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Location problems. (English) Zbl 0572.90022

Recent developments for several location problems are surveyed. These include: graph theoretic and combinatorial formulations of the simple plant location problem, the NP-hardness of some p-center problems, worst- case bounds for several polynomial-time heuristics for some p-center problems, and a general solution to a class of one facility network problems with convex cost functions.

MSC:

90B05 Inventory, storage, reservoirs
05C35 Extremal problems in graph theory
90C10 Integer programming
90-02 Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming
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[1] Cho, D. C.; Padberg, M.; Rao, M. R., On the uncapacitated plant location problem II: Facets and lifting theorems, Math. of Opns. Res., 8, 590-612 (1983) · Zbl 0536.90030
[2] Cho, D. C.; Johnson, E. L.; Padberg, M.; Rao, M. R., On the uncapacitated plant location problem I: Valid inequalities and facets, Math. of Opns. Res., 8, 579-589 (1983) · Zbl 0536.90029
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[12] Francis, R. L.; McGinnis, L. F.; White, J. A., Locational analysis, European Journal of Operational Research, 12, 220-252 (1983) · Zbl 0502.90019
[13] Guignard, M., Fractional vertices, cuts and facets of the simple plant location problem, (Math. Proc. Study, 12 (1980)), 150-162 · Zbl 0439.90061
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[15] Hochbaum, D. S.; Shmoys, D. B., A best possible heuristic for the K-center problem (1983), University of California: University of California Berkeley, CA
[16] A.J. Hoffman, A. Kolen and M. Sakarovitch, “Totally balanced and greedy matrices”, SIAM J. Algebraic and Discrete Methods, forthcoming.; A.J. Hoffman, A. Kolen and M. Sakarovitch, “Totally balanced and greedy matrices”, SIAM J. Algebraic and Discrete Methods, forthcoming. · Zbl 0573.05041
[17] Hooker, J., Solving nonlinear single facility network location problems (1985), Carnegie-Mellon University: Carnegie-Mellon University Pittsburgh, PA
[18] Kolen, A., Solving covering problems and the uncapacitated plant location problem on trees, European Journal of Operational Research, 12, 266-278 (1983) · Zbl 0508.90035
[19] Krarup, J.; Pruzan, P. M., The simple plant location problem: Survey and synthesis, European Journal of Operational Research, 12, 36-81 (1983) · Zbl 0506.90018
[20] Masuyama, S.; Ibaraki, T.; Hasegawa, T., The computational complexity of the in-center problems on the plane, Transactions of the I.E.C.E. of Japan, E64, 57-64 (1981)
[21] Megiddo, N.; Supowit, K. J., On the complexity of some common geometric location problems, SIAM J. Comp., 13, 182-196 (1984) · Zbl 0534.68032
[22] Tansel, B. C.; Francis, R. L.; Lowe, T. J., Location on networks, Part I, The p-center and p-median problems, Management Science, 29, 482-497 (1983) · Zbl 0513.90022
[23] Tansel, B. C.; Francis, R. L.; Lowe, T. J., Location on networks, Part II, Exploiting tree network structure, Management Science, 29, 498-511 (1983) · Zbl 0513.90023
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