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Volumn 46, Issue 4, 1998, Pages 548-562

Solution of the multisource Weber and conditional Weber problems by D.-C. programming

Author keywords

Facilities equipment planning: continuous location theory; Linear programming: vertex enumeration; Nonlinear programming: d. c. programming, concave minimization, algorithm, application

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; CONSTRAINT THEORY; FUNCTIONS; LINEAR PROGRAMMING; NONLINEAR PROGRAMMING; STRATEGIC PLANNING; WORLD WIDE WEB;

EID: 0032114729     PISSN: 0030364X     EISSN: None     Source Type: Journal    
DOI: 10.1287/opre.46.4.548     Document Type: Article
Times cited : (42)

References (71)
  • 2
    • 34249842390 scopus 로고
    • A Pivoting Algorithm for Convex Hulls and Vertex Enumeration Arrangements and Polyhedra
    • Avis, D. AND K. FUKUDA. 1992. A Pivoting Algorithm for Convex Hulls and Vertex Enumeration Arrangements and Polyhedra. Discrete and Computational Geometry, 8, 295-313.
    • (1992) Discrete and Computational Geometry , vol.8 , pp. 295-313
    • Avis, D.1    Fukuda, K.2
  • 4
    • 0019613267 scopus 로고
    • Local Optima Avoidance in Depot Location
    • U.K.
    • BAXTER, J. 1981. Local Optima Avoidance in Depot Location. J. Operational Res. Soc. (U.K.), 32, 815-819.
    • (1981) J. Operational Res. Soc. , vol.32 , pp. 815-819
    • Baxter, J.1
  • 5
    • 0000025164 scopus 로고
    • An Overview of Representative Problems in Location Research
    • BRANDEAU, M. L. AND S. S. CHIU. 1989. An Overview of Representative Problems in Location Research. Mgmt. Sci. 35, 645-674.
    • (1989) Mgmt. Sci. , vol.35 , pp. 645-674
    • Brandeau, M.L.1    Chiu, S.S.2
  • 6
    • 0001352404 scopus 로고
    • A Stable Algorithm for Solving the Multifacility Location Problem Involving Euclidean Distances
    • CALAMAI, P. H. AND A. R. CONN. 1980. A Stable Algorithm for Solving the Multifacility Location Problem Involving Euclidean Distances. SIAM J. Sci. Statist. Comput. 1, 512-525.
    • (1980) SIAM J. Sci. Statist. Comput. , vol.1 , pp. 512-525
    • Calamai, P.H.1    Conn, A.R.2
  • 7
    • 0016940743 scopus 로고
    • Non-linear Optimization as a Sequence of Least p-th Optimization with Finite Values of p
    • CHARALAMBOUS, C. AND J. W. BANDLER. 1976. Non-linear Optimization as a Sequence of Least p-th Optimization with Finite Values of p. Internat. J. Systems Sci. 7, 377-391.
    • (1976) Internat. J. Systems Sci. , vol.7 , pp. 377-391
    • Charalambous, C.1    Bandler, J.W.2
  • 8
    • 0000949397 scopus 로고
    • On-line and Off-line Vertex Enumeration by Adjacency Lists
    • CHEN, P.-C., P. HANSEN, AND B. JAUMARD. 1991. On-line and Off-line Vertex Enumeration by Adjacency Lists. O.R. Letts. 10, 403-409.
    • (1991) O.R. Letts. , vol.10 , pp. 403-409
    • Chen, P.-C.1    Hansen, P.2    Jaumard, B.3
  • 10
    • 0027087908 scopus 로고
    • Weber's Problem with Attraction and Repulsion
    • CHEN, P.-C., P. HANSEN, B. JAUMARD, AND H. TUY. 1992b. Weber's Problem with Attraction and Repulsion. J. Regional Sci., 32, 467-486.
    • (1992) J. Regional Sci. , vol.32 , pp. 467-486
    • Chen, P.-C.1    Hansen, P.2    Jaumard, B.3    Tuy, H.4
  • 11
    • 0000990105 scopus 로고
    • Solution of Minisum and Minimax Location-Allocation Problems with Euclidean Distances
    • CHEN, R. 1983. Solution of Minisum and Minimax Location-Allocation Problems with Euclidean Distances. Naval Res. Logist. Q., 30, 449-459.
