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

Official URL: http://dx.doi.org/10.1080/24725854.2019.1628372

This paper studies the stochastic operating room (OR) scheduling problem integrated by Post-Anesthesia Care Unit (PACU), named 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 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 constructive heuristic and meta-heuristic algorithms 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 OTR problems. 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.