Routing and Staffing in Customer Service Chat Systems with Generally Distributed Service and Patience Times

Problem definition: We study customer service chat (CSC) systems, in which agents can serve multiple customers simultaneously, with generally distributed service and patience times. The multitasking capability of agents introduces idiosyncratic challenges when making routing and staffing decisions. Methodology/results: To determine the dynamic matching of arriving customers with available agents, we first formulate a routing linear program (LP) based on system primitives. Inspired by the optimal solution of the routing LP, we design a parsimonious dynamic routing policy that is independent of arrival rate and service capacity information. We also use the optimal solution to develop closed-form approximations for crucial performance metrics and show that a similar LP can be utilized to make staffing decisions. Through extensive simulation experiments, we showcase the efficacy of our approximations and staffing decisions. Furthermore, under our proposed policy, the CSC system exhibits a unique stationary fluid model in which the steady-state performance measures align with our approximations. Managerial implications: The extant literature primarily focuses on Markovian systems with exponential distributions. In this paper, customers’ service and patience times are allowed to be generally distributed to agree with practical settings. Our findings indicate that the distributions have a significant impact on routing policies, staffing decisions, and system performance. Funding: Z. Long was supported by the National Natural Science Foundation of China [Grants 72101112, 72132005, and 72271119] and Jiangsu Province, China [Grant BK20210171]. J. Zhang was supported by the Hong Kong Research Grants Council, General Research Fund [Grants 16208120 and 16214121]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2022.0114 .