Assigning cross-trained workers to departments: A two-stage optimization model to maximize utility and skill improvement

We develop a general framework that is applicable in both manufacturing and service settings for assigning cross-trained workers across departments. The framework consists of a two-stage optimization model where two objective functions, departmental utility and skill improvement, are considered sequentially. Departmental utility is a function of departmental labor shortage and the first-stage optimization model maximizes total departmental utility subject to typical assignment constraints. The second stage model seeks to maximize total skill improvement, which is quantified by a hyperbolic learning curve, while trying not to deviate from the utility level obtained during the first stage optimization. Our computational experiments suggest that incorporating the skill improvement function explicitly in the model results in significant improvement in the total skill level of the workforce and thus leads to more effective worker assignments.