Appointment scheduling and the effects of customer congestion on service

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

Research output: Contribution to journalArticle

1 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


  • Appointment scheduling
  • optimization
  • server behavior

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