Transient staffing at the beginning of work

Abstract

Production and service systems often rely on stationary queueing formulas to determine the number of agents that need to be scheduled. However, this results in over-staffing decisions when the system starts empty. To address this issue, we propose a solution called transient staffing, which involves providing appointment times for agents to ensure that the expected queue length remains below a certain threshold. We model the system as a transient Erlang-A queue. To compute the appointment times, we employ a uniformized approximation that discretizes the elapsed time, which can be made as accurate as desired. We prove that the appointment times decrease with the arrival rate and traffic intensity, while increasing with the abandonment rate. Through numerical investigations, we find that adopting a transient staffing strategy leads to substantial cost savings, especially in scenarios where demand is high, customers are patient, traffic intensity is low, and the service level objective is intermediate. Furthermore, we use a fluid approximation to derive closed-form expressions for the agents' appointment times, and prove the impact of the system parameters. We show that this approximation performs well in predicting the first appointment times in contexts with high demand, low traffic intensity, and lax service level objective.

Keywords:

• Erlang-A queue
• transient analysis
• uniformized approximation
• fluid approximation
• appointment scheduling

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The authors confirm that the data supporting the findings of this study are available within the article [and/or] its supplementary materials.

Additional information

Notes on contributors

Benjamin Legros

Pr. Benjamin Legros is a researcher currently affiliated with EM Normandie at the Paris campus, contributing to the institution's dedication for logistics. His primary research interest lies in the field of queueing for service systems, with an interest for understanding of the intricacies of managing and optimising operational processes. Pr. Legros completed both his Ph.D. and Postdoctoral research at CentraleSupélec, where he participated in the research chair on Call Centers, contributing valuable insights to the field.

Oualid Jouini

Pr. Oualid Jouini is a researcher in Operations Management, currently holding the position of Professor with an HDR at Laboratoire Génie Industriel, CentraleSupélec. His research focusses on queueing systems modelled by queues such as call centres and emergency departments. He is Head of the research group Operations Management and coordinator of the doctoral training programme at the graduate school of engineering SIS, University Paris-Saclay. Additionally, he oversees the master portfolio in Engineering of Complex Systems at University Paris-Saclay. With a rich academic history, Pr. Jouini has previously served as the Director of the master programme in Supply Chain and Operations Management, and held a research chair in Call Centers.