What is the Impact of Labor Productivity on the Optimal Staffing Level?

An analysis of models within two canonical operations frameworks reveals that the answer exhibits a simple structure: the optimal staffing level increases and then decreases in labor productivity, when labor productivity is defined as the number of customers a worker can serve per unit time. We establish this result in the context of a newsvendor model--which captures uncertainty in demand for the service over the planning period--and a queueing model--which captures stochastic variability in customer arrivals and service requirements. In the latter model, we establish that the result holds if the service fee is exogenous or endogenous, customer valuations are homogenous or heterogenous, and the queue structure is dedicated or pooled. We show that the range of labor productivity values for which the optimal staffing level increases in labor productivity expands as the service economics become less favorable. Finally, we show that the marginal value of increasing labor productivity increases and then decreases in the staffing level.