Skip to main content
SpringerLink
Log in

Median Problems in Networks

  • Chapter
  • First Online:
Book cover Foundations of Location Analysis

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 155))

Abstract

Suppose a number of geographically distributed customers are demanding a service or good, and facilities providing it need to be optimally located. Once facilities are deployed, either customers travel to the facilities to satisfy their needs, or vehicles travel from the facilities to customers’ locations, carrying the goods to be delivered. The p-median problem finds the optimal location of exactly p facilities, so that the sum of the distances between customers and their closest facilities, measured along the shortest paths, is minimized. Since the number n of customers is known, by dividing the objective by n, the minimum average distance between customers and facilities is obtained too.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Arbib C, Marinelli F (2004) An optimization model for trim loss minimization in an automotive glass plant. Eur J Oper Res 183:1421–1432

    Google Scholar 

  • Balinski ML (1965) Integer programming: methods, uses and computation. Manag Sci 12:253–313

    Google Scholar 

  • Berman O, Larson RC, Chiu SS (1985) Optimal server location on a network operating as an M/G/1 Queue. Oper Res 33:746–771

    Google Scholar 

  • Berman O, Odoni AR (1982) Locating mobile servers on a network with Markovian properties. Networks 12:73–86

    Google Scholar 

  • Brandeau ML, Chiu SS (1989) An overview of representative problems in location research. Manag Sci 35:645–674

    Google Scholar 

  • Calvo A, Marks H (1973) Location of health care facilities: an analytical approach. Socio-Econ Plan Sci 7:407–422

    Google Scholar 

  • Christofides N (1975) Graph theory—an algorithmic approach. Academic Press, London

    Google Scholar 

  • Church R, Meadows ME (1979) Location modeling utilizing maximum service distance criteria. Geogr Anal 11:358–373

    Google Scholar 

  • Cooper L (1963) Location–allocation problems. Oper Res 11:331–343

    Google Scholar 

  • Cooper L (1964) Heuristic methods for location–allocation problems. SIAM Rev 6:37–53

    Google Scholar 

  • Drezner Z (1987) Heuristic solution methods for two location problems with unreliable facilities. J Oper Res Soc 38:509–514

    Google Scholar 

  • Drezner T, Drezner Z (2007) The gravity p-median model. Eur J Oper Res 179:1239–1251

    Google Scholar 

  • Efroymson MA, Ray TL (1966) A branch-bound algorithm for plant location. Oper Res 14:361–368

    Google Scholar 

  • Frank H (1966) Optimum locations on a graph with probabilistic demands. Oper Res 14:409–421

    Google Scholar 

  • Gass S (1958) Linear programming, 1st edn. McGraw-Hill, New York

    Google Scholar 

  • Goldman AJ (1969) Optimal locations for centers in a network. Transp Sci 3:352–360

    Google Scholar 

  • Goldman AJ (1971) Optimal center location in simple networks. Transp Sci 5:212–221

    Google Scholar 

  • Goldman AJ (1972) Approximate localization theorems for optimal facility placement. Transp Sci 6:407–418

    Google Scholar 

  • Gülicher H (1965) Einige Eigenschaften optimaler Standorte in Verkehrsnetzen. Schr Ver Socialpolit 42:111–137

    Google Scholar 

  • Hakimi SL (1964) Optimal location of switching centers and the absolute centers and medians of a graph. Oper Res 12:450–459

    Google Scholar 

  • Hakimi SL (1965) Optimum distribution of switching centers in a communication network and some related graph theoretic problems. Oper Res 13:462–475

    Google Scholar 

  • Hakimi SL, Maheshwari SN (1972) Optimum locations of centers in networks. Oper Res 20:967–973

    Google Scholar 

  • Hale TS, Moberg CR (2003) Location science research: a review. Ann Oper Res 123:21–35

    Google Scholar 

  • Hansen P, Jaumard B (1997) Cluster analysis and mathematical programming. Math Program 79:191–215

    Google Scholar 

  • Hillsman E, Rhoda R (1978) Errors in measuring distance from populations to service centers. Ann Reg Sci Assoc 12:74–88

    Google Scholar 

  • Holmes J, Williams F, Brown L (1972) Facility location under maximum travel restriction: an example using day care facilities. Geogr Anal 4:258–266

    Google Scholar 

  • Hooker JN, Garfinkel RS, Chen CK (1991) Finite dominating sets for network location problems. Oper Res 39:100–118

    Google Scholar 

  • Hortel J, Lobo JM (2005) An ED-based protocol of optimal sampling of biodiversity. Biodivers Conserv 14:2913–2947

