  Cross-training workers is one of the most efficient ways to achieve
flexibility in manufacturing and service systems to increase responsiveness to
demand variability. However, it is generally the case that cross-trained
employees are not as productive as employees who are originally trained on a
specific task. Also, the productivity of the cross-trained workers depend on
when they are cross-trained. In this work, we consider a two-stage model to
analyze the affect of variations in productivity levels of workers on
cross-training policies. Our results indicate that the most important factor
determining the problem structure is the consistency in productivity levels of
workers trained at different times. As long as cross-training can be done in a
consistent manner, the productivity differences between cross-trained workers
and workers originally trained on the task plays a minor role. We also analyze
the effect of the variabilities in demand and producivity levels. We 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,
the decision maker may prefer to invest more in cross-training earlier as
variability increases.
