Lagrangean decomposition for integer programming : theory and applications

 Access to full text

 Full (PDF)

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

1. Mohamed Haouari, Pierre Dejax, Martin Desrochers, Les problèmes de tournées avec contraintes de fenêtres de temps, l'état de l'art