A modified column generation heuristic for hybrid flow shop multiple orders per job scheduling problem

Abstract

With a comprehensive consideration of multiple product types, sequence-dependent setup time constraints and two different processing modes in wafer fabrication process, a scheduling model of multiple orders per job in a hybrid flow shop with an objective function of minimising total completion time of the system is developed. On the basis of the description, a new column generation algorithm based on a three-level (job-product-machine) disjunctive network flow is put forward. Furthermore, in order to improve degradation effects of the algorithm, a Lagrangian relaxation with sub-gradient optimisation is integrated into a frame of the column generation algorithm. Therefore, a modified column generation algorithm as a combination of Lagrangian approach and column generation algorithm is proposed. Finally, theory analysis and simulation experiments demonstrate that the presented algorithm is valid and feasible.