메뉴 건너뛰기




Volumn 179, Issue 3, 2007, Pages 1109-1125

A branch-and-price algorithm for the capacitated facility location problem

Author keywords

Branch and price; Capacitated facility location; Column generation; Lagrangean relaxation; Mixed integer programming

Indexed keywords

ALGORITHMS; COMPUTATION THEORY; INTEGER PROGRAMMING; LAGRANGE MULTIPLIERS; OPERATIONS RESEARCH; PROBLEM SOLVING;

EID: 33845922643     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejor.2005.03.078     Document Type: Article
Times cited : (66)

References (64)
  • 1
    • 0000894590 scopus 로고    scopus 로고
    • Capacitated facility location: Separation algorithm and computational experience
    • Aardal K. Capacitated facility location: Separation algorithm and computational experience. Mathematical Programming 81 (1998) 149-175
    • (1998) Mathematical Programming , vol.81 , pp. 149-175
    • Aardal, K.1
  • 5
    • 0023963030 scopus 로고
    • An algorithm for solving large capacitated warehouse location problems
    • Beasley J.E. An algorithm for solving large capacitated warehouse location problems. European Journal of Operational Research 33 (1988) 314-325
    • (1988) European Journal of Operational Research , vol.33 , pp. 314-325
    • Beasley, J.E.1
  • 9
    • 20444376164 scopus 로고
    • Applying bundle methods to the optimization of polyhedral functions: An applications-oriented development
    • Carraresi P., Frangioni A., and Nonato M. Applying bundle methods to the optimization of polyhedral functions: An applications-oriented development. Ricerca Operativa 25 (1995) 5-49
    • (1995) Ricerca Operativa , vol.25 , pp. 5-49
    • Carraresi, P.1    Frangioni, A.2    Nonato, M.3
  • 10
    • 8444241679 scopus 로고    scopus 로고
    • Hierarchical two level location problems
    • Sansò B., and Soriano P. (Eds), Kluwer Academic Publishers Group, London, Dordrecht, Boston (Chapter 3)
    • Chardaire P. Hierarchical two level location problems. In: Sansò B., and Soriano P. (Eds). Telecommunications Network Planning (1999), Kluwer Academic Publishers Group, London, Dordrecht, Boston 33-54 (Chapter 3)
    • (1999) Telecommunications Network Planning , pp. 33-54
    • Chardaire, P.1
  • 11
    • 0002401694 scopus 로고
    • Extensions to a Lagrangean relaxation approach for the capacitated warehouse location problem
    • Christofides N., and Beasley J.E. Extensions to a Lagrangean relaxation approach for the capacitated warehouse location problem. European Journal of Operational Research 12 (1983) 19-28
    • (1983) European Journal of Operational Research , vol.12 , pp. 19-28
    • Christofides, N.1    Beasley, J.E.2
  • 12
    • 0026106418 scopus 로고
    • A comparison of heuristics and relaxations for the capacitated plant location problem
    • Cornuejols G., Sridharan R., and Thizy J.-M. A comparison of heuristics and relaxations for the capacitated plant location problem. European Journal of Operational Research 50 (1991) 280-297
    • (1991) European Journal of Operational Research , vol.50 , pp. 280-297
    • Cornuejols, G.1    Sridharan, R.2    Thizy, J.-M.3
  • 13
    • 0042522794 scopus 로고    scopus 로고
    • Upper and lower bounds for the single source capacitated location problem
    • Cortinhal M.J., and Captivo M.E. Upper and lower bounds for the single source capacitated location problem. European Journal of Operational Research 151 (2003) 333-351
    • (2003) European Journal of Operational Research , vol.151 , pp. 333-351
    • Cortinhal, M.J.1    Captivo, M.E.2
  • 14
    • 0001391104 scopus 로고
    • Decomposition principle for linear programs
    • Dantzig G.B., and Wolfe P. Decomposition principle for linear programs. Operations Research 8 (1960) 101-111
    • (1960) Operations Research , vol.8 , pp. 101-111
    • Dantzig, G.B.1    Wolfe, P.2
  • 15
    • 0000039065 scopus 로고
    • The decomposition algorithm for linear programs
    • Dantzig G.B., and Wolfe P. The decomposition algorithm for linear programs. Econometrica 29 (1961) 767-778
    • (1961) Econometrica , vol.29 , pp. 767-778
    • Dantzig, G.B.1    Wolfe, P.2
  • 17
    • 0022101579 scopus 로고
    • ADD-heuristics' starting procedures for capacitated plant location models
    • Domschke W., and Drexl A. ADD-heuristics' starting procedures for capacitated plant location models. European Journal of Operational Research 21 (1985) 47-53
