one. |
