Hao Zhang

This dissertation addresses two applications of dynamic programming and provides insights for efficiently managing operational systems. The first essay (in Chapter 2) investigates a classic problem in the machine maintenance literature, where the machine has one observable state, obvious failure, and two hidden states, good and bad, and will deteriorate over time. We can choose from three actions. Production is minimal maintenance. Inspection is more expensive but enables us to avoid a high mandatory replacement cost by conducting a preventive replacement. When the machine is at an obvious failure state, we have to do a mandatory replacement. By the dual method introduced in Zhang (2010), we are able to derive the optimal solution without a time-consuming iteration and also identify an elegant optimal policy structure. We can calculate the optimal solution in one step and use the optimal policy structure to gain managerial insights. The second essay (in Chapter 3) studies a real-life resource allocation problem. BC Housing is a government agency that provides subsidized housing for low-income households. Applicants for subsidized housing are allowed to select a list of housing communities they want to move to, instead of individual housing units, without preference. We set up a dynamic programming model that helps BC Housing to accommodate as many moving requests as possible. The moving requests can come from those who are outside of the housing system, or the current tenants of the housing system who want to move to another location within the system. The one-period problem can be formulated as a combinatorial problem, whose integer solution can be found by linear programming. The multi-period problem, however, suffers from the curse of dimensionality and for this case we investigate two heuristic algorithms, a myopic algorithm and a linear approximation algorithm. We test them against the clairvoyant solution, which is an upper bound of the optimal solution. Both algorithms work well with the data from BC Housing, and their worst-case performances are only about 3% worse than the clairvoyant solution.

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