    • (1985) European Journal of Operational Research , vol.21 , pp. 47-53
    • Domschke, W.1    Drexl, A.2
  • 18
    • 33845934201 scopus 로고    scopus 로고
    • Dongarra, J.J., 2005. Performance of various computers using standard linear equations software. Technical Report CS-89-95, Computer Science Department, University of Tennessee. Available from: http://www.netlib.org/benchmark/performance.pdf.
  • 20
    • 0001618549 scopus 로고    scopus 로고
    • A bundle type dual-ascent approach to linear multi-commodity min cost flow problems
    • Frangioni A., and Gallo G. A bundle type dual-ascent approach to linear multi-commodity min cost flow problems. Informs Journal on Computing 11 (1999) 370-393
    • (1999) Informs Journal on Computing , vol.11 , pp. 370-393
    • Frangioni, A.1    Gallo, G.2
  • 21
  • 22
    • 0017942883 scopus 로고
    • Lagrangean relaxation to capacitated facility location problems
    • Geoffrion A.M., and McBride R. Lagrangean relaxation to capacitated facility location problems. AIIE Transactions 10 (1978) 40-47
    • (1978) AIIE Transactions , vol.10 , pp. 40-47
    • Geoffrion, A.M.1    McBride, R.2
  • 23
    • 0001510482 scopus 로고
    • A linear programming approach to the cutting stock problem
    • Gilmore P.C., and Gomory R.E. A linear programming approach to the cutting stock problem. Operations Research 9 (1961) 849-859
    • (1961) Operations Research , vol.9 , pp. 849-859
    • Gilmore, P.C.1    Gomory, R.E.2
  • 24
    • 0036817928 scopus 로고    scopus 로고
    • Convex nondifferentiable optimization: A survey focussed on the analytic center cutting plane method
    • Goffin J.-L., and Vial J.-P. Convex nondifferentiable optimization: A survey focussed on the analytic center cutting plane method. Optimization Methods & Software 17 (2002) 805-867
    • (2002) Optimization Methods & Software , vol.17 , pp. 805-867
    • Goffin, J.-L.1    Vial, J.-P.2
  • 25
    • 0000949338 scopus 로고
    • Decomposition and nondifferentiable optimization with the projective algorithm
    • Goffin J.-L., Haurie A., and Vial J.-P. Decomposition and nondifferentiable optimization with the projective algorithm. Management Science 38 (1992) 284-302
    • (1992) Management Science , vol.38 , pp. 284-302
    • Goffin, J.-L.1    Haurie, A.2    Vial, J.-P.3
  • 27
    • 33845927333 scopus 로고    scopus 로고
    • Gondzio, J., Sarkissian, R. 1996. Column generation with a primal-dual method. Technical Report 1996:6, LogiLab, HEC, Section of Management Studies, University of Geneva. Available from: .
  • 28
    • 33845941152 scopus 로고    scopus 로고
    • Görtz, S., Klose, A. 2004. Das kapazitierte Standortproblem: Branch-and-Price und die Wahl der Verzweigungsvariable. Arbeitspapier, Bergische Universität Wuppertal, Fachbereich Wirtschafts- und Sozialwissenschaften.
  • 29
    • 33845957063 scopus 로고    scopus 로고
    • Guignard, M., Zhu, S. 1994. A two-phase dual algorithm for solving Lagrangean duals in mixed integer programming. Report 94-10-03, Operations and Information Management Department, University of Pennsylvania, The Wharton School.
  • 30
    • 33845923388 scopus 로고    scopus 로고
    • ILOG 2002. CPLEX 8.0. User's manual.
  • 31
  • 32
    • 0016351467 scopus 로고
    • An efficient heuristic procedure for the capacitated warehouse location problem
    • Khumawala B.M. An efficient heuristic procedure for the capacitated warehouse location problem. Naval Research Logistics Quarterly 21 (1974) 609-623
    • (1974) Naval Research Logistics Quarterly , vol.21 , pp. 609-623
    • Khumawala, B.M.1
  • 33
    • 27744578680 scopus 로고    scopus 로고
    • Combinatorial optimization problems of the assignment type and a partitioning approach
    • Quantitative Approaches to Distribution Logistics and Supply Chain Management. Klose A., Van Wassenhove L.N., and Speranza M.G. (Eds), Springer-Verlag, Berlin, Heidelberg, New York
    • Klose A., and Drexl A. Combinatorial optimization problems of the assignment type and a partitioning approach. In: Klose A., Van Wassenhove L.N., and Speranza M.G. (Eds). Quantitative Approaches to Distribution Logistics and Supply Chain Management. Lecture Notes in Economics and Mathematical Systems vol. 519 (2002), Springer-Verlag, Berlin, Heidelberg, New York 215-245
