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Scheduling elective surgeries: the tradeoff among bed capacity, waiting patients and operating room utilization using goal programming

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Abstract

Scheduling of surgeries in the operating rooms under limited competing resources such as surgical and nursing staff, anesthesiologist, medical equipment, and recovery beds in surgical wards is a complicated process. A well-designed schedule should be concerned with the welfare of the entire system by allocating the available resources in an efficient and effective manner. In this paper, we develop an integer linear programming model in a manner useful for multiple goals for optimally scheduling elective surgeries based on the availability of surgeons and operating rooms over a time horizon. In particular, the model is concerned with the minimization of the following important goals: (1) the anticipated number of patients waiting for service; (2) the underutilization of operating room time; (3) the maximum expected number of patients in the recovery unit; and (4) the expected range (the difference between maximum and minimum expected number) of patients in the recovery unit. We develop two goal programming (GP) models: lexicographic GP model and weighted GP model. The lexicographic GP model schedules operating rooms when various preemptive priority levels are given to these four goals. A numerical study is conducted to illustrate the optimal master-surgery schedule obtained from the models. The numerical results demonstrate that when the available number of surgeons and operating rooms is known without error over the planning horizon, the proposed models can produce good schedules and priority levels and preference weights of four goals affect the resulting schedules. The results quantify the tradeoffs that must take place as the preemptive-weights of the four goals are changed.

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Acknowledgments

[The corresponding author deleted this section to protect author information]

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Conflicts of interest

Disclosure of potential conflicts of interest

Funding

The research of M.F. Baki has been partially supported by Research and Teaching Innovation Fund (RTIF), Odette School of Business, University of Windsor (Grant no. 809335) and Natural Sciences and Engineering Research Council (Grant No. 813000). The research of the Xiangyong Li has been partially supported by the Natural Science Foundation of China (Grant no. 71101105, 71432007), Program for New Century Excellent Talents in University (Grant no. NCET-13-0424), research fund for doctoral program of higher education of China (Grant no. 20110072120013), Shanghai philosophical and social science program (Grant no. 2011EGL004), and the Fundamental Research Funds for the Central Universities. Thanks are due to three referees for comments that improved the manuscript.

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Authors and Affiliations

  1. School of Economics and Management, Tongji University, Shanghai, 200092, China

    Xiangyong Li

  2. Rice Lake Canada ULC, Calgary, AB, T2G 5C3, Canada

    N. Rafaliya

  3. Odette School of Business, University of Windsor, 401 Sunset Avenue, Windsor, ON, N9B 3P4, Canada

    M. Fazle Baki & Ben A. Chaouch

Authors
  1. Xiangyong Li
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  2. N. Rafaliya
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  3. M. Fazle Baki
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  4. Ben A. Chaouch
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Corresponding author

Correspondence to Xiangyong Li.

Appendix: Instance data

Appendix: Instance data

Tables 8, 9, 10, and 11 show the probability that a patient of surgery team stays in the recovery area for different surgical speciality. As stated earlier, patients of each surgery team stay in the recovery unit for at most 5 days.

Table 8 Data of p il for instance 1
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Table 9 Data of p il for instance 2
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Table 10 Data of p il for instance 3
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Table 11 Data of p il for instance 4
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Li, X., Rafaliya, N., Baki, M.F. et al. Scheduling elective surgeries: the tradeoff among bed capacity, waiting patients and operating room utilization using goal programming. Health Care Manag Sci 20, 33–54 (2017). https://doi.org/10.1007/s10729-015-9334-2

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  • DOI: https://doi.org/10.1007/s10729-015-9334-2

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