Facility Location

Chapter
Part of the Algorithms and Combinatorics book series (AC, volume 21)

Abstract

Many economic decisions involve selecting and/or placing certain facilities to serve given demands efficiently. Examples include manufacturing plants, storage facilities, depots, warehouses, libraries, fire stations, hospitals, base stations for wireless services (like TV broadcasting or mobile phone service), etc. The problems have in common that a set of facilities, each with a certain position, has to be chosen, and the objective is to meet the demand (of customers, users etc.) best. Facility location problems, which occur also in less obvious contexts, indeed have numerous applications.

Keywords

Approximation Algorithm Facility Location Performance Ratio Local Search Algorithm Service Cost 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References

General Literature

  1. Cornuéjols, G., Nemhauser, G.L., and Wolsey, L.A. [1990]: The uncapacitated facility location problem. In: Discrete Location Theory (P. Mirchandani, R. Francis, eds.), Wiley, New York 1990, pp. 119–171Google Scholar
  2. Shmoys, D.B. [2000]: Approximation algorithms for facility location problems. Proceedings of the 3rd International Workshop on Approximation Algorithms for Combinatorial Optimization; LNCS 1913 (K. Jansen, S. Khuller, eds.), Springer, Berlin 2000, pp. 27–33CrossRefGoogle Scholar
  3. Vygen, J. [2005]: Approximation algorithms for facility location problems (lecture notes). Report No. 05950-OR, Research Institute for Discrete Mathematics, University of Bonn, 2005Google Scholar

