Optimization of fuzzy multi-company workers assignment problem with penalty using genetic algorithm

In this paper, we proposed the fuzzy multi-job and multi-company workers assignment problem with penalty. Our purpose is obtaining the optimal solution the assignment problem, where n jobs are assigned to m workers (m>n), each job must be assigned to one and only one worker and each worker could be received one job or do not receive any job. Furthermore, there are k company where each worker belong a special company. For finding the optimal assignment, we must optimize total cost this problem assignment. This problem has three types of costs, direct cost company cost and penalty. In this paper, first the proposed assignment problem is formulated to the crisp model by using a suitable fuzzy ranking and fuzzy arithmetic operators. Finally, a heuristic genetic algorithm is designed for solving the proposed problem and an example is given to verify the efficiency of the algorithm.