Scheduling a real-world hybrid flow shop with variable processing times using Lagrangian relaxation

Abstract

This paper studies a real-world hybrid flow shop problem arising from the steelmaking continuous casting process, which is the bottleneck of the iron and steel production. There are a variety of features to be taken into account, in particular, the batch constraints and the variable processing times in the last stages. Based on a time-index formulation and machine capacity relaxation, three Lagrangian relaxation (LR) approaches are presented to address this scheduling problem. The three LR approaches decompose the relaxed problem into job-level problems, batch-level problems, and machine-level problems, respectively. These subproblems are solved based on polynomial dynamic programming algorithms. An efficient subgradient algorithm solves the corresponding Lagrangian dual (LD) problems with global convergence. Computational results and comparisons demonstrate that the approach adopting job-level decomposition could get the nearest optimal scheduling within acceptable time among the three approaches and is suitable for making static scheduling which pursuits optimization quality rather than calculation time. The approach adopting machine-level decomposition could get acceptable optimal results in the shortest time and is the best choice for making rescheduling which requires the quick response for the dynamic disturbances.