    • (1983) Naval Res. Logist. Q. , vol.30 , pp. 449-459
    • Chen, R.1
  • 12
    • 0010818339 scopus 로고
    • Conditional Minisum and Minimax Location-Allocation Problems in Euclidean Space
    • CHEN, R. 1988. Conditional Minisum and Minimax Location-Allocation Problems in Euclidean Space. Trans. Sci., 22, 157-160.
    • (1988) Trans. Sci. , vol.22 , pp. 157-160
    • Chen, R.1
  • 13
    • 0000882113 scopus 로고
    • Newton's Method for Convex Programming and Tchebycheff Approximation
    • CHENEY, W. E. AND A. A. GOLDSTEIN. 1959. Newton's Method for Convex Programming and Tchebycheff Approximation. Numer. Math. 1, 253-268.
    • (1959) Numer. Math. , vol.1 , pp. 253-268
    • Cheney, W.E.1    Goldstein, A.A.2
  • 14
    • 0023588327 scopus 로고
    • The Minisum Location Problem on an Undirected Network with Continuous Link Demands
    • CHIU, S. S. 1987. The Minisum Location Problem on an Undirected Network with Continuous Link Demands. Comput. Oper. Res. 14, 369-383.
    • (1987) Comput. Oper. Res. , vol.14 , pp. 369-383
    • Chiu, S.S.1
  • 15
    • 0000340751 scopus 로고
    • Location-Allocation Problems
    • COOPER, L. 1963. Location-Allocation Problems. Opns. Res. 11, 301-343.
    • (1963) Opns. Res. , vol.11 , pp. 301-343
    • Cooper, L.1
  • 16
    • 0001138339 scopus 로고
    • Heuristic Methods for Location-Allocation Problems
    • COOPER, L. 1964. Heuristic Methods for Location-Allocation Problems. SIAM Rev. 6, 37-53.
    • (1964) SIAM Rev. , vol.6 , pp. 37-53
    • Cooper, L.1
  • 17
    • 84980119352 scopus 로고
    • Solutions of Generalized Locational Equilibrium Models
    • COOPER, L. 1967. Solutions of Generalized Locational Equilibrium Models. j. Regional Sci. 7, 1-18.
    • (1967) J. Regional Sci. , vol.7 , pp. 1-18
    • Cooper, L.1
  • 19
    • 0022808166 scopus 로고
    • Bounding Methods for Facility Location Algorithms
    • DOWLING, P. D. AND R. F. LOVE. 1986. Bounding Methods for Facility Location Algorithms. Naval Res. Logist. Q. 33, 775-787.
    • (1986) Naval Res. Logist. Q. , vol.33 , pp. 775-787
    • Dowling, P.D.1    Love, R.F.2
  • 20
    • 0021532114 scopus 로고
    • The Planar Two-Center and Two-Median Problems
    • DREZNER, Z. 1984. The Planar Two-Center and Two-Median Problems. Trans. Sci. 18, 351-361.
    • (1984) Trans. Sci. , vol.18 , pp. 351-361
    • Drezner, Z.1
  • 21
    • 0001876110 scopus 로고
    • The Weber Problem on the Plane with Some Negative Weights
    • DREZNER, Z. AND G. O. WESOLOWSKY. 1990. The Weber Problem on the Plane with Some Negative Weights. INFOR, 29, 87-99.
    • (1990) INFOR , vol.29 , pp. 87-99
    • Drezner, Z.1    Wesolowsky, G.O.2
  • 22
    • 0026203734 scopus 로고
    • The Facility Location Problem with Limited Distances
    • DREZNER, Z., A. MEHREZ, AND G. O. WESOLOWSKY. 1991. The Facility Location Problem with Limited Distances. Trans. Sci. 25, 183-187.
    • (1991) Trans. Sci. , vol.25 , pp. 183-187
    • Drezner, Z.1    Mehrez, A.2    Wesolowsky, G.O.3
  • 24
    • 0020799155 scopus 로고
    • The Complexity of Vertex Enumeration Methods
    • DYER, M. E. 1983. The Complexity of Vertex Enumeration Methods. Math. O.R. 8, 381-402.
    • (1983) Math. O.R. , vol.8 , pp. 381-402
    • Dyer, M.E.1
  • 25
    • 0015160689 scopus 로고
    • Generalized Cutting Plane Algorithms
    • EAVES, B. C. AND W. I. ZANGWILL. 1971. Generalized Cutting Plane Algorithms. SIAM J. Control 9, 529-542.
