Two-stage chain-reentrant hybrid flow-shop with deteriorating jobs

In this paper, we study a two-stage chain-reentrant hybrid flow shop with deteriorating jobs as follows. Each job must initially be scheduled on a primary machine M1 (first stage) which is then scheduled on one of a set of m unrelated parallel machines (second stage) and returns back to M1 for its last operation. The jobs are subjected to a linear deterioration function of their starting times. The aim is to minimize both of the makespan and the total energy consumption. For the resolution of this problem, we have developed a mixed-integer linear programming model. We then implement and compare two metaheuristics: a nondominated sorting-based multiobjective genetic algorithm (NSGA2) and an archived multiobjective simulated annealing algorithm (AMOSA). The experimental study indicates that AMOSA generally outperforms NSGA2 on small instances (for all tested values of m and n ? 30), whereas NSGA2 yields better performance on larger instances (for all tested values of m and n ? 100), with respect to both quantity and quality measures. For small instances, the comparison with the exact method (i.e., the mathematical model) confirms that the reference fronts generated by both algorithms are close to the true Pareto front. Finally, we have proposed a TOPSIS-based method to select a representative solution from the Pareto set according to the decision-maker?s preferences.