A Robust Optimization Approach for Surgical Cases Assignment Problem with Uncertain Service Time and Surgery Deadline

We study a surgical cases assignment problem (SSA) of determining whether patients can be operated in the planning period and, if so, to determine the surgery date and location with the objective of maximizing the revenue of surgical suite. A major difficulty stems from the fact that the service time for each surgery is an uncertain parameter, and even small deviations occur between the actual and estimated durations of activities related to surgery processes, the assignment may become unfeasible. We firstly build a linear hybrid integer programming model, and then describe a two-stage stochastic model for the surgical cases assignment problem with surgery deadline. To enhance the robustness of the solution, we introduces a set of interval parameters and the conservatism parameter to describe the surgery duration for each patient, establishes a robust counterpart model. We adopt a max-min criterion, whereby the revenue function is maximized against the worst surgery duration occurrence in the uncertain set. To solve the max-min SSA problem we employ the dual theory and transfer the max-min into a normal linear hybrid integer model. We apply our general model to compute a real-life instance and illustrate the influence of conservatism parameter on the operating cost, income and revenue in surgical suites. We also find that the robust method performs much faster than the stochastic model, and contrasting the results for the issue without considering surgery deadline, the issue with regard to has a profit decrease within 11%.