A distributionally robust optimization approach for stochastic elective surgery scheduling with limited intensive care unit capacity

In this paper, we study the decision process of assigning elective surgery patients to available surgical blocks in multiple operating rooms (OR) under random surgery durations, random postoperative length-of-stay in the intensive care unit (ICU), and limited capacity of ICU. The probability distributions of random parameters are assumed to be ambiguous, and only the mean values and ranges are known. We propose a distributionally robust elective surgery scheduling (DRESS) model that seeks optimal surgery scheduling decisions to minimize the cost of performing and postponing surgeries and the worst-case expected costs associated with overtime and idle time of ORs and lack of ICU capacity (which causes premature discharges or transfers). We evaluate the worst-case over a family of distributions characterized by the known mean values and ranges of random parameters. We leverage the separability of DRESS formulation in deriving an exact mixed-integer nonlinear programming reformulation. We linearize and derive a family of symmetry breaking inequalities to improve the solvability of the reformulation using an adapted column-and-constraint generation algorithm. Finally, we conduct extensive numerical experiments that demonstrate the superior performance of our DR approach as compared to the stochastic programming approach, and provide insights into DRESS.