A simulation-optimization approach for the surgery scheduling problem: a case study considering stochastic surgical times

Abstract

This work studies the scheduling of elective procedures, with stochastic durations, in surgery rooms. Given a set of rooms with limited availability and a set of procedures, it must be decided in which room and when each procedure will be performed. The problem’s objectives are to maximize the use of the operating rooms and to minimize the delays in starting the scheduled surgeries. A simulation-optimization approach is proposed. First, procedures’ durations are modeled as random variables and a set of test percentiles (i.e. it is assumed that all surgeries will last as many minutes as the 75th percentile of its probability density function) is selected. Subsequently, using these durations as a parameter, a greedy randomized adaptive search procedure (GRASP) is run. Consequently, as many solutions as selected test percentiles are generated. Finally, a Monte Carlo simulation is used to estimate three indicators: i) rooms utilization, ii) percentage of surgeries that had delays, and iii) average delay time of scheduled surgeries. The technique was tested by solving the elective procedures scheduling problem in a high-complexity hospital in Bogota. This hospital has 19 operating rooms and 35,000 surgeries performed annually. Currently, the scheduling process is manual. The simulation-optimization proposed approach allowed to determine the relation between utilization rate and delays in the service. As the occupation percentage increases, delay times also augment, implying a reduction of the service level. An average reduction of 5% in delay times entails a reduction between 3% and 9% of operating room occupancy.

Keywords

• Surgery scheduling problem
• GRASP
• Combined simulation and optimization techniques