An immune algorithm for hybrid flow shop scheduling problem with time lags and sequence-dependent setup times

This paper deals with hybrid flow shop scheduling problems considering time lags and sequence-dependent setup times which have wide application in real-world problems. Most of the researches on operations scheduling problems have ignored time lags. A mathematical model is presented which is capable of solving the small size of the considered problem in a reasonable time. Since these problems are strongly NP-hard, a meta-heuristic algorithm based on the immune algorithm is developed. The optimization criterion considered in this paper is the minimization of the makespan. Numerical experiments are used to evaluate the performance and effectiveness of the proposed algorithm. The results of the proposed algorithm are compared with the presented mathematical programming model and a benchmark algorithm. Computational results indicate that the proposed algorithm can produce near-optimal solutions in a short computational time. Moreover, it can be applied easily in real factory conditions and for large-sized problems.