Optimal Call Center Staffing and Pricing Under QoS Constraints - Soltani, Morteza; Kharoufeh, Jeffrey P; Khademi, Amin (IISE Annual Conference. Proceedings, 2023)
We present a stochastic optimization model to determine optimal staffing strategies for a call center subject to uncertain and dynamic call arrival rates. The aim is to determine what proportion of demand should be outsourced to an external service provider rather than being serviced in-house. Before demand is realized, the call center sets its in-house staffing level, and the number of external agents to place on-call, in response to the provider's prices with the goal of minimizing its total expected staffing costs. Once demand is realized, the call center has the option to activate on-call agents to satisfy quality-of-service (QoS) constraints. For its part, the external service provider seeks to maximize its total expected revenues over a finite contract period by setting per-agent reservation and activation prices. The interplay between the call center and external provider is modeled as a bilevel program. We establish the optimality of a bang-bang staffing policy, i.e., it is optimal to either completely insource or outsource.