    • (2002) Lecture Notes in Economics and Mathematical Systems , vol.519 , pp. 215-245
    • Klose, A.1    Drexl, A.2
  • 34
    • 33845932567 scopus 로고    scopus 로고
    • Klose, A., Drexl, A., 2002b. A partitioning and column generation approach for the capacitated facility location problem. Technical Report, University of St. Gallen.
  • 35
    • 27744479139 scopus 로고    scopus 로고
    • Lower bounds for the capacitated facility location problem based on column generation
    • Klose A., and Drexl A. Lower bounds for the capacitated facility location problem based on column generation. Management Science 51 (2005) 1689-1705
    • (2005) Management Science , vol.51 , pp. 1689-1705
    • Klose, A.1    Drexl, A.2
  • 36
    • 0019531809 scopus 로고
    • Facility location models for planning a transatlantic communications network
    • Kochmann G.A., and McCallum C.J. Facility location models for planning a transatlantic communications network. European Journal of Operational Research 6 (1981) 205-211
    • (1981) European Journal of Operational Research , vol.6 , pp. 205-211
    • Kochmann, G.A.1    McCallum, C.J.2
  • 37
    • 33845938238 scopus 로고    scopus 로고
    • Korupolu, M.R., Plaxton, C.G., Rajaraman, R. 1998. Analysis of a local search heuristic for facility location problems. Technical Report 98-30, DIMACS, Rutgers University.
  • 38
    • 0000369468 scopus 로고
    • A heuristic program for locating warehouses
    • Kuehn A.A., and Hamburger M.J. A heuristic program for locating warehouses. Management Science 9 (1963) 643-666
    • (1963) Management Science , vol.9 , pp. 643-666
    • Kuehn, A.A.1    Hamburger, M.J.2
  • 39
    • 77957820648 scopus 로고
    • Nondifferentiable optimization
    • Optimization. Nemhauser G.L., Rinnooy Kan A.H.G., and Todd M.J. (Eds), North-Holland, Amsterdam
    • Lemaréchal C. Nondifferentiable optimization. In: Nemhauser G.L., Rinnooy Kan A.H.G., and Todd M.J. (Eds). Optimization. Handbooks in Operations Research and Management Science vol. 1 (1989), North-Holland, Amsterdam 529-572
    • (1989) Handbooks in Operations Research and Management Science , vol.1 , pp. 529-572
    • Lemaréchal, C.1
  • 40
    • 0000957203 scopus 로고
    • Valid inequalities and facets of the capacitated plant location problem
    • Leung J.M.Y., and Magnanti T.L. Valid inequalities and facets of the capacitated plant location problem. Mathematical Programming 44 (1989) 271-291
    • (1989) Mathematical Programming , vol.44 , pp. 271-291
    • Leung, J.M.Y.1    Magnanti, T.L.2
  • 41
    • 0001332760 scopus 로고    scopus 로고
    • A computational study of search strategies for mixed integer programming
    • Linderoth J.T., and Savelsbergh M.W.P. A computational study of search strategies for mixed integer programming. INFORMS Journal on Computing 11 (1999) 173-187
    • (1999) INFORMS Journal on Computing , vol.11 , pp. 173-187
    • Linderoth, J.T.1    Savelsbergh, M.W.P.2
  • 43
    • 0019563311 scopus 로고
    • Accelerating Benders decomposition: Algorithmic enhancement and model selection criteria
    • Magnanti T.L., and Wong R.T. Accelerating Benders decomposition: Algorithmic enhancement and model selection criteria. Operations Research 29 (1981) 464-484
    • (1981) Operations Research , vol.29 , pp. 464-484
    • Magnanti, T.L.1    Wong, R.T.2
  • 45
    • 0032687866 scopus 로고    scopus 로고
    • Dynamic programming and strong bounds for the 0-1 knapsack problem
    • Martello S., Pisinger D., and Toth P. Dynamic programming and strong bounds for the 0-1 knapsack problem. Management Science 45 (1999) 414-424
    • (1999) Management Science , vol.45 , pp. 414-424
    • Martello, S.1    Pisinger, D.2    Toth, P.3
  • 47
    • 0033401666 scopus 로고    scopus 로고
    • An interior point method in Dantzig-Wolfe decomposition
    • Martinson R.K., and Tind J. An interior point method in Dantzig-Wolfe decomposition. Computers & Operations Research 26 (1999) 1195-1216
    • (1999) Computers & Operations Research , vol.26 , pp. 1195-1216
    • Martinson, R.K.1    Tind, J.2
  • 49
    • 0022038238 scopus 로고
    • Lagrangian relaxation for the star-star concentrator location problem: Approximation algorithm and bounds
