Appointment scheduling and the effects of customer congestion on service

Zheng Zhang, Bjorn P. Berg, Brian T. Denton, Xiaolan Xie

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


This article addresses an appointment scheduling problem in which the server responds to congestion of the service system. Using waiting time as a proxy for how far behind schedule the server is running, we characterize the congestion-induced behavior of the server as a function of a customer’s waiting time. Decision variables are the scheduled arrival times for a specific sequence of customers. The objective of our model is to minimize a weighted cost incurred for a customer’s waiting time, server overtime and server speedup in response to congestion. We provide alternative formulations of this problem as a Simulation Optimization (SO) model and a Stochastic Integer Programming (SIP) model, respectively. We show that the SIP model can solve moderate-sized instances exactly under certain assumptions about a server (Formula presented.) s response to congestion. We further show that the SO model achieves near-optimal solutions for moderate-sized problems while also being able to scale up to much larger problem instances. We present theoretical results for both models and we carry out a series of experiments to illustrate the characteristics of the optimal schedules and to measure the importance of accounting for a server (Formula presented.) s response to congestion when scheduling appointments using a case study for an outpatient clinic at a large medical center. Finally, we summarize the most important managerial insights obtained from this study.

Original languageEnglish (US)
Pages (from-to)1075-1090
Number of pages16
JournalIISE Transactions
Issue number10
StatePublished - Oct 3 2019

Bibliographical note

Funding Information:
This research was funded in part by the National Science Foundation under grant CMMI-0844511 (Denton). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. This research was also funded in part by the

Funding Information:
National Natural Science Foundation of China under grants 71801058, 71671111, 71432006.

Publisher Copyright:
© 2019, Copyright © 2019 “IISE”.


  • Appointment scheduling
  • optimization
  • server behavior


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