Call center capacity allocation with random workload

We consider a call center staffing problem with two types of customers of which the arrival rates are allowed to be a random and non-stationary. In order to efficiently cope with such random workload fluctuations, the workforce presents some flexibility: the agents can be, in real-time, affected to each type of customers according to the instantaneously observed workload and the associated/relative cost criteria. We model this staffing problem as a cost optimization-based newsboy-type model. We then show how to numerically solve this model. In order to deal with the randomness characterizing the workloads of the call processes, we consider several solution tracks. First, we solve the model under the assumption that the workloads are deterministic and equal to their average values. In the second approach, we explicitly formulate in the optimization model the stochastic nature of the workloads. As a third approach, we develop a robust-type solution. Via several numerical analyzes we show the impact of the arrival rates randomness on the optimal staffing policy and on the operating costs.