An Adaptive SPT Rule for Scheduling and Testing Heterogeneous Jobs

57 Pages Posted: 13 Aug 2019

See all articles by Retsef Levi

Retsef Levi

MIT Sloan School of Management - Operations Research Center

Thomas L. Magnanti

Massachusetts Institute of Technology (MIT)

Yaron Shaposhnik

University of Rochester - Simon Business School

Date Written: August 9, 2019

Abstract

Motivated by common practices in maintenance and healthcare operations, in which diagnostic activities precede service, we study the problem of scheduling jobs with random processing times on a server that can test jobs (i.e., perform a diagnostic procedure) prior to serving them in order to observe their durations. On one hand, testing utilizes the server and increases service delays, but on the other hand, testing reduces uncertainty and informs future scheduling decisions, which contributes to reducing overall delays.

We consider two cases in which tests are either optional or mandatory prerequisites for processing heterogeneous jobs whose random processing times (and in some cases weights) are statistically different. For several interesting cases of optional testing problems, we develop an adaptive shortest processing time (SPT) rule, which characterizes the optimal policy using intuitive testing thresholds given by closed-formulas. We then show that a generalization of these thresholds forms an optimal index policy for mandatory testing problems.

Our work provides tools for analyzing similar problems, as well as practical insights on how to prioritize uncertainty reduction efforts, in order to reduce delays in service systems.

Keywords: Dynamic Programming, Maintenance, Diagnosis, Scheduling

Suggested Citation

Levi, Retsef and Magnanti, Thomas L. and Shaposhnik, Yaron, An Adaptive SPT Rule for Scheduling and Testing Heterogeneous Jobs (August 9, 2019). Available at SSRN: https://ssrn.com/abstract=3435113 or http://dx.doi.org/10.2139/ssrn.3435113

Retsef Levi

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

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

Thomas L. Magnanti

Massachusetts Institute of Technology (MIT) ( email )

E40-147
Cambridge, MA 02139
United States
617-253-6604 (Phone)
617-258-9214 (Fax)

Yaron Shaposhnik (Contact Author)

University of Rochester - Simon Business School ( email )

Rochester, NY 14627
United States

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