Appointment systems under service level constraints

• Main Authors: CHEN, David, WANG, Rowan, YAN, Zhenzhen, BENJAAFAR, Saif, JOUINI, Oualid
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2016
• Subjects: Appointment scheduling; Service level constraint; Waiting time; Majorization; Business Administration, Management, and Operations
• Online Access: https://ink.library.smu.edu.sg/lkcsb_research/5302; https://ink.library.smu.edu.sg/context/lkcsb_research/article/6301/viewcontent/ASSLC.pdf
• Institution: Singapore Management University

We consider a new model of appointment scheduling where customers are given the earliest possible appointment times under the service level constraint that the expected waiting time of each individual customer cannot exceed a given threshold. We apply the theory of majorization to analytically characterize the structure of the optimal appointment schedule. We show that, the optimal inter-appointment times increase with the order of arrivals. That is, the optimal inter-arrival time between two customers later in the arrival process is longer than that between two customers earlier in the arrival process. We study the limiting behavior of our system, and prove that, when customer service times follow an exponential distribution, our system converges asymptotically to the D/M/1 queueing system as the number of arrivals approaches infinity. We also extend our analysis to systems with multiple servers.