An Efficient Bi-objective Genetic Algorithm for the Single Batch-Processing Machine Scheduling Problem with Sequence Dependent Family Setup Time and Non-identical Job Sizes

This paper considers the problem of minimizing make-span and maximum tardiness simultaneously for scheduling jobs under non-identical job sizes, dynamic job arrivals, incompatible job families,and sequence-dependentfamily setup time on the single batch- processor, where split size of jobs is allowed between batches. At first, a new Mixed Integer Linear Programming (MILP) model is proposed for this problem; then, it is solved by -constraint method.Since this problem is NP-hard, a bi-objective genetic algorithm (BOGA) is offered for real-sized problems. The efficiency of the proposed BOGA is evaluated to be comparedwith many test problemsby -constraint method based on performance measures. The results show that the proposed BOGAis found to be more efficient and faster than the -constraint method in generating Pareto fronts in most cases.