메뉴 건너뛰기




Volumn 124, Issue 1-2, 2010, Pages 93-118

New techniques for cost sharing in combinatorial optimization games

Author keywords

Combinatorial optimization games; Cooperative games; Optimal cost shares; Traveling salesman game; Valid inequalities; Vehicle routing game

Indexed keywords

COMBINATORIAL OPTIMIZATION GAMES; COOPERATIVE GAME; OPTIMAL COSTS; TRAVELING SALESMAN; VALID INEQUALITIES; VALID INEQUALITY;

EID: 77955175667     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-010-0357-7     Document Type: Article
Times cited : (27)

References (38)
  • 1
    • 0031072787 scopus 로고    scopus 로고
    • The circuit polytope: Facets
    • 0871.90099 10.1287/moor.22.1.110 1436576
    • P. Bauer 1997 The circuit polytope: facets Math. Oper. Res. 22 110 145 0871.90099 10.1287/moor.22.1.110 1436576
    • (1997) Math. Oper. Res. , vol.22 , pp. 110-145
    • Bauer, P.1
  • 2
    • 40849142215 scopus 로고    scopus 로고
    • Approximately fair cost allocation in metric traveling salesman games
    • 1135.91313 10.1007/s00224-007-9072-z 2385691
    • M. Bläser L. Shankar Ram 2008 Approximately fair cost allocation in metric traveling salesman games Theory Comput. Syst. 43 19 37 1135.91313 10.1007/s00224-007-9072-z 2385691
    • (2008) Theory Comput. Syst. , vol.43 , pp. 19-37
    • Bläser, M.1    Shankar Ram, L.2
  • 3
    • 0001250954 scopus 로고
    • Some applications of linear programming to cooperative games
    • 167335
    • O.N. Bondareva 1963 Some applications of linear programming to cooperative games Problemy Kibernetiki. 10 119 139 167335
    • (1963) Problemy Kibernetiki. , vol.10 , pp. 119-139
    • Bondareva, O.N.1
  • 4
    • 36348991370 scopus 로고    scopus 로고
    • Set-covering-based algorithms for the capacitated VRP
    • P. Toth D. Vigo (eds). SIAM Monographs on Discrete Mathematics and Applications SIAM Philadelphia
    • Bramel J., Simchi-Levi D.: Set-covering-based algorithms for the capacitated VRP. In: Toth, P., Vigo, D. (eds) The Vehicle Routing Problem, SIAM Monographs on Discrete Mathematics and Applications SIAM, Philadelphia (2002)
    • (2002) The Vehicle Routing Problem
    • Bramel, J.1    Simchi-Levi, D.2
  • 5
    • 0001391104 scopus 로고
    • Decomposition principle for linear programs
    • 0093.32806 10.1287/opre.8.1.101
    • G.B. Dantzig P. Wolfe 1960 Decomposition principle for linear programs Oper. Res. 8 101 111 0093.32806 10.1287/opre.8.1.101
    • (1960) Oper. Res. , vol.8 , pp. 101-111
    • Dantzig, G.B.1    Wolfe, P.2
  • 6
    • 33644502750 scopus 로고    scopus 로고
    • Integer program reformulation for robust branch-and-cut-and-price
    • L. Wosley (eds). Búzios Brazil
    • de Aragaõ M.P., Uchoa E.: Integer program reformulation for robust branch-and-cut-and-price. In: Wosley, L. (eds) Annals of Mathematical Programming in Rio, pp. 56-61. Búzios, Brazil (2003)
    • (2003) Annals of Mathematical Programming in Rio , pp. 56-61
    • De Aragaõ, M.P.1    Uchoa, E.2
  • 7
    • 0033358883 scopus 로고    scopus 로고
    • Algorithmic aspects of the core of combinatorial optimization games
    • 1064.91505 10.1287/moor.24.3.751 1854251
    • X. Deng T. Ibaraki H. Nagamochi 1999 Algorithmic aspects of the core of combinatorial optimization games Math. Oper. Res. 24 751 766 1064.91505 10.1287/moor.24.3.751 1854251
