Hierarchical cross-training in Work-In-Process-constrained systems

We study Work-In-Process (WIP)-constrained flowlines staffed by partially cross-trained workers with hierarchical skill sets. We characterize the optimal worker-to-task assignment policy for CONWIP systems with two workers and general stochastic processing times. This leads us to the "fixed-before-shared" principle, which states that a flexible worker should process a task he/she is uniquely qualified for before helping other workers with shared tasks. To provide insights on the performance opportunity of hierarchical cross-training in systems with limited WIP, we provide a complete characterization of the optimal policy and closed-form expressions of the resulting throughput for the case of exponential processing times. We extend our results to the more general case of floater workers, and illustrate their applicability to various real-world systems. Our analysis shows that hierarchical cross-training can provide significant benefits, but should be implemented with care in WIP-constrained environments such as those making use of pull systems.