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Volumn 137, Issue 1-2, 2013, Pages 409-452

Improved lower bounds and exact algorithm for the capacitated arc routing problem

Author keywords

Arc routing; Column generation; Dynamic programming; Set partitioning; Valid inequalities

Indexed keywords

BENCHMARKING; FLEET OPERATIONS; LINEAR PROGRAMMING; ROUTING ALGORITHMS;

EID: 84878574191     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-011-0497-4     Document Type: Article
Times cited : (36)

References (42)
  • 1
    • 84948708954 scopus 로고    scopus 로고
    • A hierarchical relaxations lower bound for the capacitated arc routing problem
    • H.R. Sprague (eds) IEEE Computer Society Washington DC
    • Amberg A.; Voß S.: A hierarchical relaxations lower bound for the capacitated arc routing problem. In: Sprague, H.R. (eds) Proceedings of the 35th Hawaii International Conference on System Sciences, vol. 3.; pp. 1-10. IEEE Computer Society, Washington DC (2002)
    • (2002) Proceedings of the 35th Hawaii International Conference on System Sciences, Vol. 3 , pp. 1-10
    • Amberg, A.1    Voß, S.2
  • 2
    • 0000684962 scopus 로고
    • Arc routing methods and applications
    • Ball, M.O.; Magnanti, T.L.; Monma, C.L.; Nemhauser, G.L. (eds.) North-Holland, Amsterdam
    • Assad, A.A.; Golden, B.L.: Arc routing methods and applications. In: Ball, M.O.; Magnanti, T.L.; Monma, C.L.; Nemhauser, G.L. (eds.) Network Routing, North-Holland, Amsterdam (1995)
    • (1995) Network Routing
    • Assad, A.A.1    Golden, B.L.2
  • 3
    • 0023234831 scopus 로고
    • The capacitated postman problem: Lower bounds and solvable cases
    • 902018 0623.90083
    • Assad A.A.; Pearn W.L.; Golden B.L.: The capacitated postman problem: lower bounds and solvable cases. Am. J. Math. Manage. Sci. 7, 63-88 (1987)
    • (1987) Am. J. Math. Manage. Sci. , vol.7 , pp. 63-88
    • Assad, A.A.1    Pearn, W.L.2    Golden, B.L.3
  • 4
    • 45149121178 scopus 로고    scopus 로고
    • An exact algorithm for the vehicle routing problem based on the set partitioning formulation with additional cuts
    • 2411402 05351844 10.1007/s10107-007-0178-5
    • Baldacci R.; Christofides N.; Mingozzi A.: An exact algorithm for the vehicle routing problem based on the set partitioning formulation with additional cuts. Math. Program. A 115, 351-385 (2008)
    • (2008) Math. Program. A , vol.115 , pp. 351-385
    • Baldacci, R.1    Christofides, N.2    Mingozzi, A.3
  • 5
    • 33645298466 scopus 로고    scopus 로고
    • Exact methods based on node-routing formulations for undirected arc-routing problems
    • 2189727 1090.90030 10.1002/net.20091
    • Baldacci R.; Maniezzo V.: Exact methods based on node-routing formulations for undirected arc-routing problems. Networks 47, 52-60 (2006)
    • (2006) Networks , vol.47 , pp. 52-60
    • Baldacci, R.1    Maniezzo, V.2
  • 6
    • 81455135706 scopus 로고    scopus 로고
    • New route relaxation and pricing strategies for the vehicle routing problem
    • 2011 to appear
    • Baldacci, R.; Mingozzi, A.; Roberti, R.: New route relaxation and pricing strategies for the vehicle routing problem. Oper. Res. (2011, to appear)
    • Oper. Res.
    • Baldacci, R.1    Mingozzi, A.2    Roberti, R.3
  • 7
    • 84867561256 scopus 로고    scopus 로고
    • New state space relaxations for solving the traveling salesman problem with time windows
    • doi: 10.1287/ijoc.1110.0456
    • Baldacci, R.; Mingozzi, A.; Roberti, R.: New state space relaxations for solving the traveling salesman problem with time windows. INFORMS J. Comput. doi: 10.1287/ijoc.1110.0456 (2011)
    • (2011) INFORMS J. Comput.
    • Baldacci, R.1    Mingozzi, A.2    Roberti, R.3
  • 8
    • 0032070222 scopus 로고    scopus 로고