    • (1971) SIAM J. Control , vol.9 , pp. 529-542
    • Eaves, B.C.1    Zangwill, W.I.2
  • 27
    • 0016986845 scopus 로고
    • A Successive Underestimation Method for Concave Minimization Problems
    • FALK, J. E. AND K. L. HOFFMAN. 1976. A Successive Underestimation Method for Concave Minimization Problems. Math. O.R. 1, 251-259.
    • (1976) Math. O.R. , vol.1 , pp. 251-259
    • Falk, J.E.1    Hoffman, K.L.2
  • 28
    • 0022819169 scopus 로고
    • Concave Minimization via Collapsing Polytopes
    • FALK, J. E. AND K. L. HOFFMAN. 1986. Concave Minimization via Collapsing Polytopes. Opns. Res. 34, 919-929.
    • (1986) Opns. Res. , vol.34 , pp. 919-929
    • Falk, J.E.1    Hoffman, K.L.2
  • 29
    • 0019057211 scopus 로고
    • Location Theory, Dominance, and Convexity: Some Further Results
    • HANSEN, P., J. PERREUR, AND J.-F. THISSE. 1980. Location Theory, Dominance, and Convexity: Some Further Results. Opns. Res. 28, 1241-1250.
    • (1980) Opns. Res. , vol.28 , pp. 1241-1250
    • Hansen, P.1    Perreur, J.2    Thisse, J.-F.3
  • 30
    • 0022149016 scopus 로고
    • The Minisum and Minimax Location Problems Revisited
    • HANSEN, P., D. PEETERS, D. RICHARD, AND J.-F. THISSE. 1985. The Minisum and Minimax Location Problems Revisited. Opns. Res. 33, 1251-1265.
    • (1985) Opns. Res. , vol.33 , pp. 1251-1265
    • Hansen, P.1    Peeters, D.2    Richard, D.3    Thisse, J.-F.4
  • 32
    • 0007225736 scopus 로고
    • A Method for Globally Minimizing Concave Functions over Convex Sets
    • HOFFMAN, K. L. 1981. A Method for Globally Minimizing Concave Functions Over Convex Sets. Math. Programming, 20, 22-32.
    • (1981) Math. Programming , vol.20 , pp. 22-32
    • Hoffman, K.L.1
  • 33
    • 0002407118 scopus 로고
    • On the Global Minimization of Concave Functions: Introduction and Survey
    • HORST, R. 1984. On the Global Minimization of Concave Functions: Introduction and Survey. Opns. Res. Spektrum, 6, 195-205.
    • (1984) Opns. Res. Spektrum , vol.6 , pp. 195-205
    • Horst, R.1
  • 34
    • 0009068820 scopus 로고
    • Outer Approximation by Polyhedral Convex Sets
    • HORST, R., N. V. THOAI, AND H. TUY. 1987. Outer Approximation by Polyhedral Convex Sets. Opns. Res. Spektrum, 9, 153-159.
    • (1987) Opns. Res. Spektrum , vol.9 , pp. 153-159
    • Horst, R.1    Thoai, N.V.2    Tuy, H.3
  • 35
    • 0008397566 scopus 로고
    • Modification, Implementation and Comparison of Three Algorithms for Globally Solving Linearly Constrained Concave Minimization Problems
    • HORST, R. AND N. V. THOAI. 1989. Modification, Implementation and Comparison of Three Algorithms for Globally Solving Linearly Constrained Concave Minimization Problems. Computing, 42, 271-289.
    • (1989) Computing , vol.42 , pp. 271-289
    • Horst, R.1    Thoai, N.V.2
  • 36
    • 34249920893 scopus 로고
    • Concave Minimization via Conical Partitions and Polyhedral Outer Approximation
    • HORST, R., N. V. THOAI, AND H. P. BENSON. 1991. Concave Minimization via Conical Partitions and Polyhedral Outer Approximation. Math. Programming, 50, 259-274.
    • (1991) Math. Programming , vol.50 , pp. 259-274
    • Horst, R.1    Thoai, N.V.2    Benson, H.P.3
  • 38
    • 0001547779 scopus 로고
    • The Cutting-Plane Method for Solving Convex Programs
    • KELLEY, J. E. 1960. The Cutting-Plane Method for Solving Convex Programs. J. SIAM, 8, 703-712.
    • (1960) J. SIAM , vol.8 , pp. 703-712
    • Kelley, J.E.1
  • 40
    • 0001260750 scopus 로고
    • Exact and Approximate Solutions to the Multisource Weber Problem
    • KUENNE, R. E. AND R. M. SOLAND. 1972. Exact and Approximate Solutions to the Multisource Weber Problem. Math. Programming, 3, 193-209.
