An Exact and Efficient Algorithm for the Constrained Dynamic Operator Staffing Problem for Call Centers

As a result of competition, call centers face increasing pressure to reduce costs while maintaining an acceptable level of customer service, which to a large extent entails reducing the time customers spend waiting for service. Pursuant to this, call center managers often face stochastic constrained optimization problems with the objective of minimizing cost, subject to certain customer waiting time constraints. Complicating this problem is the fact that in practice, customer arrival rates to call centers are often time-varying. In order to cost-effectively satisfy their service level goals in the face of this uncertainty, call centers may employ a certain number of permanent operators who always provide service, and a certain number of temporary operators who provide service only when the call center is busy, i.e.when the number of customers in system increases beyond a threshold level. This gives the call center manager the flexibility of dynamically adjusting the number of operators providing service (and thus the resources or costs dedicated) in response to the time-varying arrival rate. The Constrained Dynamic Operator Staffing (CDOS) problem involves determining the values for the number of permanent operators, the number of temporary operators, and the threshold value(s) that minimize time-average hiring and opportunity cost, subject to service level constraints. Currently, the only exact solution method for this problem is enumeration, which is often computationally intractable. We provide an exact and efficient solution method, the Modified-Balance-Equations-Disjunctive-Constraints (MBEDC) algorithm, for this problem resulting in a Mixed Integer Program formulation. Using our algorithm, we solve diverse instances of the CDOS problem, generating managerial insights regarding the effects of temporary operators and service level constraints. ∗Corresponding author; email: [email protected]