Two meta-heuristic algorithms for parallel machines scheduling problem with past-sequence-dependent setup times and effects of deterioration and learning

This paper considers identical parallel machines scheduling problem with past-sequence-dependent setup times, deteriorating jobs and learning effects, in which the actual processing time of a job on each machine is given as a function of the processing times of the jobs already processed and its scheduled position on the corresponding machine. In addition, the setup time of a job on each machine is proportional to the actual processing time of the already processed jobs on the corresponding machine, i.e., the setup time of a job is past- sequence-dependent (p-s-d). The objective is to determine jointly the jobs assigned to each machine and the order of jobs such that the total completion time (called TC) is minimized. Since that the problem is NP-hard, optimal solution for the instances of realistic size cannot be obtained within a reasonable amount of computational time using exact solution approaches. Hence, an efficient method based on ant colony optimization algorithm (ACO) is proposed to solve the given problem. The performance of the presented model and the proposed algorithm is verified by a number of numerical experiments. The related results show that ant colony optimization algorithm is effective and viable approache to generate optimal⁄near optimal solutions within a reasonable amount of computational time.