Chance-Constrained Surgery Planning Under Conditions of Limited and Ambiguous Data

Surgery planning include decisions of which operating rooms (ORs) to open, allocation of surgeries to ORs, sequence and time to start each surgery. The decisions are often made under uncertain surgery durations with limited data that leads to unknown distributional information; furthermore, cost data for criteria such as overtime and surgery delays are often difficult or impossible to estimate in practice. In this paper, we consider a distributionally robust (DR) formulation that recognizes practical limitations on data availability and obviates the need to provide accurate cost parameters for surgery planning. We minimize the cost of opening ORs for completing a set of surgeries, subject to a joint DR chance constraint on OR overtime. We use statistical $\phi$-divergence measures to build an ambiguity set of possible distributions of random surgery durations, and derive a branch-and-cut algorithm for optimizing a mixed-integer linear programming reformulation of the DR chance-constrained model formulated based on a finite sample of scenarios. We compute instances generated from real hospital-based surgery data, demonstrate the computational efficacy of our approach, and provide insights for DR surgery planning.