Appointment scheduling and the effects of customer congestion on service. (3rd October 2019)

• Record Type: Journal Article
• Authors: Zhang, Zheng; Berg, Bjorn P.; Denton, Brian T.; Xie, Xiaolan
• Is Part Of: IISE transactions. Volume 51:Number 10(2019)
• Page Start: 1075
• Page End: 1090
• Publication Date: 2019-10-03
• Subjects: Appointment scheduling -- server behavior -- optimization; Industrial engineering -- Periodicals; Systems engineering -- Periodicals; Industrial engineering; Systems engineering; Electronic journals; Periodicals; 670.285
• DOI: 10.1080/24725854.2018.1562590
• Languages: English
• ISSNs: 2472-5854

Abstract

Abstract: 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 ′ 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 ′ 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.