Distributionally robust multi-period operating room scheduling with multiple surgical disciplines under uncertain surgery durations

We study operating room (OR) scheduling with multiple surgical disciplines under uncertain surgery durations, considering time-dependent health urgency, where patient health deteriorates with the waiting time. The problem involves the opening of ORs, assignment of ORs to surgical disciplines, and assignment of surgeries (mandatory and optional surgeries) to ORs over a planning horizon, subject to the discipline-to-OR, discipline parallelism, discipline workload, and surgery deadline restrictions, and OR session capacity chance constraints. To characterize the uncertainty of surgery durations, we introduce a data-driven distributionally ambiguity set based on real surgery data, which incorporates the empirical mean and covariance. We formulate the problem as a distributionally robust chance-constrained model, where distributionally robust chance constraints are imposed on the OR session capacity. To solve the model, we transform it into a tractable mixed-integer linear program, and propose a tailored branch-and-price-and-cut algorithm based on a bounded bidirectional dynamic programming algorithm for the pricing subproblems. We use the limited-node-memory subset row inequalities to enhance the lower bounds found by column generation and apply two enhancement techniques to enhance computing efficiency. We conduct extensive numerical studies on instances generated from real surgery data. The results illustrate the computational superiority of our algorithm to the CPLEX solver, and highlight the benefits of our model over its stochastic programming counterpart and two heuristic scheduling rules. We also perform sensitivity analysis to generate managerial insights from the analytical findings.