The fuzzy quadratic assignment problem with penalty: new models and genetic algorithm

The assignment problem is to find the total costs optimal jobs assignment schedule where n jobs are allocated to n workers, and each worker receives exactly just one job, such that the total cost is optimal. The quadratic assignment problem with penalty takes three types of costs into consideration: direct cost, interactive cost and penalty. In this paper, the fuzzy quadratic assignment problem with penalty is formulated as expected value model, chance-constrained programming and dependent-chance programming according to various decision criteria, and the crisp equivalents are given. Furthermore, hybrid genetic algorithm is designed for solving the proposed fuzzy programming models.