Experiments with primal - dual decomposition and subgradient methods for the uncapacitatied facility location problem

References

• Balinski , M.L. and Wolfe , P. 1963 . On Benders Decomposition and a Plant Location Problem . Mathematica , ARO-27
   Google Scholar
• Beasley , J.E. 1993 . Lagrangean Heuristics for Location Problems . European .Journal of Operational Research , 65 : 383 – 399 .
   Web of Science ®Google Scholar
• Benders , J.F. 1962 . Partitioning Procedures for Solving Mixed-variables Programming Problems . Numerische Matematik , 4 : 238 – 252 .
   Google Scholar
• Brown G.W. Some Notes on Computation of Games Solutions The RAND Corporation 1949 RAND Report P-78
   Google Scholar
• Christofides , N. and Beasley , J.E. 1983 . Extensions to a Lagrangean Relaxation Approach for the Capacitated Warehouse Location Problem . European .Journal of Operational Research , 12 : 19 – 28 .
   Web of Science ®Google Scholar
• Conn , A.R. and Cornuejols , G. 1990 . A Projection Method for the Uncapacitated Facility Location Problem . Mathematical Programming , 46 : 273 – 298 .
   Web of Science ®Google Scholar
• Cornuejols , G. , Sridharan , R. and Thizy , J.M. 1991 . A Comparison of Heuristics and Relaxations for the Capacitated Plant Location Problem . European .Journal of Operational Research , 50 : 280 – 297 .
   Web of Science ®Google Scholar
• Cornuejols , G. and Thizy , J.M. 1982 . A Primal Approach to the Simple Plant Location Problem . SIAM Journal on Algebraic and Discrete Methods , 3 : 504 – 510 .
   Google Scholar
• Crowder , H. 1976 . “ Computational Improvements for Subgradient Optimization ” . In Symposia Mathematica , Vol. 19 , 357 – 372 . Academic Press .
   Google Scholar
• Dantzig , G.B. and Wolfe , P. 1960 . Decomposition Principle for Linear Programs . Operations Research , 8 : 101 – 111 .
   Web of Science ®Google Scholar
• Erlenkotter , D. 1978 . A Dual-Based Procedure for Uncapacitated Facility Location . Operations Research , 26 : 992 – 1009 .
   Web of Science ®Google Scholar
• Fisher , M.L. 1981 . The Lagrangean Relaxation Method for Solving Integer Programming Problems . Management Science , 27 : 1 – 18 .
   Web of Science ®Google Scholar
• Geoffrion , A.M. 1974 . Lagrangean Relaxation for Integer programming . Mathematical Programming Study , 2 : 82 – 114 .
   Google Scholar
• Geoffrion , A.M. and McBride , R. 1978 . Lagrangean Relaxation Applied to Capacitated Facility Location Problems . AIIE Transactions , 10 : 40 – 47 .
   Web of Science ®Google Scholar
• Held , M. , Wolfe , P. and Crowder , H. 1974 . Validation of Subgradient Optimization . Mathematical Programming , 6 : 62 – 68 .
   Google Scholar
• Holmberg , K. 1988 . “ Primal–dual Subgradient Optimization and Cross Decomposition with Applications to the Produce-or-purchase Problem ” . In Research Report LiTH-MAT-R-88-16 , Sweden : Linköping Institute of Technology .
   Google Scholar
• Holmberg , K. 1989 . “ Computational Experiments with Primal-dual Solution Methods for the Produce-or-purchase Problem ” . In Research Report LiTH-MAT-R-89-20 , Sweden : Linköping Institute of Technology .
   Google Scholar
• Holmberg , K. 1990 . On the Convergence of Cross Decomposition . Mathematical Programming , 47 : 269 – 296 .
   Web of Science ®Google Scholar
• Holmberg , K. 1992 . Linear Mean Value Cross Decomposition: A Generalization of the Kornai-Liptak Method . European Journal of Operational Research , 62 : 55 – 73 .
   Web of Science ®Google Scholar
• Holmberg , K. 1994 . A Convergence Proof for Linear Mean Value Cross Decomposition . ZOR-Methods and Models of Operations Research , 39 : 157 – 186 .
   Google Scholar
• Holmberg , K. 1997 . Mean Value Cross Decomposition Applied to Integer Programming Problems . European Journal of Operational Research , 97 : 124 – 138 .
   Web of Science ®Google Scholar
• Holmberg , K. and JÖrnsten , K. 1995 . “ Decomposition Methods for the Exact Formulation of the Simple Plant Location Problem with Spatial Interaction ” . In Research Report LiTH-MAT-R-1995-13 , Sweden : LinkÖping Institute of Technology .
   Google Scholar
• Kornai , J. and Liptak , Th. 1965 . Two-Level Planning . Econornetrica , 33 : 141 – 169 .
   Web of Science ®Google Scholar
• KÖrkel , M. 1989 . On the Exact Solution of Large-Scale Simple Plant Location Problems . European Journal of Operational Research , 39 : 157 – 173 .
   Web of Science ®Google Scholar
• Minoux , M. 1984 . “ Subgradient Optimization and Benders Decomposition for Large Scale Programming ” . In Mathematical Programming , Edited by: Cottle , R.W. , Kelmanson , M.L. and Korte , B. North-Holland .
   Google Scholar
• Poljak , B.T. 1967 . A General Method of Solving Extremum Problems . Soviet Mathematics Doklady , 8 : 593 – 597 .
   Google Scholar
• Poljak , B.T. 1969 . Minimization of Unsmooth Functionals . USSR Computational Mathematics and Mathematical Physics , 9 : 14 – 29 .
   Google Scholar
• Robinson , J. 1951 . An Iterative Method of Solving a Game . Annals of Mathematics , 54 : 296 – 301 .
   Web of Science ®Google Scholar
• Van Roy , T.J. and Erlenkotter , D. 1982 . A Dual-Based Procedure for Dynamic Facility Location . Management Science , 28 : 1091 – 1105 .
   Web of Science ®Google Scholar
• Van Roy , T.J. 1983 . Cross Decomposition for Mixed Integer Programming . Mathematical Programming , 25 : 46 – 63 .
   Web of Science ®Google Scholar
• Van Roy , T.J. 1986 . A Cross Decomposition Algorithm for Capacitated Facility Location . Operations Research , 34 : 145 – 163 .
   Web of Science ®Google Scholar