Decomposition Approach for the Job-Shop Scheduling Problem

Abstract

The job-shop scheduling problem is known to be NP-hard in the strong sense. Existing algorithms are thus not operational when the number of jobs and/or machines increases. To simplify the resolution of large-scale job-shop problems the decomposition methods have been investigated. However, whenever remaining links exist between the production sub-systems (the most common case in practice), then the decomposition method becomes debatable. The purpose of this paper is to show that we can replace the remaining sub-system links by fictitious entities introduced into sub-problems. At this moment we can resolve separately the new independent sub-problems.