A Sequential Bounding Approach for Optimal Appointment Scheduling

Brian Denton, Diwakar Gupta

Research output: Contribution to journalArticlepeer-review

193 Scopus citations


This study is concerned with the determination of optimal appointment times for a sequence of jobs with uncertain durations. Such appointment systems are used in many customer service applications to increase the utilization of resources, match workload to available capacity, and smooth the flow of customers. We show that the problem can be expressed as a two-stage stochastic linear program that includes the expected cost of customer waiting, server idling, and a cost of tardiness with respect to a chosen session length. We exploit the problem structure to derive upper bounds that are independent of job duration distribution type. These upper bounds are used in a variation of the standard L-shaped algorithm to obtain optimal solutions via successively finer partitions of the support of job durations. We present new analytical insights into the problem as well as a series of numerical experiments that illustrate properties of the optimal solution with respect to distribution type, cost structure, and number of jobs.

Original languageEnglish (US)
Pages (from-to)1003-1016
Number of pages14
JournalIIE Transactions (Institute of Industrial Engineers)
Issue number11
StatePublished - 2003

Bibliographical note

Funding Information:
The authors are grateful to two anonymous referees for their helpful suggestions to improve the manuscript. This research was supported in part by the Social Sciences and Humanities Research Council of Canada through a research grant to DG. The work was done, in part, when both authors were at McMaster University, Canada.

Copyright 2017 Elsevier B.V., All rights reserved.


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