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Extended open shop scheduling with resource constraints: Appointment scheduling for integrated practice units

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  • Pengfei Zhang
  • Jonathan F. Bard
  • Douglas J. Morrice
  • Karl M. Koenig

Abstract

An Integrated Practice Unit (IPU) is a new approach to outpatient care in which a co-located multidisciplinary team of clinicians, technicians, and staff provide treatment in a single patient visit. This article presents a new integer programming model for an extended open shop problem with application to clinic appointment scheduling for IPUs. The advantages of the new model are discussed and several valid inequalities are introduced to tighten the linear programming relaxation. The objective of the problem is to minimize a combination of makespan and total job processing time, or in terms of an IPU, to minimize a combination of closing time and total patient waiting time. Feasible solutions are obtained with a two-step heuristic, which also provides a lower bound that is used to judge solution quality. Next, a two-stage stochastic optimization model is presented for a joint pain IPU. The expected value solution is used to generate two different patient arrival templates. Extensive computations are performed to evaluate the solutions obtained with these templates and several others found in the literature. Comparisons with the expected value solution and the wait-and-see solution are also included. For the templates derived from the expected value solution, the results show that the average gap between the feasible solution and lower bound provided by the two-step heuristic is 2% for 14 patients. They also show that either of the two templates derived from the expected value solution is a good candidate for assigning appointment times when either the clinic closing time or the patient waiting time is the more important consideration. Sensitivity analysis confirmed that the optimality gap and clinic statistics are stable for marginal changes in key resources.

Suggested Citation

  • Pengfei Zhang & Jonathan F. Bard & Douglas J. Morrice & Karl M. Koenig, 2019. "Extended open shop scheduling with resource constraints: Appointment scheduling for integrated practice units," IISE Transactions, Taylor & Francis Journals, vol. 51(10), pages 1037-1060, October.
  • Handle: RePEc:taf:uiiexx:v:51:y:2019:i:10:p:1037-1060
    DOI: 10.1080/24725854.2018.1542544
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    Cited by:

    1. Mejía, Gonzalo & Yuraszeck, Francisco, 2020. "A self-tuning variable neighborhood search algorithm and an effective decoding scheme for open shop scheduling problems with travel/setup times," European Journal of Operational Research, Elsevier, vol. 285(2), pages 484-496.
    2. Agnihothri, Saligrama & Cappanera, Paola & Nonato, Maddalena & Visintin, Filippo, 2024. "Appointment scheduling in surgery pre-admission testing clinics," Omega, Elsevier, vol. 123(C).
    3. Youngbum Hur & Jonathan F. Bard & Douglas J. Morrice, 2021. "Appointment scheduling at a multidisciplinary outpatient clinic using stochastic programming," Naval Research Logistics (NRL), John Wiley & Sons, vol. 68(1), pages 134-155, February.

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