Hybrid Multi-Objective Methods to Solve Reentrant Shops

This article examines the multi-objective scheduling of a reentrant hybrid flow shop. This type of shop is composed of several stages made of several identical parallel machines. When a task has to be processed on a stage, it is assigned to the machine with the smallest workload. This problem shows a reentrant structure: each task must be processed several times at each stage. In this paper, this problem is solved by minimizing two objectives: the makespan (maximum completion time of the jobs) and the total tardiness of the tasks. A new method is improved with different local searches: Adjacent and Non Adjacent Pairwise Interchange, Extract and Backward-Shifted Reinsertion, and Extract and Forward-Shifted Reinsertion. Every local search is tuned with statistical method (design of experiment) and the best one is worked out. This method is compared with the best one in several instances. The results involve three different measures.