Dynamic Control of Non‐Collaborative Workers When Reassignment Is Costly

Abstract

Cross‐training is an important tool to improve the performance of manufacturing and service systems through dynamic worker allocation. This study investigates how cross‐training can be leveraged when worker collaboration is not possible and frequent worker reassignment is undesirable. We consider a tandem queueing system with finite buffers between tasks. We show that if each worker is the fastest at a different task, then the optimal policy is always dedicated, regardless of the magnitude of the reassignment costs. Otherwise, if the system is Markovian with two homogeneous tasks and a faster and a slower worker, we completely characterize how the profit‐optimal policy depends on the (constant) reassignment cost. We also prove that for any given reassignment cost, dedicated worker allocation policies are strictly suboptimal for large enough buffer sizes. Instead, the faster worker should move to the downstream task only if there are enough jobs in the intermediate buffer and return to the upstream task when the buffer is sufficiently empty. Furthermore, the benefit of task switching increases as the buffer size becomes larger. We use our theoretical results to develop worker allocation heuristics both for more general systems with two tasks and for systems with more tasks. Numerical experimentation provides insights on how the profit depends on the buffer sizes and reassignment costs, shows that policies that are optimal when workers are collaborative result in excessive switching for non‐collaborative workers, and indicates that our pick‐the‐best heuristics perform well in all settings.