    • (1972) Math. Programming , vol.3 , pp. 193-209
    • Kuenne, R.E.1    Soland, R.M.2
  • 41
    • 0342409041 scopus 로고
    • The Median Location Problem with Continuous Demand
    • LABBÉ, M. 1992. The Median Location Problem with Continuous Demand. Cahiers du CERO, 34, 103-115.
    • (1992) Cahiers du CERO , vol.34 , pp. 103-115
    • Labbé, M.1
  • 42
    • 80054805403 scopus 로고
    • A Note about the New Emergency Facility Insertion in an Undirected Connected Graph
    • Pittsburgh, Pennsylvania
    • LIN, C. C. 1975. A Note About the New Emergency Facility Insertion in an Undirected Connected Graph. In Sixth Annual Pittsburgh Conference on Modeling Simulation. Pittsburgh, Pennsylvania.
    • (1975) Sixth Annual Pittsburgh Conference on Modeling Simulation
    • Lin, C.C.1
  • 43
    • 0020126639 scopus 로고
    • Properties and Solution Methods for Large Location-allocation Problems
    • U.K.
    • LOVE, R. F. AND H. JUEL. 1982. Properties and Solution Methods for Large Location-allocation Problems. J. Opnl. Res. Soc. (U.K.), 33, 443-452.
    • (1982) J. Opnl. Res. Soc. , vol.33 , pp. 443-452
    • Love, R.F.1    Juel, H.2
  • 45
    • 0024699537 scopus 로고
    • A Generalized Bounding Method for Multifacility Location Models
    • LOVE, R. F. AND P. D. DOWLING. 1989. A Generalized Bounding Method for Multifacility Location Models. Opns. Res. 37, 653-657.
    • (1989) Opns. Res. , vol.37 , pp. 653-657
    • Love, R.F.1    Dowling, P.D.2
  • 46
    • 0019016261 scopus 로고
    • A Survey and Comparison of Methods for Finding all Vertices of Convex Polyhedral Sets
    • MATTHEIS, T. H. AND D. S. RUBIN. 1980. A Survey and Comparison of Methods for Finding all Vertices of Convex Polyhedral Sets. Math. O.R. 5, 167-185.
    • (1980) Math. O.R. , vol.5 , pp. 167-185
    • Mattheis, T.H.1    Rubin, D.S.2
  • 47
    • 0021373110 scopus 로고
    • On the Complexity of Some Common Geometric Location Problems
    • MEGIDDO, N. AND K. J. SUPOWIT. 1984. On the Complexity of Some Common Geometric Location Problems. SIAM J. Comp. 13, 182-196.
    • (1984) SIAM J. Comp. , vol.13 , pp. 182-196
    • Megiddo, N.1    Supowit, K.J.2
  • 48
    • 0010723307 scopus 로고
    • Link-length Minimization in Networks
    • MIEHLE, W. 1958. Link-length Minimization in Networks. Opns. Res. 6, 232-243.
    • (1958) Opns. Res. , vol.6 , pp. 232-243
    • Miehle, W.1
  • 49
    • 84987049811 scopus 로고
    • Conditional Centers and Medians on a Graph
    • MINIEKA, E. 1980. Conditional Centers and Medians on a Graph. Networks, 10, 265-272.
    • (1980) Networks , vol.10 , pp. 265-272
    • Minieka, E.1
  • 50
    • 0003349493 scopus 로고
    • TWAIN - Exact Solutions to the Two Source Location-Allocation Problem
    • G. Rushton, M. F. Goodchild and L. M. Ostresh Jr. (eds.). Monograph 6. Department of Geography, University of Iowa, Iowa City, IA
    • OSTRESH, L. M., JR. 1973a. TWAIN - Exact Solutions to the Two Source Location-Allocation Problem. In Computer Programs for Location-Allocation Problems. G. Rushton, M. F. Goodchild and L. M. Ostresh Jr. (eds.). Monograph 6. Department of Geography, University of Iowa, Iowa City, IA. 15-28.
