On a class of subadditive duals for the uncapacitated facility location problem

A family of subadditive functions which contains the optimal solution of subadditive duals for integer programs has been presented by Klabjan (2007). In this paper we present a subadditive dual ascent procedure to find an optimal subadditive dual function based on Klabjan's generator subadditive function. Then we use the proposed method to solve the so called uncapacitated facility location problem (UFLP). Establishing an explicit formulation for generator subadditive functions in the columns of the coefficient matrix of the UFLP, we derive some variable fixing rules for the problem. Some computational results are also presented.

[1]  J. Krarup,et al.  Sharp Lower Bounds and Efficient Algorithms for the Simple Plant Location Problem , 1977 .

[2]  Manfred Körkel.  On the exact solution of large-scale simple plant location problems , 1989 .

[3]  Pierre Hansen,et al.  Primal-Dual Variable Neighborhood Search for the Simple Plant-Location Problem , 2003, INFORMS J. Comput..

[4]  Dominique Peeters,et al.  Location on networks , 1992 .

[5]  Michel Balinski,et al.  Integer Programming: Methods, Uses, Computation , 2010, 50 Years of Integer Programming.

[6]  Ted K. Ralphs,et al.  Duality for Mixed-Integer Linear Programs , 2007 .

[7]  T. L. Ray,et al.  A Branch-Bound Algorithm for Plant Location , 1966, Oper. Res..

[8]  Michel Balinski,et al.  Integer Programming: Methods, Uses, Computations , 1965 .

[9]  Vedat Verter,et al.  Uncapacitated and Capacitated Facility Location Problems , 2011 .

[10]  Lubos Buzna,et al.  An acceleration of Erlenkotter-Körkel’s algorithms for the uncapacitated facility location problem , 2008, Ann. Oper. Res..

[11]  Juan José Salazar González,et al.  A branch-and-cut algorithm for a generalization of the Uncapacitated Facility Location Problem , 1996 .

[12]  Claude Tadonki,et al.  Solving the p-Median Problem with a Semi-Lagrangian Relaxation , 2006, Comput. Optim. Appl..

[13]  Gerard Sierksma,et al.  Branch and peg algorithms for the simple plant location problem , 2003, Comput. Oper. Res..

[14]  S. Thomas McCormick,et al.  Integer Programming and Combinatorial Optimization , 1996, Lecture Notes in Computer Science.

[15]  Zhu Han,et al.  Integer/Combinatorial Optimization , 2008 .

[16]  Jacques A. Ferland,et al.  An exact cooperative method for the uncapacitated facility location problem , 2014, Mathematical Programming Computation.

[17]  Adam N. Letchford,et al.  Fast bounding procedures for large instances of the Simple Plant Location Problem , 2012, Comput. Oper. Res..

[18]  Ted K. Ralphs,et al.  Integer and Combinatorial Optimization , 2013 .

[19]  Samir Khuller,et al.  Algorithms for facility location problems with outliers , 2001, SODA '01.

[20]  George L. Nemhauser,et al.  The uncapacitated facility location problem , 1990 .

[21]  Mauricio G. C. Resende,et al.  A hybrid multistart heuristic for the uncapacitated facility location problem , 2006, Eur. J. Oper. Res..

[22]  Brendan J. Frey,et al.  Solving the Uncapacitated Facility Location Problem Using Message Passing Algorithms , 2010, AISTATS.

[23]  Bhaba R. Sarker,et al.  Discrete location theory , 1991 .

[24]  R. D. Galvão,et al.  A method for solving to optimality uncapacitated location problems , 1990 .

[25]  Leon F. McGinnis,et al.  Facility Layout and Location: An Analytical Approach , 1991 .

[26]  Diego Klabjan.  A Practical Algorithm for Computing a Subadditive Dual Function for Set Partitioning , 2004, Comput. Optim. Appl..

[27]  Stefanie Seiler,et al.  Facility Layout And Location An Analytical Approach , 2016 .

[28]  J. Krarup,et al.  The simple plant location problem: Survey and synthesis , 1983 .

[29]  Donald Erlenkotter,et al.  A Dual-Based Procedure for Uncapacitated Facility Location , 1978, Oper. Res..

[30]  Claude-Alain Burdet,et al.  A Subadditive Approach to Solve Linear Integer Programs , 1977 .

[31]  K. Holmberg,et al.  Experiments with primal - dual decomposition and subgradient methods for the uncapacitatied facility location problem , 2001 .

[32]  M. Guignard.  A Lagrangean dual ascent algorithm for simple plant location problems , 1988 .

[33]  Adam N. Letchford,et al.  An aggressive reduction scheme for the simple plant location problem , 2014, Eur. J. Oper. Res..

[34]  R. Swain.  A Parametric Decomposition Approach for the Solution of Uncapacitated Location Problems , 1974 .

[35]  Diego Klabjan.  A New Subadditive Approach to Integer Programming , 2002, IPCO.

[36]  J. Beasley.  Lagrangean heuristics for location problems , 1993 .

[37]  Diego Klabjan,et al.  Subadditive approaches in integer programming , 2007, Eur. J. Oper. Res..

[38]  Cesar Beltran-Royo,et al.  Semi-Lagrangian relaxation applied to the uncapacitated facility location problem , 2010, Computational Optimization and Applications.

[39]  Yuri Kochetov,et al.  Computationally Difficult Instances for the Uncapacitated Facility Location Problem , 2005 .

[40]  E. L. Johnson.  Integer programming , 1980 .