Design of a genetic algorithm for bi-objective unrelated parallel machines scheduling with sequence-dependent setup times and precedence constraints

This paper presents a novel, two-level mixed-integer programming model of scheduling N jobs on M parallel machines that minimizes bi-objectives, namely the number of tardy jobs and the total completion time of all the jobs. The proposed model considers unrelated parallel machines. The jobs have non-identical due dates and ready times, and there are some precedence relations between them. Furthermore, sequence-dependent setup times, which are included in the proposed model, may be different for each machine depending on their characteristics. Obtaining an optimal solution for this type of complex, large-sized problem in reasonable computational time using traditional approaches or optimization tools is extremely difficult. This paper proposes an efficient genetic algorithm (GA) to solve the bi-objective parallel machine scheduling problem. The performance of the presented model and the proposed GA is verified by a number of numerical experiments. The related results show the effectiveness of the proposed model and GA for small and large-sized problems.