Competitive Algorithms for the Online Minimum Peak Appointment Scheduling

31 Pages Posted: 23 Feb 2021

See all articles by Célia Escribe

Célia Escribe

Massachusetts Institute of Technology (MIT) - Operations Research Center

Michael Hu

Massachusetts General Hospital

Retsef Levi

MIT Sloan School of Management - Operations Research Center

Date Written: February 17, 2021

Abstract

This paper describes a fundamental online scheduling problem called the minimum peak appointment scheduling (MPAS) problem. In this problem, there is a sequence of arriving appointments, each with specified required duration. The goal is to schedule the appointments in an online manner and to minimize the resulting peak utilization throughout the scheduling interval. While described as appointment scheduling, the MPAS has far broader applicability that captures other settings. The paper provides a formal modeling framework to analyze the aforementioned MPAS problem. It is shown that the offline version of the MPAS problem is identical to the offline version of the well-known bin packing problem. However, in the online variant, there is additional flexibility regarding how appointments are packed into chairs (bins). The paper describes the first competitive online algorithm to the MPAS problem called the harmonic rematching (HR) algorithm. The analysis shows that the HR algorithm has an asymptotic competitive ratio of 1.5. Considering that the current best lower bound on randomized online algorithms is 1.536, this highlights the fact that the HR algorithm performs better than any bin packing online algorithm in this setting.

Keywords: bin packing, online algorithm, competitive analysis

Suggested Citation

Escribe, Célia and Hu, Michael and Levi, Retsef, Competitive Algorithms for the Online Minimum Peak Appointment Scheduling (February 17, 2021). Available at SSRN: https://ssrn.com/abstract=3787306 or http://dx.doi.org/10.2139/ssrn.3787306

Célia Escribe (Contact Author)

Massachusetts Institute of Technology (MIT) - Operations Research Center ( email )

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Michael Hu

Massachusetts General Hospital ( email )

55 Fruit Street Boston
Boston, MA 02114
United States

Retsef Levi

MIT Sloan School of Management - Operations Research Center ( email )

100 Main Street
E62-416
Cambridge, MA 02142
United States

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