A job shop distributed scheduling based on Lagrangian relaxation to minimise total completion time

This paper considers a distributed job shop scheduling problem where autonomous sub-production systems share common machines with each other. Each sub-production system is responsible for the scheduling of a set of jobs to minimise the total completion time on shared machines. A sub-production system has ultimate responsibility on maintaining private information such as objective function, processing time and routings on shared machines. Also sub-production systems must cooperate each other in order to achieve a global goal while sharing minimum of private information. In this research, we propose a distributed cooperation method in which sub-production systems and shared machines interact with one another to find a compromised solution between a locally optimised solution and a system-wide solution. We tested the proposed method for small, medium and large size of job shop scheduling problems and compared to a global optimal solutions. The proposed method shows promising results in terms of solution qualities and computational times.The authors would like to thank the anonymous referees whose valuable comments helped us to improve this paper. This work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2005-041-D00895)