A two-stage flow shop with parallel dedicated machines

The paper considers the 2-stage flow shop problem with parallel dedicated machines. In such a situation, each job can only be processed on a pre specified subset of machines. A mathematical model for this problem is proposed to minimize the maximum completion time among all jobs commonly known as the makespan or the Cmax. Furthermore, two approximate methods are proposed. The first one is a heuristic based on the Johnson’s algorithm and the second one is a genetic algorithm based approach. The performances of the proposed heuristic algorithms are analyzed by comparing solutions with the optimal makespan when it is possible to reach it by solving the mathematical model with CPLEX or with the developed lower bound dedicated to this particular problem. Extensive computational experiments show that the genetic algorithm outperforms the heuristic especially for smaller instances. For larger instances, the heuristic is able to find near-optimal solutions in a very short computational time comparing to the genetic algorithm.