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

Pengfei Zhang, Jonathan F. Bard, Douglas J. Morrice, Karl Koenig

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)1037-1060
Number of pages24
JournalIISE Transactions
Volume51
Issue number10
DOIs
StatePublished - Oct 3 2019

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Scheduling
Integer programming
Linear programming
Sensitivity analysis
Statistics
Processing

Keywords

  • Integrated practice units
  • flexible flow shop
  • open shop scheduling
  • stochastic optimization

ASJC Scopus subject areas

  • Industrial and Manufacturing Engineering

Cite this

Extended open shop scheduling with resource constraints : Appointment scheduling for integrated practice units. / Zhang, Pengfei; Bard, Jonathan F.; Morrice, Douglas J.; Koenig, Karl.

In: IISE Transactions, Vol. 51, No. 10, 03.10.2019, p. 1037-1060.

Research output: Contribution to journalArticle

Zhang, Pengfei ; Bard, Jonathan F. ; Morrice, Douglas J. ; Koenig, Karl. / Extended open shop scheduling with resource constraints : Appointment scheduling for integrated practice units. In: IISE Transactions. 2019 ; Vol. 51, No. 10. pp. 1037-1060.
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