Many manufacturing and service firms operate with a workforce that is partitioned into two or more work categories (skills) to satisfy demands and reduce worker costs. In this paper, we describe a multi-skill, cross-utilization problem in many departments, and a general framework which may help in trade-offs between worker cost and met demands is developed by a two-stage stochastic programming model. To reduce the cost for total workers, the unmet demands are permitted and will be penalized. For optimizing the number of workers staffed in many departments, factors such as the worker cost coefficient, the penalty factor and the worker efficiency are considered. In Stage 1, optimization model considered in this paper is to minimize the sum of the cost for total workers and penalty, and in Stage 2 the model seeks to minimize the penalty, which is quantified by the unmet demands during assigning multi-skilled workers across departments. We propose a nested genetic algorithm to solve the proposed two-stage stochastic programming model. Finally, numerical studies are performed to examine the efficiency of the proposed algorithm.
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