Hybrid Flow Shop with Limited Transportation Scheduling Problem: A Comparison Between Genetics Algorithm, and a Novel Recursive Local Search Heuristic

In this paper, concurrent scheduling of jobs and transportation in a hybrid flow shop system is studied, where multiple jobs, transporters, and stages with parallel unrelated machines are considered. In addition to the mentioned technical features, jobs are able to omit one or more stages, and may not be executable by all the machines, and similarly, transportable by all the transporters. Unlike most studies in the literature, the transport resource is finite and needs to be simultaneously scheduled with the jobs. Initially, a new mixed integer linear programming (MILP) model is proposed to minimize the makespan. Then, a novel Recursive Local Search Heuristic (RLSH) is proposed to tackle the large-sized instances, which otherwise could not be solved via MILP solver (Gurobi) in reasonable time. RLSH is also compared against Genetics Algorithm (GA) on a set of numerical examples generated from the uniform distribution. As the computational results demonstrate, it is concluded that RLSH is extremely efficacious dealing with the problem and outperforms GA in the objective value quality. Finally, using two well-known statistical tests: Wald and analysis of variance(ANOVA), we assess the performance of the suggested approaches.