Critical Path Method for Flexible Job Shop Scheduling Problem with Preemption

This paper addressed a Flexible Job shop Scheduling Problem (FJSP) with the objective of minimization of maximum completion time (Cmax) which job splitting or lot streaming is allowed. Lot streaming is an important technique that has been used widely to reduce completion time of a production system. Due to the complexity of the problem; exact optimization techniques such as branch and bound algorithm will lose their efficiency at medium and large dimensions. Thus, metaheuristic techniques are good options in order to obtain high quality solutions within a reasonable computational time. In this study, firstly, the considered problems are solved in both permitted and not permitted of lot streaming by means of memetic algorithm and then the obtained solutions will be improved by using the critical path method heuristic. The numerical results indicate the high efficiency of the memetic algorithm in comparison with the previous methods; in addition, adding preemption and using allowable idle machines have led to a considerable improvement in the objective function.