A novel two-stage genetic algorithm for a mixed-model U-line balancing problem with duplicated tasks

A widespread supposition on mixed-model assembly line-balancing problems assigns a task, which is shared between two or more models to a single station. Bukchin and Rabinowitch (European Journal of Operational Research, 174:492–508, 2006) relaxed the restriction for mixed-model straight-line assembly line problems and allowed tasks common to multiple models to be assigned to different stations, called task duplication. In this paper, considering the same relaxation but for mixed-model U-shaped assembly lines, a novel genetic algorithm (GA) approach for solving large-scale problems is developed. Although superiorities of U-shaped assembly lines over straight lines have been discussed in several articles, this paper makes the advantage more tangible by providing a quantitative example. This paper also presents a novel two-stage genetic algorithm which is fittingly devised for solving the new proposed model. In order to evaluate the effectiveness of the GA, one small-scale and one medium-scale problem are solved using both the proposed GA and Lingo 8.0 software, and the obtained outcomes are compared. The computational results indicate that the GA is capable of providing high-quality solutions for small- and medium-scale problems in negligible central processing unit (CPU) times. It is worth mentioning that, for large-scale problems, such as Kim and Arcus test problems, no analogous results for those obtained by our proposed GA exist. To conclude, it can be said that the proposed GA performs well and is able to solve large-scale problems within acceptable CPU times.