Staffing to Maximize Profit for Call Centers with Alternate Service-Level Agreements

To ensure quality from outsourced call centers, firms sign service-level agreements (SLAs). These define service measures such as what constitutes an acceptable delay or an acceptable abandonment rate. They may also dictate penalties for failing to meet agreed-upon targets. We introduce a period-based SLA that measures performance over a short duration such as a rush hour. We compare it to alternate SLAs that measure service by individual and over a long horizon. To measure the service levels for these SLAs, we develop several approximations. We approximate the probability an acceptable delay is met by generalizing the heavy-traffic quality and efficiency driven regime. We also provide a new approximation for the abandonment rate. Further, we prove a central limit theorem for the probability of meeting a service level measured by the percentage of customers acceptably served during a period. We demonstrate how an outsourced call center operating in an environment with uncertain demand and abandonment can determine its staffing policy to maximize the expected profit for these SLAs. Numerical experiments demonstrate a high degree of accuracy for the approximations and the resulting staffing levels. We indicate several salient features of the behavior of the period-based SLA.