메뉴 건너뛰기




Volumn 33, Issue 5, 2006, Pages 1464-1487

Lagrangian duality applied to the vehicle routing problem with time windows

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CONSTRAINT THEORY; PROBLEM SOLVING; RELAXATION PROCESSES;

EID: 26444602999     PISSN: 03050548     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cor.2004.11.002     Document Type: Article
Times cited : (100)

References (34)
  • 1
    • 0008439086 scopus 로고    scopus 로고
    • Solving the asymmetric travelling salesman problem with time windows by branch-and-cut
    • N. Ascheuer, M. Fischetti, and M. Grötschel Solving the asymmetric travelling salesman problem with time windows by branch-and-cut Mathematical Programming 90 3 2001 475 506
    • (2001) Mathematical Programming , vol.90 , Issue.3 , pp. 475-506
    • Ascheuer, N.1    Fischetti, M.2    Grötschel, M.3
  • 3
    • 0000110116 scopus 로고
    • Local search in routing problems with time windows
    • M. Savelsbergh Local search in routing problems with time windows Annals of Operations Research 4 1985 285 305
    • (1985) Annals of Operations Research , vol.4 , pp. 285-305
    • Savelsbergh, M.1
  • 5
    • 85042163696 scopus 로고
    • A new optimization algorithm for the vehicle routing problem with time windows
    • M. Desrochers, J. Desrosiers, and M. Solomon A new optimization algorithm for the vehicle routing problem with time windows Operations Research 40 1992 342 354
    • (1992) Operations Research , vol.40 , pp. 342-354
    • Desrochers, M.1    Desrosiers, J.2    Solomon, M.3
  • 6
    • 0031140531 scopus 로고    scopus 로고
    • An optimization algorithm for the vehicle routing problem with time windows based on Lagrangean relaxation
    • N. Kohl, and O.B.G. Madsen An optimization algorithm for the vehicle routing problem with time windows based on Lagrangean relaxation Operations Research 45 1997 395 406
    • (1997) Operations Research , vol.45 , pp. 395-406
    • Kohl, N.1    Madsen, O.B.G.2
  • 7
    • 0001661962 scopus 로고
    • Note on the complexity of the shortest path models for column generation in VRPTW
    • M. Dror Note on the complexity of the shortest path models for column generation in VRPTW Operations Research 42 1994 977 978
    • (1994) Operations Research , vol.42 , pp. 977-978
    • Dror, M.1
  • 8
    • 0019477279 scopus 로고
    • The Lagrangian relaxation method for solving integer programming problems
    • M.L. Fisher The Lagrangian relaxation method for solving integer programming problems Management Science 27 1981 1 18
    • (1981) Management Science , vol.27 , pp. 1-18
    • Fisher, M.L.1
  • 11
    • 3342976993 scopus 로고    scopus 로고
    • A parallel cutting-plane algorithm for the vehicle routing problem with time windows
    • Rice University
    • Cook W, Rich JL. A parallel cutting-plane algorithm for the vehicle routing problem with time windows. Technical report, Rice University; 1999.
    • (1999) Technical Report
    • Cook, W.1    Rich, J.L.2
  • 12
    • 4644270575 scopus 로고    scopus 로고
    • The shortest path problem with k-cycle elimination (k ≥ 3): Improving a branch-and-price algorithm for the VRPTW
    • Lehr- und Forschungsgebiet Operations Research und Logistik Management, Rheinisch-Westfälische Technische Hochschule
    • Irnich S, Villeneuve D. The shortest path problem with k-cycle elimination (k ≥ 3 ): improving a branch-and-price algorithm for the VRPTW. Technical report, Lehr- und Forschungsgebiet Operations Research und Logistik Management, Rheinisch-Westfälische Technische Hochschule; 2003.
    • (2003) Technical Report
    • Irnich, S.1    Villeneuve, D.2
  • 13
    • 19944384657 scopus 로고    scopus 로고
    • An exact algorithm for the elementary shortest path problem with resource constraints: Application to some vehicle routing problems
    • Laboratoire d'Informatique d'Avignon, Université d'Avignon
    • Feillet D, Dejax P, Gendreau M, Gueguen C. An exact algorithm for the elementary shortest path problem with resource constraints: application to some vehicle routing problems. Technical report, Laboratoire d'Informatique d'Avignon, Université d'Avignon; 2004.
    • (2004) Technical Report
    • Feillet, D.1    Dejax, P.2    Gendreau, M.3    Gueguen, C.4
  • 14
    • 26444547613 scopus 로고    scopus 로고
    • Vehicle routing problem with elementary shortest path based column generation
    • ILOG
    • Chabrier A. Vehicle routing problem with elementary shortest path based column generation. Technical report, ILOG; 2003.
    • (2003) Technical Report
    • Chabrier, A.1
  • 15
    • 0001547779 scopus 로고
    • The cutting-plane method for solving convex programs
    • J.E. Kelley The cutting-plane method for solving convex programs Journal of SIAM 8 1960 703 712
    • (1960) Journal of SIAM , vol.8 , pp. 703-712
