Optimization of Large-Scale Single Machine and Parallel Machine Scheduling

Abstract

Hundreds of steel products need to be scheduled on a single or parallel machine in a steel plant every week. A good feasible schedule may save the company millions of dollars compared to a bad one. Single and parallel machine scheduling are also encountered often in many other industries, making it a crucial research topic for both the process system engineering and operations research communities.

Single or parallel machine scheduling can be a challenging combinatorial optimization problem when a large number of jobs are to be scheduled. Each job has unique job characteristics, resulting in different setup times/costs depending on the processing sequence. They also have specific release dates to follow and due dates to meet.

This work presents both an exact method using mixed-integer quadratic programming, and an approximate method with metaheuristics to solve real-world large-scale single/parallel machine scheduling problems faced in a steel plant. More than 1000 or 350 jobs are to be scheduled within a one-hour time limit in the single or parallel machine problem, respectively. The objective of the single machine scheduling is to minimize a combined total changeover, total earliness, and total tardiness cost, whereas the objective of the parallel machine scheduling is to minimize an objective function comprising the gaps between jobs before a critical time in a schedule, the total changeover cost, and the total tardiness cost. The exact method is developed to benchmark computation time for a small-scale single machine problem, but is not practical for solving the actual large-scale problem. A metaheuristic algorithm centered on variable neighborhood descent is developed to address the large-scale single machine scheduling with a sliding-window decomposition strategy. The algorithm is extended and modified to solve the large-scale parallel machine problem. Statistical tests, including Student's t-test and ANOVA, are conducted to determine efficient solution strategies and good parameters to be used in the metaheuristics.