    • (1973) Computer Programs for Location-Allocation Problems , pp. 15-28
    • Ostresh Jr., L.M.1
  • 51
    • 0003349493 scopus 로고
    • MULTI - Exact Solutions to the M-Center Location-Allocation Problem
    • G. Rushton, M. F. Goodchild, and L. M. Ostresh Jr. (eds.). Monograph 6. Department of Geography, University of Iowa, Iowa City, IA
    • OSTRESH, L. M., JR. 1973b. MULTI - Exact Solutions to the M-Center Location-Allocation Problem. In Computer Programs for Location-Allocation Problems. G. Rushton, M. F. Goodchild, and L. M. Ostresh Jr. (eds.). Monograph 6. Department of Geography, University of Iowa, Iowa City, IA. 29-53.
    • (1973) Computer Programs for Location-Allocation Problems , pp. 29-53
    • Ostresh Jr., L.M.1
  • 53
    • 84979417831 scopus 로고
    • An Efficient Algorithm for Solving the Two Center Location-Allocation Problem
    • OSTRESH, L. M., JR. 1975. An Efficient Algorithm for Solving the Two Center Location-Allocation Problem. J. Regional Sci. 15, 209-216.
    • (1975) J. Regional Sci. , vol.15 , pp. 209-216
    • Ostresh Jr., L.M.1
  • 54
    • 0003150632 scopus 로고
    • A Quadratically Convergent Method for Minimizing a Sum of Euclidean Norms
    • OVERTON, M. L. 1983. A Quadratically Convergent Method for Minimizing a Sum of Euclidean Norms. Math. Programming, 27, 34-63.
    • (1983) Math. Programming , vol.27 , pp. 34-63
    • Overton, M.L.1
  • 55
    • 0000293948 scopus 로고
    • Methods for Global Concave Minimization: A Bibliographic Survey
    • PARDALOS, P. M. AND J. B. ROSEN. 1986. Methods for Global Concave Minimization: A Bibliographic Survey. SIAM Review, 28, 367-379.
    • (1986) SIAM Review , vol.28 , pp. 367-379
    • Pardalos, P.M.1    Rosen, J.B.2
  • 56
    • 0004267646 scopus 로고
    • Princeton University Press, Princeton, NJ
    • ROCKAFELLAR, R. T. 1970. Convex Analysis. Princeton University Press, Princeton, NJ.
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 57
    • 0026174720 scopus 로고
    • Computational Comparison of Two Algorithms for the Euclidean Single Facility Location Problem
    • ROSEN, J. B. AND G.-L. XUE. 1991. Computational Comparison of Two Algorithms for the Euclidean Single Facility Location Problem. ORSA J. Computing, 3, 207-212.
    • (1991) ORSA J. Computing , vol.3 , pp. 207-212
    • Rosen, J.B.1    Xue, G.-L.2
  • 58
    • 0026869479 scopus 로고
    • An Optimal Method for Solving the (Generalized) Multi-Weber Problem
    • ROSING, K. E. 1992. An Optimal Method for Solving the (Generalized) Multi-Weber Problem. Eur. J. Opnl. Res. 58, 414-426.
    • (1992) Eur. J. Opnl. Res. , vol.58 , pp. 414-426
    • Rosing, K.E.1
  • 59
    • 84989593213 scopus 로고
    • Location-Allocation Systems: A Review
    • SCOTT, A. J. 1970. Location-Allocation Systems: A Review. Geographical Analysis, 2, 95-119.
    • (1970) Geographical Analysis , vol.2 , pp. 95-119
    • Scott, A.J.1
  • 60
    • 0019213683 scopus 로고
    • A Flexible User Oriented Location Allocation Algorithm
    • SULLIVAN, P. J. AND N. PETERS. 1980. A Flexible User Oriented Location Allocation Algorithm. J. Environmental Mgmt. 10, 181-193.
    • (1980) J. Environmental Mgmt. , vol.10 , pp. 181-193
    • Sullivan, P.J.1    Peters, N.2
  • 61
    • 0024783348 scopus 로고
    • The Weber Problem: Frequency of Different Solution Types and Extension to Repulsive Forces and Dynamic Processes
    • TELLIER, L.-N. AND B. POLANSKI. 1989. The Weber Problem: Frequency of Different Solution Types and Extension to Repulsive Forces and Dynamic Processes. J. Regional Sci. 29, 387-405.
    • (1989) J. Regional Sci. , vol.29 , pp. 387-405
    • Tellier, L.-N.1    Polanski, B.2
  • 62
    • 34250096516 scopus 로고
    • The Design Centering Problem as a D.C. Programming Problem
    • THACH, P. T. 1988. The Design Centering Problem as a D.C. Programming Problem. Math. Programming, 41, 229-248.
