Hybrid artificial immune system and simulated annealing algorithms for solving hybrid JIT flow shop with parallel batches and machine eligibility

This research deals with a hybrid flow shop scheduling problem with parallel batching, machine eligibility, unrelated parallel machine, and different release dates to minimize the sum of the total weighted earliness and tardiness (ET) penalties. In parallel batching situation, it is supposed that number of machine in some stages are able to perform a certain number of jobs simultaneously. Firstly, with respect to the proposed problem a mixed integer linear programming model is developed. Since the problem is NP-hard, for solving large size problems, a hybrid meta-heuristic algorithm which combines artificial immune system and simulated annealing is proposed. The performance of hybrid algorithm is tested by some numerical experiments and the results show its superiority to the other two algorithms.