Capacitated facility location problem with general setup cost

This paper presents an extension of the capacitated facility location problem (CFLP), in which the general setup cost functions and multiple facilities in one site are considered. The setup costs consist of a fixed term (site setup cost) plus a second term (facility setup costs). The facility setup cost functions are generally non-linear functions of the size of the facility in the same site. Two equivalent mixed integer linear programming (MIP) models are formulated for the problem and solved by general MIP solver. A Lagrangian heuristic algorithm (LHA) is also developed to find approximate solutions for this NP-hard problem. Extensive computational experiments are taken on randomly generated data and also well-known existing data (with some necessary modifications). The detailed results are provided and the heuristic algorithm is shown to be efficient.

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

[2]  Marshall L. Fisher,et al.  The Lagrangian Relaxation Method for Solving Integer Programming Problems , 2004, Manag. Sci..

[3]  Naum Zuselevich Shor,et al.  Minimization Methods for Non-Differentiable Functions , 1985, Springer Series in Computational Mathematics.

[4]  Said Salhi,et al.  Discrete Location Theory , 1991 .

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

[6]  Pierre Hansen,et al.  The simple plant location problem , 1976 .

[7]  Charles S. Revelle,et al.  Facility location with increasing production costs , 2003, Eur. J. Oper. Res..

[8]  K. Jörnsten,et al.  Computational results from a new Lagrangean relaxation algorithm for the capacitated plant location problem , 1991 .

[9]  J. Barceló,et al.  A heuristic lagrangean algorithm for the capacitated plant location problem , 1984 .

[10]  G. Cornuéjols,et al.  A comparison of heuristics and relaxations for the capacitated plant location problem , 1991 .

[11]  Vahab S. Mirrokni,et al.  The facility location problem with general cost functions , 2003, Networks.

[12]  B. M. Khumawala.  An Efficient Branch and Bound Algorithm for the Warehouse Location Problem , 1972 .

[13]  B. M. Khumawala,et al.  An Efficient Branch and Bound Algorithm for the Capacitated Warehouse Location Problem , 1977 .

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

[15]  J. Beasley.  An algorithm for solving large capacitated warehouse location problems , 1988 .

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

[17]  Tony J. Van Roy,et al.  A Cross Decomposition Algorithm for Capacitated Facility Location , 1986, Oper. Res..

[18]  Richard M. Soland,et al.  Optimal Facility Location with Concave Costs , 1974, Oper. Res..

[19]  Monique Guignard-Spielberg,et al.  Lagrangean decomposition: A model yielding stronger lagrangean bounds , 1987, Math. Program..

[20]  Marshall L. Fisher,et al.  An Applications Oriented Guide to Lagrangian Relaxation , 1985 .

[21]  Nicos Christofides,et al.  Extensions to a Lagrangean relaxation approach for the capacitated warehouse location problem , 1983 .

[22]  Roberto Musmanno,et al.  A Lagrangean heuristic for the plant location problem with multiple facilities in the same site , 2002, Optim. Methods Softw..

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

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

[25]  R. Sridharan.  The capacitated plant location problem , 1995 .

[26]  Roberto Musmanno,et al.  The capacitated plant location problem with multiple facilities in the same site , 2002, Comput. Oper. Res..

[27]  T. L. Ray,et al.  Warehouse Location Under Continuous Economies of Scale , 1966 .

[28]  A. M. Geoffrion,et al.  Lagrangean Relaxation Applied to Capacitated Facility Location Problems , 1978 .

[29]  Søren Kruse Jacobsen,et al.  Heuristics for the capacitated plant location model , 1983 .

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