Optimizing the staffing and routing of small-size hierarchical call centers

Multiple-skill call centers propagate rapidly with the development of telecommunications. An abundance of literature has already been published on call centers. Here, we want to focus on centers that would typically occur in business-to-business environments; these are call centers that handle many types of calls but where the arrival rate for each type is low. To find an optimal configuration, the integrality of the decision variables is a much more important issue than for larger call centers. The present paper proposes an approach that uses elements of combinatorial optimization to find optimal configurations. We develop an approximation method for the evaluation of the service performance. Next, we search for the minimum-cost configuration subject to service-level constraints using a branch-and-bound algorithm. What is at stake is to find the right balance between gains resulting from the economies of scale of pooling and the higher cost or cross-trained agents. The article shows that in most cases this method significantly decreases the staffing cost compared with configurations with only cross-trained or dedicated operators.