    • The capacitated arc routing problem: Valid inequalities and facets
    • 1613322 0895.90083 10.1023/A:1018316919294
    • Belenguer J.M.; Benavent E.: The capacitated arc routing problem: valid inequalities and facets. Comput. Optim. Appl. 10, 165-187 (1998)
    • (1998) Comput. Optim. Appl. , vol.10 , pp. 165-187
    • Belenguer, J.M.1    Benavent, E.2
  • 9
    • 0037393086 scopus 로고    scopus 로고
    • A cutting plane algorithm for the capacitated arc routing problem
    • 1951064 1026.90014 10.1016/S0305-0548(02)00046-1
    • Belenguer J.M.; Benavent E.: A cutting plane algorithm for the capacitated arc routing problem. Comput. Oper. Res. 30, 705-728 (2003)
    • (2003) Comput. Oper. Res. , vol.30 , pp. 705-728
    • Belenguer, J.M.1    Benavent, E.2
  • 10
    • 21144460871 scopus 로고
    • The capacitated arc routing problem: Lower bounds
    • 1189294 0762.90077 10.1002/net.3230220706
    • Benavent E.; Campos V.; Corberán A.; Mota E.: The capacitated arc routing problem: lower bounds. Networks 22, 669-690 (1992)
    • (1992) Networks , vol.22 , pp. 669-690
    • Benavent, E.1    Campos, V.2    Corberán, A.3    Mota, E.4
  • 12
    • 0037449219 scopus 로고    scopus 로고
    • A guided local search heuristic for the capacitated arc routing problem
    • 1965259 1026.90015 10.1016/S0377-2217(02)00334-X
    • Beullens P.; Muyldermans L.; Cattrysse D.; Van Oudheusden D.: A guided local search heuristic for the capacitated arc routing problem. Eur. J. Oper. Res. 147, 629-643 (2003)
    • (2003) Eur. J. Oper. Res. , vol.147 , pp. 629-643
    • Beullens, P.1    Muyldermans, L.2    Cattrysse, D.3    Van Oudheusden, D.4
  • 13
    • 0042744917 scopus 로고    scopus 로고
    • Exact solution of the generalized routing problem through graph transformations
    • 1095.90522 10.1057/palgrave.jors.2601590
    • Blais M.; Laporte G.: Exact solution of the generalized routing problem through graph transformations. J. Oper. Res. Soc. 54, 906-910 (2003)
    • (2003) J. Oper. Res. Soc. , vol.54 , pp. 906-910
    • Blais, M.1    Laporte, G.2
  • 14
    • 84876966022 scopus 로고    scopus 로고
    • Cut-first branch-and-price-second for the capacitated arc-routing problem
    • Gutenberg School of Management and Economics, Johannes Gutenberg University, Mainz, Germany
    • Bode, C.; Irnich, S.: Cut-first branch-and-price-second for the capacitated arc-routing problem. Technical Report LM-2011-01 (preliminary version), Chair of Logistics Management, Gutenberg School of Management and Economics, Johannes Gutenberg University, Mainz, Germany (2011)
    • (2011) Technical Report LM-2011-01 (Preliminary Version), Chair of Logistics Management
    • Bode, C.1    Irnich, S.2
  • 15
    • 0000496959 scopus 로고
    • The optimum traversal of a graph
    • 10.1016/0305-0483(73)90089-3
    • Christofides N.: The optimum traversal of a graph. Omega 1, 719-732 (1973)
    • (1973) Omega , vol.1 , pp. 719-732
    • Christofides, N.1
  • 16
    • 34250247769 scopus 로고
    • Exact algorithms for the vehicle routing problem based on spanning tree and shortest path relaxation
    • 612623 0461.90067 10.1007/BF01589353
    • Christofides N.; Mingozzi A.; Toth P.: Exact algorithms for the vehicle routing problem based on spanning tree and shortest path relaxation. Math. Program. 20, 255-282 (1981)
    • (1981) Math. Program. , vol.20 , pp. 255-282
    • Christofides, N.1    Mingozzi, A.2    Toth, P.3
  • 17
    • 77955444898 scopus 로고    scopus 로고
    • Recent results on arc routing problems: An annotated bibliography
    • 2676655 1200.90019
    • Corberán A.; Prins C.: Recent results on arc routing problems: an annotated bibliography. Networks 56, 50-69 (2010)
    • (2010) Networks , vol.56 , pp. 50-69
