Lagrangian-relaxation-based solution procedures for a multiproduct capacitated facility location problem with choice of facility type

This paper presents exact and heuristic solution procedures for a multiproduct capacitated facility location (MPCFL) problem in which the demand for a number of different product families must be supplied from a set of facility sites, and each site offers a choice of facility types exhibiting different capacities. MPCFL generalizes both the uncapacitated (or simple) facility location (UFL) problem and the pure-integer capacitated facility location problem. We define a branch-and-bound algorithm for MPCFL that utilizes bounds formed by a Lagrangian relaxation of MPCFL which decomposes the problem into UFL subproblems and easily solvable 0-1 knapsack subproblems. The UFL subproblems are solved by the dual-based procedure of Erlenkotter. We also present a subgradient optimization-Lagrangian relaxation-based heuristic for MPCFL. Computational experience with the algorithm and heuristic are reported. The MPCFL heuristic is seen to be extremely effective, generating solutions to the test problems that are on average within 2% of optimality, and the branch-and-bound algorithm is successful in solving all of the test problems to optimality.

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

[2]  Hasan Pirkul,et al.  Computer and Database Location in Distributed Computer Systems , 1986, IEEE Transactions on Computers.

[3]  Choong Y. Lee,et al.  A cross decomposition algorithm for a multiproduct-multitype facility location problem , 1993, Comput. Oper. Res..

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

[5]  M. R. Rao,et al.  An Algorithm for the Fixed-Charge Assigning Users to Sources Problem , 1983 .

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

[7]  Tony J. Van Roy,et al.  Cross decomposition for mixed integer programming , 1983, Math. Program..

[8]  G. Nemhauser,et al.  Exceptional Paper—Location of Bank Accounts to Optimize Float: An Analytic Study of Exact and Approximate Algorithms , 1977 .

[9]  M. Guignard,et al.  Lagrangean dual ascent algorithms for computing bounds in capacitated plant location problems , 1990 .

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

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

[12]  K. Jörnsten,et al.  A new Lagrangian relaxation approach to the generalized assignment problem , 1986 .

[13]  Choong Y. Lee.  An optimal algorithm for the multiproduct capacitated facility location problem with a choice of facility type , 1991, Comput. Oper. Res..

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

[15]  Jean-Louis Goffin,et al.  On convergence rates of subgradient optimization methods , 1977, Math. Program..

[16]  E. Balas.  An Additive Algorithm for Solving Linear Programs with Zero-One Variables , 1965 .

[17]  George L. Nemhauser,et al.  Note--On "Location of Bank Accounts to Optimize Float: An Analytic Study of Exact and Approximate Algorithms" , 1979 .

[18]  A. M. Geoffrion,et al.  Multicommodity Distribution System Design by Benders Decomposition , 1974 .

[19]  Hanan Luss,et al.  A Dual-Based Algorithm for Multiproduct Uncapacitated Facility Location , 1987, Transp. Sci..

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

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

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

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

[24]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988, Wiley interscience series in discrete mathematics and optimization.

[25]  J. Mazzola,et al.  Multiple‐facility loading under capacity‐based economies of scope , 1997 .

[26]  Joseph B. Mazzola,et al.  Resource-Constrained Assignment Scheduling , 1986, Oper. Res..

[27]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988 .

[28]  Philip Wolfe,et al.  Validation of subgradient optimization , 1974, Math. Program..

[29]  K. Jörnsten,et al.  Lagrangean relaxation and constraint generation procedures for capacitated plant location problems with single sourcing , 1990 .

[30]  Hanan Luss,et al.  A Lagrangian Relaxation Heuristic for Capacitated Facility Location with Single-Source Constraints , 1986 .

[31]  H. Tempelmeier,et al.  A Lagrangean-based heuristic for dynamic multilevel multiitem constrained lotsizing with setup times , 1996 .