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Facility Location

  • Reference work entry
  • First Online:
Encyclopedia of Algorithms

  • 376 Accesses

Years and Authors of Summarized Original Work

  • 1997; Shmoys, Tardos, Aardal

Problem Definition

Facility location problems concern situations where a planner needs to determine the location of facilities intended to serve a given set of clients. The objective is usually to minimize the sum of the cost of opening the facilities and the cost of serving the clients by the facilities, subject to various constraints, such as the number and the type of clients a facility can serve. There are many variants of the facility location problem, depending on the structure of the cost function and the constraints imposed on the solution. Early references on facility location problems include Kuehn and Hamburger [35], Balinski and Wolfe [8], Manne [40], and Balinski [7]. Review works include Krarup and Pruzan [34] and Mirchandani and Francis [42]. It is interesting to notice that the algorithm that is probably one of the most effective ones to solve the uncapacitated facility location problem to...

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Recommended Reading

  1. Aardal K, Chudak FA, Shmoys DB (1999) A 3-approximation algorithm for the k-level uncapacitated facility location problem. Inf Process Lett 72:161–167

    Article  MathSciNet  MATH  Google Scholar 

  2. Ageev AA, Sviridenko MI (1999) An 0.828-approximation algorithm for the uncapacitated facility location problem. Discret Appl Math 93:149–156

    Article  MathSciNet  MATH  Google Scholar 

  3. Anagnostopoulos A, Bent R, Upfal E, van Hentenryck P (2004) A simple and deterministic competitive algorithm for online facility location. Inf Comput 194(2):175–202

    Article  MathSciNet  MATH  Google Scholar 

  4. Andrews M, Zhang L (1998) The access network design problem. In: Proceedings of the 39th annual IEEE symposium on foundations of computer science (FOCS). IEEE Computer Society, Los Alamitos, pp 40–49

    Google Scholar 

  5. Arora S, Raghavan P, Rao S (1998) Approximation schemes for Euclidean k-medians and related problems. In: Proceedings of the 30th annual ACM symposium on theory of computing (STOC). ACM, New York, pp 106–113

    Google Scholar 

  6. Arya V, Garg N, Khandekar R, Meyerson A, Munagala K, Pandit V (2001) Local search heuristics for k-median and facility location problems. In: Proceedings of the 33rd annual ACM symposium on theory of computing (STOC). ACM, New York, pp 21–29

    Google Scholar 

  7. Balinski ML (1966) On finding integer solutions to linear programs. In: Proceedings of the IBM scientific computing symposium on combinatorial problems. IBM, White Plains, pp 225–248

    Google Scholar 

  8. Balinski ML, Wolfe P (1963) On Benders decomposition and a plant location problem. In: ARO-27. Mathematica Inc., Princeton

    Google Scholar 

  9. Beasley JE (2008) Operations research library. http://people.brunel.ac.uk/~mastjjb/jeb/info.html. Accessed 2008

  10. Byrka J (2007) An optimal bifactor approximation algorithm for the metric uncapacitated facility location problem. In: Proceedings of the 10th international workshop on approximation algorithms for combinatorial optimization problems (APPROX). Lecture notes in computer science, vol 4627. Springer, Berlin, pp 29–43

    Google Scholar 

  11. Charikar M, Guha S, Tardos E, Shmoys DB (1999) A constant factor approximation algorithm for the k-median problem. In: Proceedings of the 31st annual ACM symposium on theory of computing (STOC). ACM, New York, pp 1–10

    Google Scholar 

  12. Charikar M, Khuller S, Mount D, Narasimhan G (2001) Facility location with outliers. In: Proceedings of the 12th annual ACM-SIAM symposium on discrete algorithms (SODA). SIAM, Philadelphia, pp 642–651

    Google Scholar 

  13. Chudak FA, Shmoys DB (2003) Improved approximation algorithms for the uncapacitated facility location problem. SIAM J Comput 33(1):1–25

    Article  MathSciNet  MATH  Google Scholar 

  14. Chudak FA, Wiliamson DP (1999) Improved approximation algorithms for capacitated facility location problems. In: Proceedings of the 7th conference on integer programing and combinatorial optimization (IPCO). Lecture notes in computer science, vol 1610. Springer, Berlin, pp 99–113

    Google Scholar 

  15. Cornuéjols G, Fisher ML, Nemhauser GL (1977) Location of bank accounts to optimize float: an analytic study of exact and approximate algorithms. Manag Sci 8:789–810

    Article  MathSciNet  MATH  Google Scholar 

  16. Erlenkotter D (1978) A dual-based procedure for uncapacitated facility location problems. Oper Res 26:992–1009

    Article  MathSciNet  MATH  Google Scholar 

  17. Feige U (1998) A threshold of ln n for approximating set cover. J ACM 45:634–652

    Article  MathSciNet  MATH  Google Scholar 

  18. Fotakis D (2003) On the competitive ratio for online facility location. In: Proceedings of the 30th international colloquium on automata, languages and programming (ICALP). Lecture notes in computer science, vol 2719. Springer, Berlin, pp 637–652