    • (1999) Math. Oper. Res. , vol.24 , pp. 751-766
    • Deng, X.1    Ibaraki, T.2    Nagamochi, H.3
  • 8
    • 0001214263 scopus 로고
    • Maximum matching and a polyhedron with 0,1-vertices
    • 0141.21802 183532
    • J. Edmonds 1965 Maximum matching and a polyhedron with 0,1-vertices J. Res. Natl. Bur. Stand. 69 125 130 0141.21802 183532
    • (1965) J. Res. Natl. Bur. Stand. , vol.69 , pp. 125-130
    • Edmonds, J.1
  • 9
    • 85047673979 scopus 로고    scopus 로고
    • On approximately fair cost allocation for the Euclidean traveling salesman problem
    • 0897.90199 10.1007/BF01545526
    • U. Faigle S.P. Fekete W. Hochstättler W. Kern 1998 On approximately fair cost allocation for the Euclidean traveling salesman problem OR Spektrum 20 29 37 0897.90199 10.1007/BF01545526
    • (1998) OR Spektrum , vol.20 , pp. 29-37
    • Faigle, U.1    Fekete, S.P.2    Hochstättler, W.3    Kern, W.4
  • 11
    • 35048870538 scopus 로고    scopus 로고
    • Robust branch-and-cut-and-price for the capacitated vehicle routing problem
    • Nemhauser, G., Bienstock, D. (eds.) Lecture Notes in Computer Science 3064, Berlin, Springer
    • Fukasawa, R., Lysgaard, J., de Aragão, M.P., Reis, M., Uchoa, E., Werneck, R.F.: Robust branch-and-cut-and-price for the capacitated vehicle routing problem. In Nemhauser, G., Bienstock, D. (eds.) Integer Programming and Combinatorial Optimization 10, pp. 1-15. Lecture Notes in Computer Science 3064, Berlin, Springer (2004)
    • (2004) Integer Programming and Combinatorial Optimization , vol.10 , pp. 1-15
    • Fukasawa, R.1
  • 12
    • 0002324262 scopus 로고
    • Solutions to general non-zero-sum games
    • A.W. Tucker R.D. Luce (eds). Princeton University Press Princeton
    • Gillies D.B.: Solutions to general non-zero-sum games. In: Tucker, A.W., Luce, R.D. (eds) Contributions to the Theory of Games, vol. 4, pp. 47-85. Princeton University Press, Princeton (1959)
    • (1959) Contributions to the Theory of Games, Vol. 4 , pp. 47-85
    • Gillies, D.B.1
  • 14
    • 1442313867 scopus 로고    scopus 로고
    • Cooperative facility location games
    • 1106.91009 10.1016/S0196-6774(03)00098-1 2049792
    • M.X. Goemans M. Skutella 2004 Cooperative facility location games J. Algorithms 50 194 214 1106.91009 10.1016/S0196-6774(03)00098-1 2049792
    • (2004) J. Algorithms , vol.50 , pp. 194-214
    • Goemans, M.X.1    Skutella, M.2
  • 15
    • 0042267452 scopus 로고    scopus 로고
    • On the nucleolus of the basic vehicle routing game
    • 10.1007/BF02592333
    • M. Göthe-Lundgren K. Jörnsten P. Värbrand 1996 On the nucleolus of the basic vehicle routing game Math. Program. 72 83 100 10.1007/BF02592333
    • (1996) Math. Program. , vol.72 , pp. 83-100
    • Göthe-Lundgren, M.1    Jörnsten, K.2    Värbrand, P.3
  • 16
    • 0019587745 scopus 로고
    • Minimum cost spanning tree games
    • 0461.90099 10.1007/BF01584227 618611
    • D. Granot G. Huberman 1981 Minimum cost spanning tree games Math. Program. 21 1 18 0461.90099 10.1007/BF01584227 618611
    • (1981) Math. Program. , vol.21 , pp. 1-18
    • Granot, D.1    Huberman, G.2
  • 18
    • 34250268954 scopus 로고
    • On the symmetric travelling salesman problem I: Inequalities
    • 0413.90048 10.1007/BF01582116
