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# Dynamic Coordination in Manufacturing and Healthcare Systems

As the manufacturing and healthcare systems becomes more complex, efficiently managing these systems requires cooperation and coordination between different parties. This dissertation examines the coordination issues in a supply chain problem and diagnostic decision making in the healthcare system. Below, we provide a brief description of the problem and results achieved.

With supply chain becoming increasingly extended, the uncertainty in the upstream production process can greatly affect the material flow that aims toward meeting the uncertain demand at the downstream. In Chapter 2, we analyze a two-location system in which the upstream production facility experiences random capacities and the downstream store faces random demands. Instead of decomposing the profit function widely used to treat multi-echelon systems, our approach builds on the notions of stochastic functions, in particular, the stochastic linearity in midpoint and the directional concavity in midpoint, which establishes the concavity and submodularity of the profit functions. In general, it is optimal to follow a two-level state-dependent threshold policy such that an order is issued at a location if and only if the inventory position of that location is below the corresponding threshold. When the salvage values of the ending inventories are linear, the profit function becomes decomposable in the inventory positions at different locations and the optimal threshold policy reduces to the echelon base-stock policy. The effect of production and demand uncertainty on inventory levels depends critically on whether the production capacity is limited or ample in relation to the demand. Only when the capacity is about the demand, the upstream facility holds positive inventory; otherwise, all units produced are immediately shipped to the downstream. We further extend our analysis to situations with general stochastic production functions and with multiple locations.

In Chapter 3, we examine the two-stage supply chain problem (described in Chapter 2) under the decentralized control. We consider two scenarios. In the first scenario, the retail store does not have any supply information including the inventory level at the manufacturing facility. We show that the upstream and downstream can be dynamically coordinated with proper transfer payment defined on local inventories and their own value function in the dynamic recursion. In the second scenario, the demand distribution is unknown to the manufacturing facility as well as the retail store does not know the supply information. We characterize the optimal transfer contracts under which coordination can be achieved, and propose an iterative algorithm to compute the optimal transfer contracts in the decentralized setting. The total profit of the decentralized system under our algorithm is guaranteed to converge to the centralized optimal channel profit for any demand and supply distribution functions.

In Chapter 4, we provide a case study for the framework developed in [1]. The authors study the evaluation and integration of new medical research considering the operational impacts. As a case study, we first describe their two-station queueing control model using the MDP framework. We then present the structural properties of the MDP model. Since multiple classes of patients are considered in the MDP model, it becomes challenging to solve when the the number of patient classes increases. We describe an efficient heuristic algorithm developed by [1] to overcome the curse of dimensionality. We also test the numerical performance of their heuristic algorithm, and find that the largest optimality gap is less than 1.50% among all the experiments.