Math modeling and GA approach to simultaneously make overtime decisions, load cells and sequence products

Abstract

The problem studied in this paper was inspired from an actual textile company. The problem is more complex than usual scheduling problems in that we need to decide additional capacity requirements at the same time we make scheduling decisions. It is assumed that tardy jobs are lost sales and since this is not desirable, we allow overtime to minimize the number of tardy jobs. However, overtime brings additional costs to a company. Therefore, the overall objective is to maximize profits. We propose both a Mathematical Model and a Genetic Algorithm (GA) approach to solve this problem. We experimented with 20-job, 30-job, 40-job, 50-job, 60-job, 70-job, 80-job and 90-job problems in the paper. Math model was fast in solving 20-job and 30-job problems. GA found optimal solutions with a high frequency in these job categories as well. GA found near optimal solutions for large problems that Math Model could find optimal solution. GA includes some newly proposed mutation operators, dynamic and twin. The proposed twin mutation strategy produced the best results in all problem sizes. Finally, OPL software was run with 2-min restriction for large problems where optimal solutions could not be found due to memory restrictions. In this case, “Best-so-far” results obtained from OPL runs outperformed corresponding GA results in all instances. The paper concludes that math model is the preferred solution approach for the problem on hand.