Lagrangean decomposition for integer programming : theory and applications

Monique Guignard; Siwhan Kim

RAIRO - Operations Research - Recherche Opérationnelle (1987)

  • Volume: 21, Issue: 4, page 307-323
  • ISSN: 0399-0559

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Guignard, Monique, and Kim, Siwhan. "Lagrangean decomposition for integer programming : theory and applications." RAIRO - Operations Research - Recherche Opérationnelle 21.4 (1987): 307-323. <http://eudml.org/doc/104926>.

@article{Guignard1987,
author = {Guignard, Monique, Kim, Siwhan},
journal = {RAIRO - Operations Research - Recherche Opérationnelle},
keywords = {variable splitting; layering; implicit constraints; facets; integer polytopes; mixed-integer programming; decomposition in the Lagrangean relaxation; duality; Lagrangean decomposition; subtour elimination constraints; matching inequalities},
language = {eng},
number = {4},
pages = {307-323},
publisher = {EDP-Sciences},
title = {Lagrangean decomposition for integer programming : theory and applications},
url = {http://eudml.org/doc/104926},
volume = {21},
year = {1987},
}

TY - JOUR
AU - Guignard, Monique
AU - Kim, Siwhan
TI - Lagrangean decomposition for integer programming : theory and applications
JO - RAIRO - Operations Research - Recherche Opérationnelle
PY - 1987
PB - EDP-Sciences
VL - 21
IS - 4
SP - 307
EP - 323
LA - eng
KW - variable splitting; layering; implicit constraints; facets; integer polytopes; mixed-integer programming; decomposition in the Lagrangean relaxation; duality; Lagrangean decomposition; subtour elimination constraints; matching inequalities
UR - http://eudml.org/doc/104926
ER -

References

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  1. H. CROWDER and M. W. PADBERG, Solving Large-Scale Symmetric Traveling Salesm an Problems to Optimality, Management Science, Vol. 26, 1980, pp. 495-509. Zbl0444.90068MR585424
  2. J. EDMONDS, Maximum Matching and a Polyhedron with (0, 1) Vertices, Journal of Research of National Bureau of Standards, Vol. 69B, 1965, pp. 125-130. Zbl0141.21802MR183532
  3. M. L. FISHER, R. JAIKUMAR and L. VAN WASSENHOVE, A Multiplier Adjustment Method for the Generalized Assignment Problem, Management Science, Vol. 32, 1986, pp. 1095-1103. Zbl0626.90036
  4. A. GEOFFRION, Lagrangean Relaxation and its Uses in Integer Programming, Math. Prog. Study, Vol. 2, 1974, pp. 82-114. Zbl0395.90056MR439172
  5. F. GLOVER and J. MULVEY, The Equivalence of the 0-1 Integer Programming Problem to Discrete Generalized and Pure Network Models, Report HBS 75-46, Harvard University (1975), also Op. Res., Vol. 28(3), 1980, pp. 829-933. Zbl0443.90064
  6. F. GLOVER and D. KLINGMAN, Layering Strategies for Creating Exploitable Structure in Linear and Integer Programs, Center for Business Decision Analysis Report, Vol. 119 (Nov. 1984, revised June 1985). Zbl0667.90070
  7. M. GUIGNARD and M. ROSENWEIN, An Application of Lagrangean Decomposition to the Generalized Assignment Problem, Department of Decision Sciences Report # 85-09-02, Univ. of Penn., 1985. 
  8. M. GUIGNARD and M. ROSENWEIN, An Application of Lagrangean Decomposition to the Resource-Constrained Minimum Weighted Arborescence Problem, Research Report, Department of Decision Sciences, University of Pennsylvania, and AT & T Bell Laboratories, Holmdel, NJ, 1987. Zbl0701.90064
  9. M. GUIGNARD, Lagrangean Decomposition: An Ideal Approach for Problems with Implicit Constraints, Dept. of Statistics, Report # 88, University of Pennsylvania, 1986. 
  10. M. HELD and R. M. KARP, The Traveling Salesman Problem and Minimum Spanning Trees: Part I, Operations Research, Vol. 18, 1970, pp. 1138-1162. Zbl0226.90047MR278710
  11. K. O. JÖRNSTEN, M. NÄSBERG and P. A. SMEDS, Variable splitting. A New Lagrangean Relaxation Approach to Some Mathematical Programming Models, Department of Mathematics Report LiTH-MAT-R-85-04, Linköping Institute of Technology, Sweden, 1985. 
  12. K. O. JÖRNSTEN and M. NÄSBERG, A New Lagrangean Relaxation Approach to the Generalized Assignment Problem, European Journal of Operational Research, Vol. 27, No. 3, 1986, pp. 313-323. Zbl0617.90068MR864903
  13. S. MARTELLO and P. TOTH, An Algorithm for the Generalized Assignment Problem, in J. P. Brans (Ed.), Operational Research 81, North Holland, Amsterdam, 1981, pp. 589-603. Zbl0473.90047MR651209
  14. R. M. NAUSS, An Improved Algorithm for the Capacitated Facility Location Problem, Vol. 29, 1978, Operational Research Society, pp. 1195-1202. Zbl0402.90063
  15. C. RIBEIRO, Algorithmes de recherche de plus courts chemins avec contraintes : Étude théorique, implémentation et parallélisation, Doctoral Dissertation, Paris, 1983. 
  16. M. ROSENWEIN, Design and Application of Solution Methodologies to Optimize Problems in Transportation Logistics, Doctoral Dissertation, Dept. of Decision Sciences, University of Pennsylvania, 1986. 
  17. G. T. ROSS and R. M. SOLAND, A Branch and Bound Algorithm for the Generalized Assignment Problem, Mathematical Programming, Vol. 8, 1975, pp. 92-103. Zbl0308.90028MR368757
  18. F. SHEPARDSON and R. MARSTEN, A Lagrangean Relaxation Algorithm for the Two-Duty Period Scheduling Problem, Man. Sc., 26(3), 1980, pp. 274-281. Zbl0448.90042MR591284
  19. T. J. VAN ROY, A Cross Decomposition Algorithm For Capacitated Facility Location, Working Paper 80-8A, Afdeling Industrieel Beleid, Katholieke Universiteit Leuven, 1980. Zbl0594.90022

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