Efficient optimization algorithms for surgical scheduling under uncertainty

In this paper, we develop a stochastic optimization model for a surgical scheduling problem considering a single operating room. We arrange a set of elective surgeries into appropriate time blocks, and determine their planned start time and specific sequence. Due to the complexity of the original formulation, we reformulate our model as a two-stage mixed-integer problem. We consider the planning decision in the first stage and the sequencing decision in the second stage (based on the first one). The goal of this paper is to obtain a nearly optimal schedule in reasonable computational time. The term “optimal” is defined as the lowest surgically related cost while achieving the given threshold with respect to some specific deterministic or stochastic performance measures. The optimization model involves expected and probabilistic formulations that are analytically intractable. This implies that traditional mathematical programming techniques cannot be used directly. Therefore, we propose adapted rapid-screening and stochastic-approximation algorithms to deal with the first-stage and the second-stage problems, respectively. In both algorithms, we can apply either the Laplace transform or simulation methods to either evaluate or estimate the desired performance measures. The experimental results demonstrate that the proposed algorithms are more favorable compared to existing approaches.