A branch-and-price approach to p-median location problems

Computers and Operations Research

Volumn 32, Issue 6, 2005, Pages 1655-1664

  Senne, Edson L F ^a   Lorena, Luiz A N ^b   Pereira, Marcos A ^b  

^a SÃO PAULO STATE UNIVERSITY UNESP   (Brazil)

^b INSTITUTO NACIONAL DE PESQUISAS ESPACIAIS   (Brazil)

Author keywords

Branch and price; Column generation; Lagrangean surrogate relaxation; P median

Indexed keywords

COMPUTATIONAL COMPLEXITY; HEURISTIC METHODS; LAGRANGE MULTIPLIERS; OPTIMIZATION; PROBLEM SOLVING; TREES (MATHEMATICS);

BRANCH AND PRICE; COLUMN GENERATION; LAGRANGEAN/SURROGATE RELAXATION; P-MEDIAN;

ALGORITHMS;

EID: 9544237158     PISSN: 03050548     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cor.2003.11.024     Document Type: Article

References (24)

1. Senne ELF, Lorena LAN. Lagrangean/surrogate heuristics for p-median problems. In: Laguna M, Gonzalez-Velarde JL, editors. Computing tools for modeling, optimization and simulation: interfaces in computer science and operations research. Dordrecht: Kluwer Academic Publishers; 2000. p. 115-30.
2. Narciso MG, Lorena LAN. Lagrangean/surrogate relaxation for generalized assignment problems. European Journal of Operational Research 1999; 114(1): 165-77.
3. Dantzig GB, Wolfe P. Decomposition principle for linear programs. Operations Research 1960;8:101-11.
4. Day PR, Ryan DM. Flight Attendant rostering for short-haul airline operations. Operations Research 1997;45: 649-61.
5. Desrochers M, Soumis F. A column generation approach to the urban transit crew scheduling problem. Transportation Science 1989;23:1-13.
6. Desrochers M, Desrosiers J, Solomon M. A new optimization algorithm for the vehicle routing problem with time windows. Operations Research 1992;40:342-54.
7. Gilmore PC, Gomory RE. A linear programming approach to the cutting stock problem. Operations Research 1961;9:849-59.
8. Gilmore PC, Gomory RE. A linear programming approach to the cutting stock problem - part II. Operations Research 1963;11:863-88.
9. Wolsey LA. Integer programming. New York: Wiley; 1998.
10. Valério de Carvalho JM. Exact solution of bin-packing problems using column generation and branch-and-bound, Working Paper, Universidade do Minho, Departamento Produção e Sistemas; 1996.
11. Vance PH, Barnhart C, Johnson EL, Nemhauser GL. Solving binary cutting stock problems by column generation and branch-and-bound. Computational Optimization and Applications 1994;3:111-30.
12. Neame PJ. Nonsmooth dual methods in integer programming. PhD thesis, Department of Mathematics and Statistics, The University of Melbourne; March, 1999.
13. Senne ELF, Lorena LAN. Stabilizing column generation using Lagrangean/surrogate relaxation: an application to p-median location problems. Presented at EURO2001 Conference, Erasmus University, Rotterdam; July 2001 (http://www.lac.inpe.br/∼lorena/ejor/EURO2001.pdf).
14. Lorena LAN, Senne ELF. A column generation approach to capacitated p-median problems. Computers and Operations Research 2003;31:863-76.
15. Marsten RM, Hogan W, Blankenship J. The boxstep method for large-scale optimization. Operations Research 1975;23:389-405.
16. du Merle O, Goffin JL, Vial JP. On improvements to the analytic centre cutting plane method. Computational Optimization and Applications 1998;11:37-52.
17. du Merle O, Villeneuve D, Desrosiers J, Hansen P. Stabilized column generation. Discrete Mathematics 1999; 194: 229-37.
18. Barnliart C, Johnson EL, Nemhauser GL, Savelsbergh MWP, Vance PH. Branch-and-price: column generation for solving huge integer programs. Operations Research 1998;46:316-29.
19. Ceselli A, Righini G. A branch-and-price algorithm for the capacitated p-median problem. Working Paper 2002, University of Milano (http://sansone. crema.unimi.it/∼righini/Papers/CPMP.pdf).
20. Garfinkel RS, Neebe W, Rao MR. An algorithm for the M-median location problem. Transportation Science 1974;8:217-36.
21. Swain RW. A parametric decomposition approach for the solution of uncapacitated location problems. Management Science 1974;21:955-61.
22. ILOG Inc., CPLEX 6.5, Cplex Division. Mountain View, CA, 1999.
23. Beasley JE. OR-Library: distributing test problems by electronic mail. Journal Operational Research Society 1990;41:1069-72.
24. Christofides N, Beasley JE. A tree search algorithm for the p-median problems. European Journal of Operational Research 1982;10:196-204.