    • M. Grötschel M.W. Padberg 1979 On the symmetric travelling salesman problem I: inequalities Math. Program. 16 265 280 0413.90048 10.1007/BF01582116
    • (1979) Math. Program. , vol.16 , pp. 265-280
    • Grötschel, M.1    Padberg, M.W.2
  • 20
    • 0022809003 scopus 로고
    • Clique tree inequalities and the symmetric travelling salesman problem
    • 0626.90060 10.1287/moor.11.4.537 865552
    • M. Grötschel W. Pulleyblank 1986 Clique tree inequalities and the symmetric travelling salesman problem Math. Oper. Res. 11 537 569 0626.90060 10.1287/moor.11.4.537 865552
    • (1986) Math. Oper. Res. , vol.11 , pp. 537-569
    • Grötschel, M.1    Pulleyblank, W.2
  • 21
    • 58149318797 scopus 로고
    • A result on projection for the vehicle routing problem
    • 0912.90118 10.1016/0377-2217(94)00025-8
    • L. Gouveia 1995 A result on projection for the vehicle routing problem Eur. J. Opl. Res. 85 610 684 0912.90118 10.1016/0377-2217(94)00025-8
    • (1995) Eur. J. Opl. Res. , vol.85 , pp. 610-684
    • Gouveia, L.1
  • 22
    • 0346061790 scopus 로고
    • The travelling salesman problem as a constrained shortest path problem: Theory and computational experience
    • 0446.90084 605414
    • D.J. Houck J.-C. Picard M. Queyranne R.R. Vemuganti 1980 The travelling salesman problem as a constrained shortest path problem: theory and computational experience Opsearch 17 93 109 0446.90084 605414
    • (1980) Opsearch , vol.17 , pp. 93-109
    • Houck, D.J.1    Picard, J.-C.2    Queyranne, M.3    Vemuganti, R.R.4
  • 23
    • 84926087963 scopus 로고    scopus 로고
    • Cost sharing
    • N. Nisan T. Roughgarden E. Tardos V. Vazirani (eds). Cambridge University Press Cambridge
    • Jain K., Mahdian M.: Cost sharing. In: Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V. (eds) Algorithmic Game Theory, Cambridge University Press, Cambridge (2007)
    • (2007) Algorithmic Game Theory
    • Jain, K.1    Mahdian, M.2
  • 24
    • 8344253908 scopus 로고    scopus 로고
    • Multistars, partial multistars and the capacitated vehicle routing problem
    • DOI 10.1007/s10107-002-0336-8
    • A.N. Letchford R.W. Eglese J. Lysgaard 2002 Multistars, partial multistars and the capacitated vehicle routing problem Math. Program. 94 21 40 1023.90073 10.1007/s10107-002-0336-8 1953164 (Pubitemid 44744729)
    • (2002) Mathematical Programming, Series B , vol.94 , Issue.1 , pp. 21-40
    • Letchford, A.N.1    Eglese, R.W.2    Lysgaard, J.3
  • 25
    • 29044438268 scopus 로고    scopus 로고
    • Projection results for vehicle routing
    • DOI 10.1007/s10107-005-0652-x
    • A.N. Letchford J.J. Salazar Gonzalez 2006 Projection results for vehicle routing Math. Program. 105 251 274 1085.90032 10.1007/s10107-005-0652-x 2190821 (Pubitemid 41788320)
    • (2006) Mathematical Programming , vol.105 , Issue.2-3 , pp. 251-274
    • Letchford, A.N.1    Salazar-Gonzalez, J.-J.2
  • 26
    • 4344639338 scopus 로고    scopus 로고
    • Polyhedral theory and branch-and-cut algorithms for the symmetric TSP
    • G. Gutin A. Punnen (eds). Kluwer Dordrecht
    • Naddef D.: Polyhedral theory and branch-and-cut algorithms for the symmetric TSP. In: Gutin, G., Punnen, A. (eds) The Traveling Salesman Problem and Its Variations, Kluwer, Dordrecht (2001)
    • (2001) The Traveling Salesman Problem and Its Variations
    • Naddef, D.1
