Stochastic Optimization Methods for Outpatient Appointment Scheduling & COVID Testing Under Limited Testing Capacity

This talk comprises of two parts based on two unrelated research topics:

Part 1 deals with outpatient appointment scheduling problems when patients are unpunctual. We first look at data regarding patient unpunctuality and examine distributional factors such as sources of heterogeneity. When considering an optimization model, we consider a weighed cost of the total queue wait time, doctor idle time, and clinic overtime. We consider two modelling approaches. The first approach considers heterogeneous patient distributions in both service time and unpunctuality along with multiple service disciplines. Due to the complexity of the system and nonconvexity of the objective under more complicated assumptions, we propose several heuristics for solving the problem. The second approach examines the fluid-limits of the arrival-departure process and finds the queue-idle process is a solution to the one-dimensional Skorokhod problem associated with the arrival-departure process. Using this formulation, we derive a fluid control problem that can be solved numerically as a quadratic program.

Part 2 looks at the problem of optimally choosing when to use COVID tests for a single patient when the supply of tests is limited. We consider an underlying SIR Markov model for the patient that is unobservable; instead, the only observations that are made are whether the patient is exhibiting symptoms at any point in time or whether a used test returns a negative or positive result. We propose a partially-observed Markov decision process (POMDP) for deciding when to use tests relative to the probability of being in each state. We are able to analytically derive an optimal policy for an arbitrary number of tests under the model assumptions.

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