A fast staffing algorithm for multistage call centers with impatient customers and time-dependent overflow

Ensuring customer satisfaction is one of the main objectives of a call center. We focus on the question of how many agents are necessary and how they should be allocated to maintain a service level threshold and reduce the expected waiting time of the customers. In this paper, we consider a multistage call center that consists of a front and a back office, impatient customers, and an overflow mechanism. Based on the performance evaluation of such a system using a continuous-time Markov chain, a configuration of agents is determined using a binary search algorithm. We focus on structural insights, e.g., convexity conditions, to obtain a quick solution for the staffing problem. Since monotonicity does not always hold, the approach is heuristic. The numerical results show the performance of the algorithm. The influence of the fraction requiring second-level service in the back office and the impatience rate for the minimum number of agents is shown.