Work expands to fill the time available: Capacity estimation and staffing under Parkinson's Law

We develop a method to estimate the capacity of agents who answer e-mail in a contact center, given aggregate historical data that have been distorted both by constraints on work availability and by internal incentives to slow down when true capacity exceeds demand. We use the capacity estimate to find a contact center's optimal daily staffing levels. The implementation results, from an actual contact center, demonstrate that the method provides accurate staffing recommendations. We also examine and test models in which agents exhibit speed-up behavior and in which capacity varies over time. Finally, we use the capacity estimates to examine the implications of solving the staffing problem with two different model formulations, the service-level constraint formulation used by the contact center and an alternate profit-maximization formulation.