Applications of the Lagrangian Relaxation Method to Operations Scheduling
Lagrangian Relaxation is a combinatorial optimization method which is mainly used as decomposition method. A complex problem can be divided into smaller and easier problems. Lagrangian Relaxation method has been applied to solve scheduling problems in diverse manufacturing environments such as single machine, parallel machine, flow shop, job shop or even in complex real-world environments. We highlight the two key issues on the application of the method: the first one is the resolution of the dual problem and the second one is the choice which constraints should be relaxed. We present the main characteristics of these approaches and survey the existing works in this area.
KeywordsLagrangian relaxation Scheduling Combinatorial optimization Integer programming
The authors acknowledge support from the Spanish Ministry of Science and Innovation Project CSD2010-00034 (SimulPast CONSOLIDER-INGENIO 2010) and by the Regional Government of Castile and Leon (Spain) Project VA056A12-2.
- 1.Arauzo JA (2007) Control distribuido de sistemas de fabricación flexibles: un enfoque basado en agentes. Thesis. University of ValladolidGoogle Scholar
- 2.Araúzo JA, Pavón J, Lopez-Paredes A, Pajares J (2009) Agent based Modeling and Simulation of Multi-project Scheduling. In MALLOW, The Multi-Agent Logics, Languages, and Organisations Federated WorkshopsGoogle Scholar
- 5.Chen H, Chu C, Proth J-M (1995) More efficient Lagrangian relaxation approach to job-shop scheduling problems. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp 496–501Google Scholar
- 10.Edis EB, Araz C, Ozkarahan I (2008) Lagrangian-based solution approaches for a resource-constrained parallel machine scheduling problem with machine eligibility restrictions. In Proceedings of the 21st international conference on Industrial, Engineering and Other Applications of Applied Intelligent Systems: New Frontiers in Applied Artificial Intelligence. Springer, Wrocław, pp 337–346Google Scholar
- 14.Jeong I-J, Leon VJ (2002) Decision-making and cooperative interaction via coupling agents in organizationally distributed systems. IIE Trans 34(9):789–802Google Scholar
- 17.Jiang S, Tang L (2008) Lagrangian relaxation algorithm for a single machine scheduling with release dates. In: Second International Symposium on Intelligent Information Technology Application, pp 811–815Google Scholar
- 18.Kaskavelis CA, Caramanis MC (1998) Efficient Lagrangian relaxation algorithms for industry size job-shop scheduling problems. IIE Trans 30(11):1085–1097Google Scholar
- 20.Liu N, Abdelrahman MA, Ramaswamy S (2004) A multi-agent model for reactive job shop scheduling. In: Proceedings of the Thirty-Sixth Southeastern Symposium on System Theory, pp 241–245Google Scholar
- 27.Nishi T, Hiranaka Y, Inuiguchi M (2007) A successive Lagrangian relaxation method for solving flow shop scheduling problems with total weighted tardiness. In: IEEE International Conference on Automation Science and Engineering, pp 875–880Google Scholar
- 28.Sun X, Noble JS, Klein CM (1999) Single-machine scheduling with sequence dependent setup to minimize total weighted squared tardiness. IIE Trans 31(2):113–124Google Scholar
- 29.Sun T, Luh PB, Min L (2006) Lagrangian relaxation for complex job shop scheduling. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp 1432–1437Google Scholar
- 34.Zhao X, Luh P, Wang J (1997) The surrogate gradient algorithm for Lagrangian relaxation method. In: Proceedings of the 36th IEEE Conference on Decision and Control 1:310, 305Google Scholar