Stochastic chance-constrained surgery planning model and algorithm

To address the uncertainty of surgery duration, this paper investigates surgery planning scheduling problem with multiple servers, which proposes chance constraints of operating rooms overtime to guarantee the surgery durations of patients is no more than the time limit of operating rooms with a high probability. A stochastic chance-constrained program is proposed to determine which operating rooms to operate, and surgeries to operating rooms allocation. Based on a finite support set of the surgery duration, this paper introduces 0-1 variables to formulate the chance constraints, and derives 0-1 integer linear program counterpart. To improve the efficiency of the model, this paper presents two classes of valid inequalities and uses the longest path algorithm to separate the second class of valid inequalities, which are implemented in a branch-and-cut framework. Computational experiments based on real-life data from hospital in Beijing are conducted to verify the algorithm performance and determine the optimal planning scheme, so as to take full utilization of healthcare resources, i.e. operating rooms.