Column generation method for unit commitment

Takayuki Shiina*, Jun Imaizumi

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution


We propose a new algorithm for the stochastic unit commitment problem which is based on the Lagrangian relaxation and the column generation approach. This problem is formulated as a multi-stage nonlinear integer programming problem because the fuel cost function is assumed to be a convex quadratic function. The algorithm consists of two phases. After solving the problem by Lagrangian relaxation, the algorithm continues adding schedules from the dual solution of the restricted linear master program until the algorithm cannot generate new schedules. The schedule generation problem is solved by the calculation of dynamic programming on the scenario tree. We applied the Lagrangian relaxation-column generation approach to a test problem based on the system of a certain Japanese electric power company. Numerical results indicate a significant improvement in the quality of the solution.

Original languageEnglish
Title of host publicationProceedings of the 2008 International Conference on Scientific Computing, CSC 2008
Number of pages7
Publication statusPublished - 2008 Dec 1
Externally publishedYes
Event2008 International Conference on Scientific Computing, CSC 2008 - Las Vegas, NV, United States
Duration: 2008 Jul 142008 Jul 17

Publication series

NameProceedings of the 2008 International Conference on Scientific Computing, CSC 2008


Other2008 International Conference on Scientific Computing, CSC 2008
Country/TerritoryUnited States
CityLas Vegas, NV


  • Column generation
  • Lagrangian relaxation
  • Stochastic programming
  • Unit commitment

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Computer Science Applications
  • Software


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