Cross-Training with Imperfect Training Schemes

Cross‐training workers is one of the most efficient ways of achieving flexibility in manufacturing and service systems for increasing responsiveness to demand variability. However, it is generally the case that cross‐trained employees are not as productive on a specific task as employees who were originally trained for that task. Also, the productivity of the cross‐trained workers depends on when they are cross‐trained. In this work, we consider a two‐stage model to analyze the effects of variations in productivity levels on cross‐training policies. We define a new metric called achievable capacity and show that it plays a key role in determining the structure of the problem. If cross‐training can be done in a consistent manner, the achievable capacity is not affected when the training is done, which implies that the cross‐training decisions are independent of the opportunity cost of lost demand and are based on a trade‐off between cross‐training costs at different times. When the productivities of workers trained at different times differ, there is a three‐way trade‐off between cross‐training costs at different times and the opportunity cost of lost demand due to lost achievable capacity. We analyze the effects of variability and show that if the productivity levels of workers trained at different times are consistent, the decision maker is inclined to defer the cross‐training decisions as the variability of demand or productivity levels increases. However, when the productivities of workers trained at different times differ, an increase in the variability may make investing more in cross‐training earlier more preferable.