    • (1988) Math. Programming , vol.41 , pp. 229-248
    • Thach, P.T.1
  • 63
    • 0002467167 scopus 로고
    • An Outer Approximation Method for Globally Minimizing a Concave Function over a Compact Convex Set
    • THIEU, T. V., B. T. TAM, AND V. T. BAN. 1983. An Outer Approximation Method for Globally Minimizing a Concave Function Over a Compact Convex Set. Acta Mathematica Vietnamica, 8, 21-40.
    • (1983) Acta Mathematica Vietnamica , vol.8 , pp. 21-40
    • Thieu, T.V.1    Tam, B.T.2    Ban, V.T.3
  • 64
    • 20044368086 scopus 로고
    • Implementation of Some Algorithms for Nonconvex Optimization Problems
    • Springer Verlag
    • THIEU, T. V. 1985. Implementation of Some Algorithms for Nonconvex Optimization Problems. Lecture Notes of Mathematics, 1405, Springer Verlag, 159-170.
    • (1985) Lecture Notes of Mathematics , vol.1405 , pp. 159-170
    • Thieu, T.V.1
  • 65
    • 0007221068 scopus 로고
    • On Outer Approximation Methods for Solving Concave Minimization Problems
    • TUY, H. 1983. On Outer Approximation Methods for Solving Concave Minimization Problems. Acta Mathematica Vietnamica, 8, 3-34.
    • (1983) Acta Mathematica Vietnamica , vol.8 , pp. 3-34
    • Tuy, H.1
  • 66
    • 0040686493 scopus 로고
    • A General Deterministic Approach to Global Optimization via D.-C. Programming
    • J. B. Hiriart-Urruty (ed.). North-Holland, Amsterdam
    • TUY, H. 1985. A General Deterministic Approach to Global Optimization via D.-C. Programming. In Fermat Days 1985: Mathematics for Optimization. J. B. Hiriart-Urruty (ed.). North-Holland, Amsterdam. 137-162.
    • (1985) Fermat Days 1985: Mathematics for Optimization , pp. 137-162
    • Tuy, H.1
  • 67
    • 0020702691 scopus 로고
    • Global Minimization of a Difference of Two Convex Functions
    • TUY, H. 1987. Global Minimization of a Difference of Two Convex Functions. Math. Prog. Study, 30, 150-182.
    • (1987) Math. Prog. Study , vol.30 , pp. 150-182
    • Tuy, H.1
  • 68
    • 0008405967 scopus 로고
    • The Supporting Hyperplane Method for Unimodal Programming
    • VEINOTT, A. F. 1967. The Supporting Hyperplane Method for Unimodal Programming. Opns. Res. 15, 147-152.
    • (1967) Opns. Res. , vol.15 , pp. 147-152
    • Veinott, A.F.1
  • 69
    • 0003479294 scopus 로고
    • Tübingen. Translated as Alfred Weber's Theory of the Location of Industries. University of Chicago, Chicago, IL
    • WEBER, A. 1909. Über den Standort der Industrien. Tübingen. Translated as Alfred Weber's Theory of the Location of Industries. University of Chicago, Chicago, IL.
    • (1909) Über Den Standort der Industrien
    • Weber, A.1
  • 70
    • 0000281286 scopus 로고
    • Sur le Point Pour Lequel la Somme des Distances de n Points Donnés est Minimum
    • WEISZFELD, E. 1937. Sur le Point Pour Lequel la Somme des Distances de n Points Donnés est Minimum. Tôhoku Mathematical J. 43, 355-386.
    • (1937) Tôhoku Mathematical J. , vol.43 , pp. 355-386
    • Weiszfeld, E.1
  • 71
    • 0010719738 scopus 로고
    • A Polynomial Time Dual Algorithm for the Euclidean Multifacility Location Problem
    • E. Balas, G. Cornuejols and R. Kannan (eds.). Carnegie-Mellon University Press, Pittsburgh, PA
    • XUE, G. L., J. B. ROSEN, AND P. M. PARDALOS. 1992. A Polynomial Time Dual Algorithm for the Euclidean Multifacility Location Problem. In Integer Programming and Combinatorial Optimization. E. Balas, G. Cornuejols and R. Kannan (eds.). Carnegie-Mellon University Press, Pittsburgh, PA. 227-236.
    • (1992) Integer Programming and Combinatorial Optimization , pp. 227-236
    • Xue, G.L.1    Rosen, J.B.2    Pardalos, P.M.3


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