Managing Learning and Turnover in Employee Staffing

We study the employee staffing problem in a service organization that uses employee service capacities to meet random, non-stationary service requirements. The employees experience learning and turnover on the job, and we develop a Markov Decision Process (MDP) model that explicitly represents the stochastic nature of these effects. Theoretical results are developed that show the optimal hiring policy is of a state-dependent "hire-up-to" type, similar to the inventory "order-up-to" policy. This holds for discounted-costs MDP's under both finite and infinite planning horizons. We also develop structural properties of the optimal policy to facilitate computation of the optimal hiring numbers. For two important special cases of the general model, we prove the optimality of a myopic policy under both stationary and stochastically increasing service requirements. Moreover, we show that in these two cases, when service requirements are k-periodic, it is sufficient to solve a k-period MDP problem with appropriate end-of-horizon cost function. When general, non-stationary service requirements are present, we prove the existence of a one-sided "smoothing effect" of the optimal hire-up-to-levels. Numerical results show that the use of state-dependent hire-up-to policies may offer significant cost savings over simpler hiring policies. In particular, our results show that when employee capacity increase due to learning is substantial and flexible incremental capacity (overtime) is tight, a fully state-dependent policy out-performs a policy that hires only on the basis of the total number of employees in the system. Our problem formulation and results suggest natural connections to the classic results in inventory literature. We also discuss many of the connections and distinctions in the paper.