Operating room scheduling problem under uncertainty: Application of continuous phase-type distributions

This article studies the stochastic Operating Room (OR) scheduling problem integrated with a Post-Anesthesia Care Unit (PACU), the overall problem is called the Operating Theater Room (OTR) problem. Due to the inherent uncertainty in surgery duration and its consecutive PACU time, the completion time of a patient should be modeled as the sum of a number of random variables. Some researchers have proposed the use of the normal distribution for its well-known additive property, but there are questions regarding its fitting adequacy to real OTR data, which tends to be asymmetric with a long tail. We propose to estimate the surgery and PACU times with the family of Continuous PHase-type (CPH) distributions, which provides both fitting adequacy and additive property. We first compute the completion time of each patient analytically and compare the results with normal and lognormal distributions on a series of real OTR datasets. Then, we develop a search algorithm embedding a constructive heuristic and a meta-heuristic algorithm as a sequence generator engine for the patients, and apply the CPH distribution as a chance constraint to eventually find the schedule of each sequence in the OTR problem. The best algorithm among several tested constructive heuristic algorithms is used as the neighborhood structure of meta-heuristic algorithms. We finally construct a numerical example of OTR problem to illustrate the application of the proposed algorithm.