Valuing labor flexibility in cross-training using a real options approach

Cross-training is an effective way to acquire labor flexibility which can be defined by multifunctionality and redundancy. This study concentrates on redundancy and considers how much capacity is required to satisfy present and future demand. A two-phase cross-training problem is investigated to discuss how much redundant capacity should be pooled for the bottleneck work station of a new product with the consideration of demand uncertainty. The problem determines the number of workers should be trained in the first phase and in which period they should fulfill the second phase. Workers participate in the first phase should be more than the current demand needed. These extra workers act as a capacity buffer against demand uncertainty, and training costs paid for them can be treated as an investment in flexibility. The decision process is analogous to an expansion option, and a real options approach is employed to solve the problem. A stochastic dynamic programming model, in which the dynamic of demand is approximated by a trinomial lattice, is formulated. Based on differences in the expected NPV brought by training extra workers, the monetary value of labor flexibility can be measured. Then, the impact of demand uncertainty, workers’ multi-skill level and penalty cost for unsatisfied demand on the optimal training plan and the value of flexibility are tested by using numerical experiments. The results verify that flexibility brings more value when demand variation is great and pooling redundant capacity in advance is necessary to cope with demand uncertainty. Besides, the results have several implications. (1) In order to rise profits, a lower multi-skill level is suggested for products with great demand variation. (2) The quantity of capacity pooled for the bottleneck is crucial to the value of flexibility. (3) Excessive multifunctionality hurts the value of flexibility brought by redundancy. (4) Flexibility brought by capacity buffer is valuable for companies who are afraid of losing customers.