    Google Scholar 

  19. Guha S, Khuller S (1998) Greedy strikes back: improved facility location algorithms. In: Proceedings of the 9th ACM-SIAM symposium on discrete algorithms (SODA). SIAM, Philadelphia, pp 228–248

    Google Scholar 

  20. Guha S, Khuller S (1999) Greedy strikes back: improved facility location algorithms. J Algorithm 31:228–248

    Article  MathSciNet  MATH  Google Scholar 

  21. Guha S, Meyerson A, Munagala K (2001) A constant factor approximation for the single sink edge installation problem. In: Proceedings of the 33rd annual ACM symposium on theory of computing (STOC). ACM, New York, pp 383–388

    Google Scholar 

  22. Guha S, Meyerson A, Munagala K (2000) Hierarchical placement and network design problems. In: Proceedings of the 41st annual IEEE symposium on foundations of computer science (FOCS). IEEE Computer Society, Los Alamitos, pp 603–612

    Google Scholar 

  23. Gupta A, Pál M, Ravi R, Sinha A (2004) Boosted sampling: approximation algorithms for stochastic optimization. In: Proceedings of the 36st annual ACM symposium on theory of computing (STOC). ACM, New York, pp 417–426

    Google Scholar 

  24. Hajiaghayi M, Mahdian M, Mirrokni VS (2003) The facility location problem with general cost functions. Networks 42(1):42–47

    Article  MathSciNet  MATH  Google Scholar 

  25. Hochbaum DS (1982) Heuristics for the fixed cost median problem. Math Program 22(2):148–162

    Article  MathSciNet  MATH  Google Scholar 

  26. Hochbaum DS, Shmoys DB (1985) A best possible approximation algorithm for the k-center problem. Math Oper Res 10:180–184

    Article  MathSciNet  MATH  Google Scholar 

  27. Hoefer M (2003) Experimental comparison of heuristic and approximation algorithms for uncapacitated facility location. In: Proceedings of the 2nd international workshop on experimental and efficient algorithms (WEA). Lecture notes in computer science, vol 2647. Springer, Berlin, pp 165–178

    Google Scholar 

  28. Jain K, Mahdian M, Markakis E, Saberi A, Vazirani VV (2003) Approximation algorithms for facility location via dual fitting with factor-revealing LP. J ACM 50(6):795–824

    Article  MathSciNet  MATH  Google Scholar 

  29. Jain K, Mahdian M, Saberi A (2002) A new greedy approach for facility location problems. In: Proceedings of the 34st annual ACM symposium on theory of computing (STOC). ACM, New York, pp 731–740

    Google Scholar 

  30. Jain K, Vazirani VV (2000) An approximation algorithm for the fault tolerant metric facility location problem. In: Approximation algorithms for combinatorial optimization, proceedings of APPROX. Lecture notes in computer science, vol 1913. Springer, Berlin, pp 177–183

    Google Scholar 

  31. Jamin S, Jin C, Jin Y, Raz D, Shavitt Y, Zhang L (2000) On the placement of internet instrumentations. In: Proceedings of the 19th annual joint conference of the IEEE computer and communications Societies (INFOCOM), vol 1. IEEE Computer Society, Los Alamitos, pp 295–304

    Google Scholar 

  32. Karger D, Minkoff M (2000) Building Steiner trees with incomplete global knowledge. In: Proceedings of the 41st annual IEEE symposium on foundations of computer science (FOCS). IEEE Computer Society, Los Alamitos, pp 613–623

    Google Scholar 

  33. Krarup J, Pruzan PM (1990) Ingredients of locational analysis. In: Mirchandani P, Francis R (eds) Discrete location theory. Wiley, New York, pp 1–54

    Google Scholar 

  34. Krarup J, Pruzan PM (1983) The simple plant location problem: survey and synthesis. Eur J Oper Res 12:38–81

    MathSciNet  MATH  Google Scholar 

  35. Kuehn AA, Hamburger MJ (1963) A heuristic program for locating warehouses. Manag Sci 9:643–666

    Article  Google Scholar 

  36. Li B, Golin M, Italiano G, Deng X, Sohraby K (1999) On the optimal placement of web proxies in the internet. In: Proceedings of the 18th annual joint conference of the IEEE computer and communications societies (INFOCOM). IEEE Computer Society, Los Alamitos, pp 1282–1290

    Google Scholar 

  37. Mahdian M (2004) Facility location and the analysis of algorithms through factor-revealing programs. PhD thesis, MIT, Cambridge

    Google Scholar 

  38. Mahdian M, Pál M (2003) Universal facility location. In: Proceedings of the 11th annual european symposium on algorithms (ESA). Lecture notes in computer science, vol 2832. Springer, Berlin, pp 409–421

