Applications of the Lagrangian Relaxation Method to Operations Scheduling

  • Juan José LaviosEmail author
  • José Alberto Arauzo
  • Ricardo del Olmo
  • Miguel Ángel Manzanedo
Conference paper
Part of the Lecture Notes in Management and Industrial Engineering book series (LNMIE)


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.


Lagrangian 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.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Juan José Lavios
    • 1
    Email author
  • José Alberto Arauzo
    • 2
  • Ricardo del Olmo
    • 3
  • Miguel Ángel Manzanedo
    • 3
  1. 1.Grupo INSISOC. EPSUniversidad de BurgosBurgosSpain
  2. 2.Grupo INSISOC. EIIUniversidad de ValladolidValladolidSpain
  3. 3.Department of Civil Engineering, Higher Polytechnic SchoolUniversity of BurgosBurgosSpain

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