Dynamic Optimization of Workforce Talent

Abstract

We study the problem of repeatedly assigning recurring jobs to a pool of workers under two dynamics: (i) workers gain or lose familiarity with each job type over time based on whether or not they are assigned to the job, and (ii) the availability of workers and jobs evolves stochastically. The ability of workers to learn from experience favors having specialized workers, but the uncertain availability necessitates developing cross-functional ones. These dynamics, common across applications, impose a major hurdle for managers to trade off specialization versus cross-functionality. We formulate this problem as a Markov decision process, which includes high-dimensional elements to capture both dynamics. We propose a familiarity-agnostic (FA) policy and show that it approximates familiarity dynamics via their steady-state counterparts, can result in a pool of cross-functional workers, and is near optimal when learning and forgetting occur slowly. We also propose a Lagrangian relaxation (LR) policy that dualizes combinatorial constraints modeling feasible assignments based on available jobs and workers. We show that the LR policy results in a deterministic approximation of availability dynamics, fosters a pool of specialized workers, and is near-optimal when evolving availability minimally impacts the assignment feasibility constraints. This condition arises, for example, when availability is nearly deterministic, with the same workers and jobs available in almost every period. For environments with highly evolving familiarity and availability, we design an approximate linear programming policy. While general and well-suited for these more challenging environments, this policy requires nontrivial approximations for computational feasibility and is unnecessary in settings where our tailored FA and LR policies guarantee strong performance and offer valuable insight into how they navigate the trade-off. In numerical experiments, we show that the best-proposed policy performs well across diverse instances and illustrate how each policy balances specialization versus cross-functionality. More broadly, our research offers a framework for actively developing and deploying talent across a workforce.

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