Balancing flexibility and inventory in workforce planning with learning

We examine the problem of assigning workers to tasks, seeking to maximize profits, while taking in consideration learning through experience and stochasticity in demand. As quantitative descriptions of human learning are non-linear, we employ a reformulation technique that uses binary and continuous variables and linear constraints and is mathematically equivalent in nearly all cases. Similarly, as demand is not assumed to be known with certainty, we embed this mixed integer representation of how experience translates to productivity in a stochastic workforce assignment model. With an extensive computational study and analysis of (near-)optimal solutions, we demonstrate that modeling both learning and uncertainty in demand leads to improved task assignments. Furthermore, we formulate and test hypotheses based on these solutions that yield insights into how best to manage practice, cross training, and inventory. We show that cross training increases as demand uncertainty increases, worker practice increases as inventory holding costs increase, and workers with less initial experience receive more practice than workers with higher initial experience.