    • Corberán, A.1    Prins, C.2
  • 20
    • 38149147463 scopus 로고
    • Routeing winter gritting vehicles
    • 0790.90031 10.1016/0166-218X(92)00003-5
    • Eglese R.W.: Routeing winter gritting vehicles. Discr. Appl. Math. 48, 231-244 (1994)
    • (1994) Discr. Appl. Math. , vol.48 , pp. 231-244
    • Eglese, R.W.1
  • 21
    • 0000238217 scopus 로고
    • Arc routing problems, part I: The Chinese postman problem
    • 1327413 0837.90037 10.1287/opre.43.2.231
    • Eiselt H.A.; Gendreau M.; Laporte G.: Arc routing problems, part I: The Chinese postman problem. Oper. Res. 43, 231-242 (1995)
    • (1995) Oper. Res. , vol.43 , pp. 231-242
    • Eiselt, H.A.1    Gendreau, M.2    Laporte, G.3
  • 22
    • 0000624218 scopus 로고
    • Arc routing problems, part II: The rural postman problem
    • 1327413 0853.90042 10.1287/opre.43.3.399
    • Eiselt H.A.; Gendreau M.; Laporte G.: Arc routing problems, part II: The rural postman problem. Oper. Res. 43, 399-414 (1995)
    • (1995) Oper. Res. , vol.43 , pp. 399-414
    • Eiselt, H.A.1    Gendreau, M.2    Laporte, G.3
  • 24
    • 0033887939 scopus 로고    scopus 로고
    • An efficient transformation of the generalized vehicle routing problem
    • 1778243 0968.90010 10.1016/S0377-2217(99)00073-9
    • Ghiani G.; Improta G.: An efficient transformation of the generalized vehicle routing problem. Eur. J. Oper. Res. 122, 11-17 (2000)
    • (2000) Eur. J. Oper. Res. , vol.122 , pp. 11-17
    • Ghiani, G.1    Improta, G.2
  • 25
    • 0020543990 scopus 로고
    • Computational experiments with algorithms for a class of routing problems
    • 758161 10.1016/0305-0548(83)90026-6
    • Golden B.L.; DeArmon J.S.; Baker E.K.: Computational experiments with algorithms for a class of routing problems. Comput. Oper. Res. 10, 47-59 (1983)
    • (1983) Comput. Oper. Res. , vol.10 , pp. 47-59
    • Golden, B.L.1    Dearmon, J.S.2    Baker, E.K.3
  • 26
    • 0019609540 scopus 로고
    • Capacitated arc routing problems
    • 636235 0459.90083 10.1002/net.3230110308
    • Golden B.L.; Wong R.T.: Capacitated arc routing problems. Networks 11, 305-315 (1981)
    • (1981) Networks , vol.11 , pp. 305-315
    • Golden, B.L.1    Wong, R.T.2
  • 27
    • 85037548981 scopus 로고    scopus 로고
    • Cutting plane and column generation for the capacitated arc routing problem
    • Valencia, Spain
    • Gómez-Cabrero, D.; Belenguer, J.M.; Benavent, E.: Cutting plane and column generation for the capacitated arc routing problem. Presented at ORP3 MEETING, Valencia, Spain (2005)
    • (2005) ORP3 MEETING
    • Gómez-Cabrero, D.1    Belenguer, J.M.2    Benavent, E.3
  • 28
    • 27344441401 scopus 로고
    • Node duplication lower bounds for the capacitated arc routing problems
    • 1184746 0766.90080
    • Hirabayashi R.; Nishida N.; Saruwatari Y.: Node duplication lower bounds for the capacitated arc routing problems. J. Oper. Res. Soc. Jpn 35, 119 (1992)
    • (1992) J. Oper. Res. Soc. Jpn , vol.35 , pp. 119
    • Hirabayashi, R.1    Nishida, N.2    Saruwatari, Y.3
  • 29
    • 61449183550 scopus 로고    scopus 로고
    • Subset-row inequalities applied to the vehicle routing problem with time windows
    • 1167.90413 10.1287/opre.1070.0449
    • Jepsen M.; Petersen B.; Spoorendonk S.; Pisinger D.: Subset-row inequalities applied to the vehicle routing problem with time windows. Oper. Res. 56, 497-511 (2008)
    • (2008) Oper. Res. , vol.56 , pp. 497-511
    • Jepsen, M.1    Petersen, B.2    Spoorendonk, S.3    Pisinger, D.4
  • 31
    • 57649233522 scopus 로고    scopus 로고
    • Exploiting sparsity in pricing routines for the capacitated arc routing problem
    • 2586498 1158.90321 10.1016/j.cor.2008.09.008
    • Letchford A.N.; Oukil A.: Exploiting sparsity in pricing routines for the capacitated arc routing problem. Comput. Oper. Res. 36, 2320-2327 (2009)
