Abstract
Medium to large network location problems can often be solved only approximatelywithin reasonable computing time. Standard solution techniques focus on the tentative choiceof locations embedded in an enumerative search. In contrast, the method presented hereselects or rejects facilities conclusively and thus avoids costly backtracking schemes. Itdraws on supermodularity and Lagrangian relaxation. We rank well‐known variable‐fixingtests and propose a hierarchy of tests that provides an attractive time‐accuracy trade‐offwhich we assess computationally.
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References
K. Aardal, Y. Pochet and L.A. Wolsey, Capacitated facility location: Valid inequalities and facets, Mathematics of Operations Research 20(1995)562-582.
C.H. Aikens, Facility location models for distribution planning, European Journal of Operational Research 22(1985)263-279.
U. Akinc and B.M. Khumawala, An efficient branch and bound algorithm for the capacitated warehouse location problem, Management Science 23(1977)585-594.
R.S. Barr, F. Glover and D. Klingman, A new optimization method for large scale fixed charge transportation problems, Operations Research 29(1981)448-463.
J.E. Beasley, An algorithm for solving large capacitated warehouse location problems, Journal of the Operational Research Society 33(1988)314-325.
G.H. Bradley, G.G. Brown and G.W. Graves, Design and implementation of large scale primal transshipment algorithms, Management Science 24(1977)1-34.
N. Christofides and J.E. Beasley, Extensions to a Lagrangean relaxation approach for the capacitated warehouse location problem, European Journal of Operational Research 12(1983)19-28.
G. Cornuéjols and J.-M. Thizy, A primal approach to the simple plant location problem, SIAM Journal of Algebraic and Discrete Methods 3(1982)504-510.
A.M. Geoffrion and G.W. Graves, Multicommodity distribution system design by Benders decomposition, Management Science 20(1974)822-844.
S.K. Jacobsen, Heuristics for the capacitated plant location model, European Journal of Operational Research 12(1983)253-261.
B.M. Khumawala, An efficient heuristic procedure for the capacitated warehouse location problem, Naval Research Logistics Quaterly 21(1974)609-623.
J.M.Y. Leung and T.L. Magnanti, Valid inequalities and facets of the capacitated plant location problem, Mathematical Programming 44(1989)271-291.
G.R. Mateus and C.T. Bornstein, Dominance criteria for the capacitated warehouse location problem, Journal of the Operational Research Society 42(1991)145-149.
G. Sá, Branch-and-bound and approximate solutions to the capacitated plant-location problem, Operations Research 17(1969)1005-1016.
M.B. Teitz and P. Bart, Heuristic methods for estimating the generalized vertex median of a weighted graph, Operations Research 16(1968)955-961.
D.M. Topkis, Minimizing a submodular function on a lattice, Operations Research 26(1978)305-321.
T.J. Van Roy, A cross decomposition algorithm for capacitated facility location, Operations Research 34(1986)145-163.
L.A. Wolsey, Submodularity and valid inequalities in capacitated fixed charge networks, Operations Research Letters 8(1989)119-124.
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Mateus, G., Thizy, J. Exact sequential choice of locations in a network. Annals of Operations Research 86, 199–219 (1999). https://doi.org/10.1023/A:1018950617642
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DOI: https://doi.org/10.1023/A:1018950617642