    • Kelley, J.E.1
  • 16
    • 0000882113 scopus 로고
    • Newton's method for convex programming and tchebycheff approximation
    • E.W. Cheney, and A.A. Goldstein Newton's method for convex programming and tchebycheff approximation Numerische Mathematik 1 1959 253 268
    • (1959) Numerische Mathematik , vol.1 , pp. 253-268
    • Cheney, E.W.1    Goldstein, A.A.2
  • 17
    • 0001391104 scopus 로고
    • A decomposition principle for linear programs
    • G.B. Dantzig, and P. Wolfe A 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
  • 19
    • 0023313252 scopus 로고
    • Algorithms for the vehicle routing and scheduling problems with time window constraints
    • M.M. Solomon Algorithms for the vehicle routing and scheduling problems with time window constraints Operations Research 35 1987 254 265
    • (1987) Operations Research , vol.35 , pp. 254-265
    • Solomon, M.M.1
  • 20
    • 0035330038 scopus 로고    scopus 로고
    • A parallel two-phase metaheuristic for routing problems with time windows
    • H. Gehring, and J. Homberger A parallel two-phase metaheuristic for routing problems with time windows Asia-Pacific Journal of Operational Research 18 2001 35 47
    • (2001) Asia-Pacific Journal of Operational Research , vol.18 , pp. 35-47
    • Gehring, H.1    Homberger, J.2
  • 22
    • 26444474149 scopus 로고    scopus 로고
    • An outer approximate subdifferential method for piecewise affine optimization
    • P. Neame, N. Boland, and D. Ralph An outer approximate subdifferential method for piecewise affine optimization Mathematical Programming 87 2000 57 86
    • (2000) Mathematical Programming , vol.87 , pp. 57-86
    • Neame, P.1    Boland, N.2    Ralph, D.3
  • 23
    • 0002144209 scopus 로고
    • A generalized permanent labelling algorithm for the shortest path problem with time windows
    • M. Desrochers, and F. Soumis A generalized permanent labelling algorithm for the shortest path problem with time windows INFOR 26 1988 191 211
    • (1988) INFOR , vol.26 , pp. 191-211
    • Desrochers, M.1    Soumis, F.2
  • 24
    • 4644268001 scopus 로고
    • An algorithm for the shortest path problem with resource constraints
    • GERAD
    • Desrochers M. An algorithm for the shortest path problem with resource constraints. Technical report, GERAD; 1988.
    • (1988) Technical Report
    • Desrochers, M.1
  • 25
    • 0346061790 scopus 로고
    • The travelling salesman problem as a constrained shortest path problem: Theory and computational experience
    • D.J. Houck, J.C. Picard, M. Queyranne, and R.R. Vemuganti The travelling salesman problem as a constrained shortest path problem theory and computational experience OPSEARCH 17 1980 93 109
    • (1980) OPSEARCH , vol.17 , pp. 93-109
    • Houck, D.J.1    Picard, J.C.2    Queyranne, M.3    Vemuganti, R.R.4
  • 28
    • 0000894063 scopus 로고
    • A nonlinear programming technique for the optimization of continuous processing systems
    • R.E. Griffith, and R.A. Stewart A nonlinear programming technique for the optimization of continuous processing systems Management Science 7 1961 379 392
    • (1961) Management Science , vol.7 , pp. 379-392
    • Griffith, R.E.1    Stewart, R.A.2
  • 29
    • 0013467366 scopus 로고
    • An algorithm for minimax solution of overdetermined systems of non-linear equations
    • K. Madsen An algorithm for minimax solution of overdetermined systems of non-linear equations Journal of the Institute of Mathematics and its Applications 16 1975 321 328
    • (1975) Journal of the Institute of Mathematics and Its Applications , vol.16 , pp. 321-328
    • Madsen, K.1
  • 31
    • 0000873069 scopus 로고
    • A method for the solution of certain problems in least squares
    • K. Levenberg A method for the solution of certain problems in least squares Quarterly Applied Mathematics 2 1944 164 168
    • (1944) Quarterly Applied Mathematics , vol.2 , pp. 164-168
    • Levenberg, K.1
  • 32
    • 0000169232 scopus 로고
    • An algorithm for least squares estimation of nonlinear parameters
    • D. Marquardt An algorithm for least squares estimation of nonlinear parameters SIAM Journal of Applied Mathematics 11 1963 431 441
    • (1963) SIAM Journal of Applied Mathematics , vol.11 , pp. 431-441
    • Marquardt, D.1
  • 33
    • 0342571667 scopus 로고    scopus 로고
    • The ABACUS system for branch-and-cut-and-price algorithms in integer programming and combinatorial optimization
    • M. Jünger, and S. Thienel The ABACUS system for branch-and-cut-and- price algorithms in integer programming and combinatorial optimization Software Practice and Experience 30 11 2000 1325 1352
    • (2000) Software: Practice and Experience , vol.30 , Issue.11 , pp. 1325-1352
    • Jünger, M.1    Thienel, S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.