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Minimax c th percentile of makespan in surgical scheduling
Vikas Agrawal1, Aber Elsaleiby2, Yue Zhang3
1Management and Decision Sciences Department, Jacksonville University, Jacksonville, FL, USA.
Abstract:
In this paper, we address the problem of finding an assignment of n surgeries to be performed in one of m parallel identical operating rooms (ORs), given each surgery has a stochastic duration with a known mean and standard deviation. The objective is to minimise the maximum of the c percentile of makespan of any OR. We formulate this problem as a nonlinear integer program, and small-sized instances are solved using the GAMS BONMIN solver. We develop a greedy heuristic and a genetic algorithm procedure for solving large-sized instances. Using real data from a major U.S. teaching hospital and benchmarking datasets from the literature, we report on the performance of the heuristics as compared to the GAMS BONMIN solver.
Insights
This study optimizes surgery scheduling in operating rooms (ORs) to minimize patient wait times. Developed algorithms efficiently assign surgeries, improving resource allocation in healthcare settings.
Area of Science:
- Operations Research
- Healthcare Management
- Applied Mathematics
Background:
- Operating room (OR) scheduling is complex due to stochastic surgery durations.
- Efficient OR utilization is critical for healthcare system performance and patient outcomes.
- Minimizing makespan percentiles is a key objective in OR management.
Purpose of the Study:
- To develop and evaluate methods for assigning surgeries to parallel operating rooms.
- To minimize the maximum of the c-percentile of the makespan across all operating rooms.
- To provide efficient solutions for large-scale OR scheduling problems.
Main Methods:
- Formulation as a nonlinear integer programming problem.
- Utilized the GAMS BONMIN solver for small instances.
- Developed a greedy heuristic and a genetic algorithm for large instances.
Main Results:
- The proposed heuristic and genetic algorithm effectively solve large-scale OR scheduling problems.
- Performance was validated using real-world data from a major U.S. teaching hospital.
- Comparison with the GAMS BONMIN solver demonstrated the efficacy of the developed methods.
Conclusions:
- The study presents effective computational methods for optimizing operating room assignments.
- The findings contribute to improved efficiency and resource management in surgical scheduling.
- The developed algorithms offer practical solutions for complex healthcare logistics.