  • 27
    • 34249919158 scopus 로고
    • The symmetric traveling salesman polytope and its graphical relaxation: Composition of valid inequalities
    • 0748.90072 10.1007/BF01586945 1130332
    • D. Naddef G. Rinaldi 1991 The symmetric traveling salesman polytope and its graphical relaxation: composition of valid inequalities Math. Program. 51 359 400 0748.90072 10.1007/BF01586945 1130332
    • (1991) Math. Program. , vol.51 , pp. 359-400
    • Naddef, D.1    Rinaldi, G.2
  • 29
    • 1642601803 scopus 로고    scopus 로고
    • Traveling salesman games with the Monge property
    • 1056.90120 10.1016/j.dam.2003.08.005
    • Y. Okamoto 2004 Traveling salesman games with the Monge property Discr. Appl. Math. 138 349 369 1056.90120 10.1016/j.dam.2003.08.005
    • (2004) Discr. Appl. Math. , vol.138 , pp. 349-369
    • Okamoto, Y.1
  • 30
    • 0020092747 scopus 로고
    • Odd minimum cut-sets and b-matchings
    • 0499.90056 10.1287/moor.7.1.67 665219
    • M.W. Padberg M.R. Rao 1982 Odd minimum cut-sets and b-matchings Math. Oper. Res. 7 67 80 0499.90056 10.1287/moor.7.1.67 665219
    • (1982) Math. Oper. Res. , vol.7 , pp. 67-80
    • Padberg, M.W.1    Rao, M.R.2
  • 33
    • 0026692482 scopus 로고
    • Traveling salesman games
    • 0749.90094 10.1007/BF01585702 1148013
    • J.A.M. Potters I.J. Curiel S.H. Tijs 1992 Traveling salesman games Math. Program. 53 199 211 0749.90094 10.1007/BF01585702 1148013
    • (1992) Math. Program. , vol.53 , pp. 199-211
    • Potters, J.A.M.1    Curiel, I.J.2    Tijs, S.H.3
  • 34
    • 0002146418 scopus 로고
    • Sums of circuits
    • J.A. Bondy U.S.R. Murty (eds). Academic Press London
    • Seymour P.D.: Sums of circuits. In: Bondy, J.A., Murty, U.S.R. (eds) Graph Theory and Related Topics, pp. 341-355. Academic Press, London (1979)
    • (1979) Graph Theory and Related Topics , pp. 341-355
    • Seymour, P.D.1
  • 35
    • 0001077642 scopus 로고
    • On balanced sets and cores
    • 10.1002/nav.3800140404
    • L.S. Shapley 1967 On balanced sets and cores Nav. Res. Log. Quart. 14 453 460 10.1002/nav.3800140404
    • (1967) Nav. Res. Log. Quart. , vol.14 , pp. 453-460
    • Shapley, L.S.1
  • 36
    • 34250451672 scopus 로고
    • The assignment game I: The core
    • 10.1007/BF01753437 311290
    • L.S. Shapley M. Shubik 1972 The assignment game I: the core Int. J. Game Theory 1 111 130 10.1007/BF01753437 311290
    • (1972) Int. J. Game Theory , vol.1 , pp. 111-130
    • Shapley, L.S.1    Shubik, M.2
  • 37
    • 0042962250 scopus 로고
    • Game theory models and methods in political economy
    • Arrow, K.J., Intriligator, M.D. (eds.) North-Holland
    • Shubik, M.: Game theory models and methods in political economy. In Arrow, K.J., Intriligator, M.D. (eds.) Handbook of Mathematical Economics, vol. I. North-Holland, pp. 285-330 (1981)
    • (1981) Handbook of Mathematical Economics , vol.1 , pp. 285-330
    • Shubik, M.1
  • 38
    • 0024607362 scopus 로고
    • On the core of a traveling salesman cost allocation game
    • 10.1016/0167-6377(89)90030-8 983571
    • A. Tamir 1988 On the core of a traveling salesman cost allocation game Oper. Res. Lett. 8 31 34 10.1016/0167-6377(89)90030-8 983571
    • (1988) Oper. Res. Lett. , vol.8 , pp. 31-34
    • Tamir, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.