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Stochastic patient appointment scheduling for chemotherapy

Demir, Nur Banu
Chemotherapy appointment scheduling is a challenging problem due to uncertainty in pre-medication and infusion durations. We formulate a two-stage stochastic mixed integer programming model for chemotherapy appointment scheduling problem under the limited availability and number of nurses, and infusion chairs. The objective is to minimize the expected weighted sum of nurse overtime and patient waiting time. We sampled the pre-medication and infusion durations based on real data of a major oncology hospital. The computation times for the problem are significantly long even for the case of single-scenario problems. In order to strengthen the formulation, valid bounds and symmetry breaking constraints are incorporated. A Progressive Hedging Algorithm is implemented in order to solve the improved formulation. We enhance the algorithm through a penalty update method, cycle detection and variable fixing mechanisms, and linearization of the model objective function. We conduct numerical experiments to compare the progressive hedging algorithm with several scheduling heuristics from the relevant literature. We generate managerial insights related to the impact of the number of nurses and chairs on appointment schedules. Finally, we estimate the value of stochastic solution to assess the significance of considering uncertainty.