Optimization Models for Scheduling and Rescheduling Elective Surgery Patients Under the Constraint of Downstream Units

Abstract

Healthcare is a unique industry in terms of the associated requirements and services provided to patients. Currently, healthcare industry is facing challenges of reducing the cost and improving the quality and accessibility of service. Operating room is one of the biggest major cost and revenue centers in any healthcare facility. In this study, we develop optimization models and the corresponding solution strategies for addressing the problem of scheduling and rescheduling of the elective patients for surgical operations in the operating room. In the first stage, scheduling of the elective patients based on the availability of the resources is optimized. The resources considered in the study are the availability of the operating rooms, surgical teams, and the beds/equipment in the downstream post anesthesia care units (PACUs). Discrete distributions governing surgical durations for selected surgical specialties are developed for representing variability for duration of surgery. Based on the distributions, a stochastic mathematical programming model is developed. It is indicated that with the increase of problem sizes, the model may not be solved by using a leading commercial solver for optimization problems. As a result, a heuristic solution approach based on genetic algorithm is also developed. It is found out that the genetic algorithm provides close results as compared to the commercial solver in terms of solution quality. For large problem sizes, where the commercial solver is unable to solve the problem due to the memory restrictions, the genetic algorithm based approach is able to find a solution within a reasonable amount of computation time. In the second stage, the rescheduling of the elective patients due to the sudden arrival of the emergency patients is considered. A mathematical programming model for minimizing the costs related with expanding the current capacity and disruption caused by the inclusion of the emergency patient is developed. Also, two different solution approaches are brought forward, one with using the commercial solver, and the other based on genetic algorithm. Genetic algorithm based approach can always make efficient decision regarding whether to accept the emergency patients and how to minimize the reshuffling effort of the original elective surgery schedule.