    • (2009) Comput. Oper. Res. , vol.36 , pp. 2320-2327
    • Letchford, A.N.1    Oukil, A.2
  • 32
    • 0030086498 scopus 로고
    • An interactive algorithm for vehicle routing for winter-gritting
    • Li L.Y.O.; Eglese R.W.: An interactive algorithm for vehicle routing for winter-gritting. J. Oper. Res. Soc. 47, 217-228 (1966)
    • (1966) J. Oper. Res. Soc. , vol.47 , pp. 217-228
    • Li, L.Y.O.1    Eglese, R.W.2
  • 33
    • 27344446543 scopus 로고    scopus 로고
    • Solving capacitated arc routing problems using a transformation to the CVRP
    • 1087.90054 10.1016/j.cor.2004.11.020
    • Longo H.; Poggi de Aragão M.; Uchoa E.: Solving capacitated arc routing problems using a transformation to the CVRP. Comput. Oper. Res. 33, 1823-1837 (2006)
    • (2006) Comput. Oper. Res. , vol.33 , pp. 1823-1837
    • Longo, H.1    Poggi De Aragão, M.2    Uchoa, E.3
  • 35
    • 21144444352 scopus 로고    scopus 로고
    • A new branch-and-cut algorithm for the capacitated vehicle routing problem
    • 2062936 1073.90068 10.1007/s10107-003-0481-8
    • Lysgaard J.; Letchford A.N.; Eglese R.W.: A new branch-and-cut algorithm for the capacitated vehicle routing problem. Math. Program. A 100, 423-445 (2004)
    • (2004) Math. Program. A , vol.100 , pp. 423-445
    • Lysgaard, J.1    Letchford, A.N.2    Eglese, R.W.3
  • 36
    • 84878558343 scopus 로고    scopus 로고
    • Column generation bounds for the capacitated arc routing problem
    • Bento Gonçalves, Brazil
    • Martinelli, R.; Pecin, D.; Poggi de Aragão, M.; Longo, H.: Column generation bounds for the capacitated arc routing problem. Presented at XLII SBPO, Bento Gonçalves, Brazil (2010)
    • (2010) XLII SBPO
    • Martinelli, R.1    Pecin, D.2    Poggi De Aragão, M.3    Longo, H.4
  • 37
    • 0020092747 scopus 로고
    • Odd minimum cut-sets and b-matchings
    • 665219 10.1287/moor.7.1.67
    • Padberg M.W.; Rao M.R.: Odd minimum cut-sets and b-matchings. Math. Oper. Res. 1, 67-80 (1982)
    • (1982) Math. Oper. Res. , vol.1 , pp. 67-80
    • Padberg, M.W.1    Rao, M.R.2
  • 38
    • 0024069865 scopus 로고
    • New lower bounds for the capacitated arc routing problem
    • 953921 0655.90084 10.1002/net.3230180305
    • Pearn W.L.: New lower bounds for the capacitated arc routing problem. Networks 18, 181-191 (1988)
    • (1988) Networks , vol.18 , pp. 181-191
    • Pearn, W.L.1
  • 39
    • 73349137288 scopus 로고    scopus 로고
    • An improved ant colony optimization based algorithm for the capacitated arc routing problem
    • 10.1016/j.trb.2009.07.004
    • Santos L.; Coutinho-Rodrigues J.; Current J.R.: An improved ant colony optimization based algorithm for the capacitated arc routing problem. Transport. Res. B 44, 246-266 (2010)
    • (2010) Transport. Res. B , vol.44 , pp. 246-266
    • Santos, L.1    Coutinho-Rodrigues, J.2    Current, J.R.3
  • 41
    • 33645155430 scopus 로고    scopus 로고
    • New lower bound for the capacitated arc routing problem
    • 2230207 10.1016/j.cor.2005.02.015
    • Wøhlk S.: New lower bound for the capacitated arc routing problem. Comput. Oper. Res. 33, 3458-3472 (2006)
    • (2006) Comput. Oper. Res. , vol.33 , pp. 3458-3472
    • Wøhlk, S.1
  • 42
    • 70350574988 scopus 로고    scopus 로고
    • A decade of capacitated arc routing
    • B.L. Golden S. Raghavan A. Wasil (eds) Springer New York
    • Wøhlk S.: A decade of capacitated arc routing. In: Golden, B.L.; Raghavan, S.; Wasil, A. (eds) The Vehicle Routing Problem: Latest Advances and New Challenges, Springer, New York (2008)
    • (2008) The Vehicle Routing Problem: Latest Advances and New Challenges
    • Wøhlk, S.1


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