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A network flow approach for tactical resource planning in outpatient clinics

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Abstract

This paper introduces a deterministic model to plan the physician requirements for outpatient clinics to achieve service targets for the appointment lead-times of patients. The Ministry of Health of Singapore has established targets for the median, 95th percentile, and 100th percentile of appointment lead-times for patients, since long appointment postponements are regarded as being unacceptable for health care services. The study is to match the capacity of the healthcare providers to the patient demand for a re-entry system, subject to restrictions on the appointment lead-times for patients. We propose a mixed-integer programming model for planning capacity with the minimization of the maximum required capacity as its objective. In the model we assume a finite planning horizon, deterministic arrivals, multiple types of patients, identical physicians, and dependent demand between types of patients. We solve this model with a Branch and Cut algorithm. We test the model with numerical experiments using real data from the chosen specialty at the outpatient clinic of the studied hospital. The results show the value of the proposed model via a systematic push-pull mechanism in scheduling patients’ requests to minimize the objective. The clinic should use one of the appointment lead-time targets to determine the patients’ appointment dates. Finally, from the sensitivity analyses we demonstrate that the objective is negatively correlated with first-visit patients’ appointment lead-time targets, the discharge rates, and the re-visit patients’ mean appointment lead-time; we find a positive correlation between the first-visit patients’ mean appointment lead-time and the appointment lead-time targets.

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Acknowledgments

The authors are grateful to Dr. Jamie Mervyn Lim of Tan Tock Seng Hospital, Singapore for providing us the opportunity to study this interesting field. The authors would like to thank the hospital’s administrators for providing data and necessary help to conduct this research.

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Authors and Affiliations

  1. Manufacturing Systems and Technology Program, Singapore-MIT Alliance, Nanyang Technological University, 65 Nanyang Drive, Singapore, 637460, Singapore

    Thu Ba T. Nguyen, Appa Iyer Sivakumar & Stephen C. Graves

  2. School of Mechanical and Aerospace Engineering, Nanyang Technological University, 65 Nanyang Drive, Singapore, 637460, Singapore

    Appa Iyer Sivakumar

  3. Department of Mechanical Engineering and Engineering Systems, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139, USA

    Stephen C. Graves

Authors
  1. Thu Ba T. Nguyen
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  2. Appa Iyer Sivakumar
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  3. Stephen C. Graves
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Corresponding author

Correspondence to Thu Ba T. Nguyen.

Appendix

Appendix

Table 7 Sets of the appointment lead-time targets
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Nguyen, T.B.T., Sivakumar, A.I. & Graves, S.C. A network flow approach for tactical resource planning in outpatient clinics. Health Care Manag Sci 18, 124–136 (2015). https://doi.org/10.1007/s10729-014-9284-0

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  • DOI: https://doi.org/10.1007/s10729-014-9284-0

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