    Google Scholar 

  39. Mahdian M, Ye Y, Zhang J (2006) Approximation algorithms for metric facility location problems. SIAM J Comput 36(2):411–432

    Article  MathSciNet  MATH  Google Scholar 

  40. Manne AS (1964) Plant location under economies-of-scale – decentralization and computation. Manag Sci 11:213–235

    Article  Google Scholar 

  41. Meyerson A (2001) Online facility location. In: Proceedings of the 42nd annual IEEE symposium on foundations of computer science (FOCS). IEEE Computer Society, Los Alamitos, pp 426–431

    Google Scholar 

  42. Mirchandani PB, Francis RL (1990) Discrete location theory. Wiley, New York

    MATH  Google Scholar 

  43. Nemhauser GL, Wolsey LA (1990) Integer and combinatorial optimization. Wiley, New York

    MATH  Google Scholar 

  44. Pál M, Tardos E, Wexler T (2001) Facility location with nonuniform hard capacities. In: Proceedings of the 42nd annual IEEE symposium on foundations of computer science (FOCS). IEEE Computer Society, Los Alamitos, pp 329–338

    Google Scholar 

  45. Qiu L, Padmanabhan VN, Voelker G (2001) On the placement of web server replicas. In: Proceedings of the 20th annual joint conference of the IEEE computer and communications societies (INFOCOM). IEEE Computer Society, Los Alamitos, pp 1587–1596

    Google Scholar 

  46. Ravi R, Sinha A (2006) Hedging uncertainty: approximation algorithms for stochastic optimization problems. Math Program 108(1):97–114

    Article  MathSciNet  MATH  Google Scholar 

  47. Ravi R, Sinha A (2002) Integrated logistics: approximation algorithms combining facility location and network design. In: Proceedings of the 9th conference on integer programming and combinatorial optimization (IPCO). Lecture notes in computer science, vol 2337. Springer, Berlin, pp 212–229

    Google Scholar 

  48. Ravi R, Sinha A (2004) Multicommodity facility location. In: Proceedings of the 15th annual ACM-SIAM symposium on discrete algorithms (SODA). SIAM, Philadelphia, pp 342–349

    Google Scholar 

  49. Shmoys DB (2000) Approximation algorithms for facility location problems. In: Jansen K, Khuller S (eds) Approximation algorithms for combinatorial optimization, vol 1913, Lecture notes in computer science. Springer, Berlin, pp 27–33

    Chapter  Google Scholar 

  50. Shmoys DB (2004) The design and analysis of approximation algorithms: facility location as a case study. In: Thomas RR, Hosten S, Lee J (eds) Proceedings of symposia in applied mathematics, vol 61. AMS, Providence, pp 85–97

    Google Scholar 

  51. Shmoys DB, Tardos E, Aardal K (1997) Approximation algorithms for facility location problems. In: Proceedings of the 29th annual ACM symposium on theory of computing (STOC). ACM, New York, pp 265–274

    Google Scholar 

  52. Svitkina Z, Tardos E (2006) Facility location with hierarchical facility costs. In: Proceedings of the 17th annual ACM-SIAM symposium on discrete algorithm (SODA). SIAM, Philadelphia, pp 153–161

    Google Scholar 

  53. Swamy C, Kumar A (2004) Primal-dual algorithms for connected facility location problems. Algorithmica 40(4):245–269

    Article  MathSciNet  MATH  Google Scholar 

  54. Swamy C, Shmoys DB (2003) Fault-tolerant facility location. In: Proceedings of the 14th annual ACM-SIAM symposium on discrete algorithms (SODA). SIAM, Philadelphia, pp 735–736

    Google Scholar 

  55. Vygen J (2005) Approximation algorithms for facility location problems (lecture notes). Technical report No. 05950-OR, Research Institute for Discrete Mathematics, University of Bonn. http://www.or.uni-bonn.de/~vygen/fl.pdf

  56. Zhang J (2004) Approximating the two-level facility location problem via a quasi-greedy approach. In: Proceedings of the 15th annual ACM-SIAM symposium on discrete algorithms (SODA). SIAM, Philadelphia, pp 808–817. Also, Math Program 108:159–176 (2006)

    Google Scholar 

  57. Zhang J, Chen B, Ye Y (2005) A multiexchange local search algorithm for the capacitated facility location problem. Math Oper Res 30(2):389–403

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Centrum Wiskunde & Informatica (CWI), Amsterdam, The Netherlands

    Karen Aardal & Jaroslaw Byrka

  2. Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands

    Karen Aardal & Jaroslaw Byrka

  3. Yahoo! Research, Santa Clara, CA, USA

    Mohammad Mahdian

Authors
  1. Karen Aardal
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  2. Jaroslaw Byrka
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  3. Mohammad Mahdian
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Corresponding author

Correspondence to Karen Aardal .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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Aardal, K., Byrka, J., Mahdian, M. (2016). Facility Location. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_139

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