Efficient solution techniques for large Mix Integer Linear Programming problems

Objectives: To present relaxation and decomposition techniques  to  tackle  Mix Integer Linear Programming problems of large dimensions effectively. To analyse and implement resolution methods using  columns and/or constraints generation techniques.

Contents:

  • Dantzig-Wolfe Decomposition Methods and Column Generation  for  LPs 

  • Branch and Price for MILPs

  • Benders Decomposition Methods for  LPs 

  • Lagrangian Relaxation

  • Applications

Bibliography

  • G. Fleury, Ph. Lacomme Programmation linéaire avancée (Programmes Java pour Macintosh, Linux et  Windows), Ellipses, 2010.

  • Guy Desaulniers , Jacques Desrosiers, Marius M. Solomon. Column Generation.    Springer, 2005.

  • François Vanderbeck, Laurence A. Wolsey. Reformulation and Decomposition of Integer Programs. 50 Years of Integer Programming 1958-2008, 2010, pp 431-502.

  • J. F. Benders. Partitioning procedures for solving mixed-variables programming problems.  Numer. Math. 4, 3,  1962, pp. 238–252.