Cited References

  1. Archer, A., Rajagopalan, R., and Shmoys, D.B. [2003]: Lagrangian relaxation for the k-median problem: new insights and continuity properties. Algorithms — Proceedings of the 11th Annual European Symposium on Algorithms, Springer, Berlin 2003, pp. 31–42.Google Scholar
  2. Arora, S., Raghavan, P., and Rao, S. [1998]: Approximation schemes for Euclidean k-medians and related problems. Proceedings of the 30th Annual ACM Symposium on Theory of Computing (1998), 106–113Google Scholar
  3. Arya, V., Garg, N., Khandekar, R., Meyerson, A., Munagala, K., and Pandit, V. [2004]: Local search heuristics for k-median and facility location problems. SIAM Journal on Computing 33 (2004), 544–562MATHCrossRefMathSciNetGoogle Scholar
  4. Balinski, M.L. [1965]: Integer programming: methods, uses, computation. Management Science 12 (1965), 253–313MathSciNetCrossRefGoogle Scholar
  5. Balinski, M.L., and Wolfe, P. [1963]: On Benders decomposition and a plant location problem. Working paper ARO-27. Mathematica, Princeton 1963Google Scholar
  6. Byrka, J. [2007]: An optimal bifactor approximation algorithm for the metric uncapacitated facility location problem. Proceedings of the 10th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems; LNCS 4627 (M. Charikar, K. Jansen, O. Reingold, J.D.P. Rolim, eds.), Springer, Berlin 2007, pp. 29–43Google Scholar
  7. Byrka, J., and Aardal, K. [2007]: The approximation gap for the metric facility location problem is not yet closed. Operations Research Letters 35 (2007), 379–384CrossRefMathSciNetMATHGoogle Scholar
  8. Charikar, M., and Guha, S. [2005]: Improved combinatorial algorithms for the facility location and k-median problems. SIAM Journal on Computing 34 (2005), 803–824MATHCrossRefMathSciNetGoogle Scholar
  9. Charikar, M., Guha, S., Tardos, É., and Shmoys, D.B. [2002]: A constant-factor approximation algorithm for the k-median problem. Journal of Computer and System Sciences 65 (2002), 129–149MATHCrossRefMathSciNetGoogle Scholar
  10. Chudak, F.A., and Shmoys, D.B. [2003]: Improved approximation algorithms for the uncapacitated facility location problem. SIAM Journal on Computing 33 (2003), 1–25MATHCrossRefMathSciNetGoogle Scholar
  11. Feige, U. [1998]: A threshold of ln n for the approximating set cover. Journal of the ACM 45 (1998), 634–652MATHCrossRefMathSciNetGoogle Scholar
  12. Guha, S., and Khuller, S. [1999]: Greedy strikes back: improved facility location algorithms. Journal of Algorithms 31 (1999), 228–248MATHCrossRefMathSciNetGoogle Scholar
  13. Hochbaum, D.S. [1982]: Heuristics for the fixed cost median problem. Mathematical Programming 22 (1982), 148–162MATHCrossRefMathSciNetGoogle Scholar
  14. Jain, K., Mahdian, M., Markakis, E., Saberi, A., and Vazirani, V.V. [2003]: Greedy facility location algorithms analyzed using dual fitting with factor-revealing LP. Journal of the ACM 50 (2003), 795–824CrossRefMathSciNetGoogle Scholar
  15. Jain, K., and Vazirani, V.V. [2001]: Approximation algorithms for metric facility location and k-median problems using the primal-dual schema and Lagrangian relaxation. Journal of the ACM 48 (2001), 274–296CrossRefMathSciNetMATHGoogle Scholar
  16. Kolliopoulos, S.G., and Rao, S. [2007]: A nearly linear-time approximation scheme for the Euclidean k-median problem. SIAM Journal on Computing 37 (2007), 757–782CrossRefMATHMathSciNetGoogle Scholar
  17. Korupolu, M., Plaxton, C., and Rajaraman, R. [2000]: Analysis of a local search heuristic for facility location problems. Journal of Algorithms 37 (2000), 146–188MATHCrossRefMathSciNetGoogle Scholar
  18. Kuehn, A.A., and Hamburger, M.J. [1963]: A heuristic program for locating warehouses. Management Science 9 (1963), 643–666Google Scholar
  19. Levi, R., Shmoys, D.B., and Swamy, C. [2004]: LP-based approximation algorithms for capacitated facility location. In: Integer Programming and Combinatorial Optimization; Proceedings of the 10th International IPCO Conference; LNCS 3064 (G. Nemhauser, D. Bienstock, eds.), Springer, Berlin 2004, pp. 206–218Google Scholar
  20. Mahdian, M., and Pál, M. [2003]: Universal facility location. In: Algorithms — Proceedings of the 11th European Symposium on Algorithms (ESA); LNCS 2832 (G. di Battista, U. Zwick, eds.), Springer, Berlin 2003, pp. 409–421Google Scholar
  21. Mahdian, M., Ye, Y., and Zhang, J. [2006]: Approximation algorithms for metric facility location problems. SIAM Journal on Computing 36 (2006), 411–432MATHCrossRefMathSciNetGoogle Scholar
  22. Manne, A.S. [1964]: Plant location under economies-of-scale-decentralization and computation. Management Science 11 (1964), 213–235Google Scholar
  23. Pál, M., Tardos, É., and Wexler, T. [2001]: Facility location with hard capacities. Proceedings of the 42nd Annual IEEE Symposium on the Foundations of Computer Science (2001), 329–338Google Scholar
  24. Shmoys, D.B., Tardos, É., and Aardal, K. [1997]: Approximation algorithms for facility location problems. Proceedings of the 29th Annual ACM Symposium on Theory of Computing (1997), 265–274Google Scholar
  25. Stollsteimer, J.F. [1963]: A working model for plant numbers and locations. Journal of Farm Economics 45 (1963), 631–645CrossRefGoogle Scholar
  26. Sviridenko, M. [2002]: An improved approximation algorithm for the metric uncapacitated facility location problem. In: Integer Programming and Combinatorial Optimization; Proceedings of the 9th International IPCO Conference; LNCS 2337 (W. Cook, A. Schulz, eds.), Springer, Berlin 2002, pp. 240–257CrossRefGoogle Scholar
  27. Vygen, J. [2007]: From stars to comets: improved local search for universal facility location. Operations Research Letters 35 (2007), 427–433MATHCrossRefMathSciNetGoogle Scholar
  28. Zhang, J., Chen, B., and Ye, Y. [2004]: Multi-exchange local search algorithm for the capacitated facility location problem. In: Integer Programming and Combinatorial Optimization; Proceedings of the 10th International IPCO Conference; LNCS 3064 (G. Nemhauser, D. Bienstock, eds.), Springer, Berlin 2004, pp. 219–233Google Scholar

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