Call Center Staffing: Service-Level Constraints and Index Priorities

Call centers attribute different values to different customer segments. These values are reflected in qualityof-service targets. The prevelant Target Service Factor (TSF) formulation requires, for example, that 80% of VIP customers wait less than 20 seconds while setting the target to 30 seconds for non-VIP customers. The call center must determine the staffing level together with a prioritization rule that meets these targets at minimal cost. In practice, due to the underlying complexity of these systems, the prioritization rule is often selected in a heuristic manner rather than being systematically optimized. When considering the universe of prioritization policies, index rules provide a customizable and easy to define heuristic and for this reason are implemented in various call-center software packages. In this paper we use the TSF formulation as a stepping stone towards a better understanding of index rules. We first asymptotically solve the, yet unsolved, TSF staffing problem. We prove that, despite index rules’ significant flexibility, no instance of these is optimal for the TSF problem. The sub-optimality of index rules, we prove, follows from an essential characteristic of these: restricting attention to index rules (as is heuristically done in practice) is asymptotically equivalent to requiring that a VIP customer always waits less than a regular (non-VIP) customer who arrives at the same time. This, in particular, implies that the use of index rules in practice can be rationalized if (and only if) the manager requires such strong differentiation.