    • Mirzaian A. Lagrangian relaxation for the star-star concentrator location problem: Approximation algorithm and bounds. Networks 15 (1985) 1-20
    • (1985) Networks , vol.15 , pp. 1-20
    • Mirzaian, A.1
  • 50
    • 0018056041 scopus 로고
    • An improved algorithm for the capacitated facility location problem
    • Nauss R.M. An improved algorithm for the capacitated facility location problem. The Journal of the Operational Research Society 29 (1978) 1195-1201
    • (1978) The Journal of the Operational Research Society , vol.29 , pp. 1195-1201
    • Nauss, R.M.1
  • 51
    • 0020849839 scopus 로고
    • An algorithm for the fixed-charge assigning users to sources problem
    • Neebe A.W., and Rao M.R. An algorithm for the fixed-charge assigning users to sources problem. The Journal of the Operational Research Society 34 (1983) 1107-1113
    • (1983) The Journal of the Operational Research Society , vol.34 , pp. 1107-1113
    • Neebe, A.W.1    Rao, M.R.2
  • 52
    • 0023246782 scopus 로고
    • Efficient algorithms for the capacitated concentrator location problem
    • Pirkul H. Efficient algorithms for the capacitated concentrator location problem. Computers & Operations Research 14 (1987) 197-208
    • (1987) Computers & Operations Research , vol.14 , pp. 197-208
    • Pirkul, H.1
  • 53
    • 34250090501 scopus 로고
    • Lot-size models with backlogging: Strong reformulations and cutting planes
    • Pochet Y., and Wolsey L.A. Lot-size models with backlogging: Strong reformulations and cutting planes. Mathematical Programming 40 (1988) 317-335
    • (1988) Mathematical Programming , vol.40 , pp. 317-335
    • Pochet, Y.1    Wolsey, L.A.2
  • 56
    • 33845937340 scopus 로고    scopus 로고
    • Ryu, C., 1993. Capacity-oriented planning and scheduling in production and distributions systems. Ph.D. thesis, Department of Operations and Information Management, University of Pennsylvania, Philadelphia, PA.
  • 57
    • 33845950876 scopus 로고    scopus 로고
    • Ryu, C., Guignard, M., 1992. An efficient algorithm for the capacitated plant location problem. Working Paper 92-11-02, Decision Sciences Department, University of Pennsylvania, The Wharton School.
  • 59
    • 38249016170 scopus 로고
    • Approximate solutions to large scale capacitated facility location problems
    • Shetty B. Approximate solutions to large scale capacitated facility location problems. Applied Mathematics and Computation 39 (1990) 159-175
    • (1990) Applied Mathematics and Computation , vol.39 , pp. 159-175
    • Shetty, B.1
  • 60
    • 0030645561 scopus 로고    scopus 로고
    • Shmoys, D.B., Tardos, E., Aardal, K., 1997. Approximation algorithms for facility location problems. In: Proceedings of the 29th Annual ACM Symposium on Theory of Computing, pp. 265-274.
  • 61
    • 0027591103 scopus 로고
    • A Lagrangian heuristic for the capacitated plant location problem with single source constraints
    • Sridharan R. A Lagrangian heuristic for the capacitated plant location problem with single source constraints. European Journal of Operational Research 66 (1993) 305-312
    • (1993) European Journal of Operational Research , vol.66 , pp. 305-312
    • Sridharan, R.1
  • 62
    • 0022613611 scopus 로고
    • A cross decomposition algorithm for capacitated facility location
    • Van Roy T.J. A cross decomposition algorithm for capacitated facility location. Operations Research 34 (1986) 145-163
    • (1986) Operations Research , vol.34 , pp. 145-163
    • Van Roy, T.J.1
  • 63
    • 5244284084 scopus 로고    scopus 로고
    • Accelerating Benders' decomposition for the capacitated facility location problem
    • Wentges P. Accelerating Benders' decomposition for the capacitated facility location problem. Mathematical Methods of Operations Research 44 (1996) 267-290
    • (1996) Mathematical Methods of Operations Research , vol.44 , pp. 267-290
    • Wentges, P.1
  • 64
    • 0342832274 scopus 로고    scopus 로고
    • Weighted Dantzig-Wolfe decomposition for linear mixed-integer programming
    • Wentges P. Weighted Dantzig-Wolfe decomposition for linear mixed-integer programming. International Transactions in Operational Research 4 (1997) 151-162
    • (1997) International Transactions in Operational Research , vol.4 , pp. 151-162
    • Wentges, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.