Sequencing a tri-criteria multiple job classes and customer orders problem on a single machine by using heuristics and simulated annealing method

Multiple-job-class sequencing problems solve a group of jobs belonging to multiple classes, where to decrease the processing time, jobs in the same class tend to be performed together with the same setup time. In contrast, customer order scheduling problems focus on completing all jobs (belonging to different classes) in the same order at the same time to reduce shipping costs. Because related studies on multiple-job-class sequencing problems with more than one criterion are quite limited in the current research community, this study investigates tri-criteria scheduling problems with multiple job classes and customer orders on a single machine, where the goal is to minimize a linear combination of the makespan, total completion times of all jobs, and sum of the ranges of all orders. Due to the high complexity of the proposed problem, mixed integer programming is developed to formulate the problem, and a branch-and-bound method along with a lower bound and a property is utilized for finding the optimal schedules. Then, two heuristics and a simulated annealing algorithm are proposed to solve the problem approximately. The simulation results of the proposed heuristics and algorithm are evaluated through statistical methods.