To optimally rotate workers among different work areas to reduce their daily noise exposures, it is essential that a set of work assignments that minimize the maximum noise exposure that any one of the workers receives be determined. While it is possible to use a quantitative work assignment model to determine minimax work assignments for "balanced" work assignment problems (m workers, m work areas), the task becomes impractical when m is large. In this paper, we propose a genetic algorithm (GA) approach to determine minimax work assignments. Three numerical examples are given. Both the quantitative work assignment model and the GA approach are used to determine the optimal set of work assignments for the first and second examples. It is found that the GA approach obtains the solutions that are as good as those from the work assignment model. Further, the GA approach can solve large-sized work assignment problems.