On Dantzig-Wolfe decomposition in integer programming and ways to perform branching in a branch-and-price algorithm

Operations Research

Volumn 48, Issue 1, 2000, Pages 111-128

  Vanderbeck, François ^a  

^a UNIVERSITÉ DE BORDEAUX   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; CONSTRAINT THEORY; LINEAR PROGRAMMING; MATHEMATICAL MODELS; PROBLEM SOLVING; PROCESS ENGINEERING; SCHEDULING;

BRANCH AND PRICE ALGORITHM; COLUMN GENERATION SUBPROBLEM; CUTTING STOCK PROBLEM; DANTZIG-WOLFE DECOMPOSITION;

INTEGER PROGRAMMING;

EID: 0033725783     PISSN: 0030364X     EISSN: None     Source Type: Journal    
DOI: 10.1287/opre.48.1.111.12453     Document Type: Article

References (25)

1. Anbil, R., C. Barnhart, L. Hatay, E. L. Johnson, V. S. Ramakrishnan. 1993. Crew-pairing optimization at American Airlines Decision Technologies. T.A. Cirani, R.C. Leachman, eds. Optimization in Industry. Wiley, New York, 31-36.
2. Barnhart, C., E. L. Johnson, G. L. Nemhauser, M. W. P. Savelsbergh, P. H. Vance. 1994. Branch-and-price: column generation for solving huge integer programs. J. R. Birge, K. G. Murty, eds. Mathematical Programming, State of the Art. International Symposium on Mathematical Programming.
3. Beasley, J. E. 1990. OR-Library: distributing test problems by electronic mail. J. Oper. Res. Soc. 41 1069-1072.
4. CPLEX Optimization, Inc. 1994. Using the CPLEX Linear Optimizer, version 3.0. Incline Village, NV.
5. Dantzig, G. B., P. Wolfe. 1960. Decomposition principle for linear programs. Oper. Res. 8 101-111.
6. Desaulniers, G., J. Desrosiers, I. Ioachim, M. M. Solomon, F. Soumis. 1998. A unified framework for deterministic time constrained vehicle routing and crew scheduling problems. T.G. Crainic, G. Laporte, eds. Fleet Management and Logistics. Kluwer, Boston, MA, 57-93.
7. Desrosiers, J., Y. Dumas, M. M. Solomon, F. Soumis. 1994. Time constrained routing and scheduling. M.E. Ball, T.L. Magnanti, C. Monma, G.L. Nemhauser, eds. Handbooks in Operations Research and Management Sciences: Networks. North-Holland, Amsterdam.
8. Geoffrion, A. M. 1974. Lagrangian relaxation for integer programming. Math. Programming Study 2 82-114.
9. Gilmore, P. C., R. E. Gomory. 1961. A linear programming approach to the cutting stock problem. Oper. Res. 9 849-859.
10. _, _. 1963. A linear programming approach to the cutting stock problem: Part II. Oper. Res. 11 863-888.
11. Hurkens, C. 1995. Private communications.
12. Johnson, E. L., A. Mehrotra, G. L. Nemhauser. 1993. Min-cut clustering. Math. Programming 62 133-151.
13. Marcotte, O. 1985. The cutting stock problem and integer rounding. Math. Programming 33 89-92.
14. Martello, S., P. Toth. 1990. Knapsack Problems: Algorithms and Computer Implementations. Wiley Interscience Series in Discrete Mathematics and Optimization, Wiley, New York.
15. Martin, R. K. 1987. Generating alternative mixed-integer programming models using variable redefinition. Oper. Res. 35 (6) 820-831.
16. _. 1991. Using separation algorithms to generate mixed integer model formulations. Oper. Res. Letters 10 119-128.
17. Nemhauser, G. L., L. A. Wolsey. 1988. Integer and Combinatorial Optimization. John Wiley & Sons, Inc., New York.
18. Savelsbergh, M. W. P. 1997. A branch-and-price algorithm for the generalized assignment problem. Oper. Res. 45 831-841.
19. Sutter, A., F. Vanderbeck, L. A. Wolsey. 1998. Optimal placement of add/drop multiplexers: heuristic and exact algorithms. Oper. Res. 46 719-728.
20. Valerio de Carvalho, J. M. 1996. Exact solution of bin-packing problems using column generation and branch-and-bound. Working Paper. Depart. Prouducao e Sistemas, Universidade do Minho, Portugal.
21. Vance, P. H., C. Barnhard, E. L. Johnson, G. L. Nemhauser. 1994. Solving binary cutting stock problems by column generation and branch-and-bound. Comput. Optim. Appl. 3 111-130.
22. _. 1996. Branch-and-price algorithms for the one-dimensional cutting stock problem. Working Paper. Department of Industrial Engineering, Auburn University, Auburn, AL. To appear in Comput. Optim. Appl.
23. Vanderbeck, F. 1994. Decomposition and column generation for integer programs. Ph.D. Thesis. Faculté des Sciences Appliqées, Université Catholique de Louvain, Louvain-la-Neuve.
24. _. 1996. Computational study of a column generation algorithm for bin packing and cutting stock problems. Research Papers in Management Studies. University of Cambridge. To appear in Math. Programming.
25. _, L. A. Wolsey. 1996. An exact algorithm for IP column generation. Oper. Res. Letters 19(4) 151-159.