    Google Scholar 

  • Hua Lo-Keng, others (1962) Application of mathematical methods to wheat harvesting. Chin Math 2:77–91

    Google Scholar 

  • Kariv O, Hakimi SL (1979) An algorithmic approach to network location problems. Part II: The p-medians. SIAM J Appl Math 37:539–560

    Google Scholar 

  • Kolesar P (1980) Testing for vision loss in glaucoma suspects. Manag Sci 26:439–450

    Google Scholar 

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

    Google Scholar 

  • Land AH, Doig AG (1960) An automatic method for solving discrete programming problems. Econometrica 28:497–520

    Google Scholar 

  • Levy J (1972) An extended theorem for location on a network. Oper Res Q 18:433–442

    Google Scholar 

  • Maranzana F (1964) On the location of supply points to minimize transport costs. Oper Res Q 15:261–270

    Google Scholar 

  • Marianov V (2003) Location of multiple-server congestible facilities for maximizing expected demand, when services are non-essential. Ann Oper Res 123:125–141

    Google Scholar 

  • Marianov V, Serra D (1998) Probabilistic maximal covering location-allocation models for congested systems. J Reg Sci 13:401–424

    Google Scholar 

  • Marianov V, Serra D (2001) Hierarchical location-allocation models for congested systems. Eur J Oper Res 135:195–208

    Google Scholar 

  • Marianov V, Serra D (2002) Location problems in the public sector. In: Drezner Z, Hamacher H (eds) Facility location: applications and theory. Springer, Berlin

    Google Scholar 

  • Marianov V, Taborga P (2001) Optimal location of public health centres which provide free and paid services. J Oper Res Soc 52:391–400

    Google Scholar 

  • Minieka E (1977) The centers and medians of a graph. Oper Res 25:641–650

    Google Scholar 

  • Mirchandani PB (1980) Locational decisions on stochastic networks. Geogr Anal 12:172–183

    Google Scholar 

  • Mirchandani PB (1990) The p-median problem and generalizations. In: Mirchandani PB, Francis RL (eds) Discrete location theory. Wiley, New York

    Google Scholar 

  • Mirchandani PB, Odoni AR (1979) Locations of medians on stochastic networks. Transp Sci 13:85–97

    Google Scholar 

  • Mladenović N, Brimberg J, Hansen P, Moreno-Pérez JA (2007) The p-median problem: a survey of metaheuristic approaches. Eur J Oper Res 179:927–939

    Google Scholar 

  • Morris J (1978) On the extent to which certain fixed-charge depot location problems can be solved by LP. J Oper Res Soc 29:71–76

    Google Scholar 

  • Narula SC (1984) Hierarchical location–allocation problems: a classification scheme. Eur J Oper Res 15:183–189

    Google Scholar 

  • Ng RT, Han J (1994) Efficient and effective clustering methods for spatial data mining. Proceedings of the 20th international conference on very large data bases. Santiago pp 144–154

    Google Scholar 

  • Reese J (2006) Solution methods for the p-median problem: an annotated bibliography. Networks 48:125–142

    Google Scholar 

  • ReVelle CS, Swain RW (1970) Central facilities location. Geogr Anal 2:30–42

    Google Scholar 

  • Rojeski P, ReVelle C (1970) Central facilities location under an investment constraint. Geogr Anal 2:343–360

    Google Scholar 

  • Rosing K, ReVelle C, Rosing-Vogelaar H (1979) The p-median model and its linear programming relaxation: an approach to large problems. J Oper Res Soc 30:815–823

    Google Scholar 

  • Serra D, Marianov V (1998) The p-median problem in a changing network: the case of Barcelona. Locat Sci 6:383–394

    Google Scholar 

  • Shiode S, Drezner Z (2003) A competitive facility location problem on a tree network with stochastic weights. European J Oper Res 149:47–52

    Google Scholar 

  • Snyder LV (2006) Facility location under uncertainty: a review. IIE Trans 38:537–554

    Google Scholar 

  • Tansel BC, Francis RL, Lowe TJ (1983a) Location on networks: a survey. Part I: the p-center and p-median problems. Manag Sci 29:482–497

    Google Scholar 

  • Tansel BC, Francis RL, Lowe TJ (1983b) Location on networks: a survey. Part II: exploiting tree network structure. Manag Sci 29:498–511

    Google Scholar 

  • Teitz M, Bart P (1968) Heuristic methods for estimating the generalized vertex median of a weighted graph. Oper Res 16:955–961

    Google Scholar 

  • Toregas C, Swain RW, ReVelle CS, Bergman L (1971) The location of emergency service facilities. Oper Res 19:1363–1373

    Google Scholar 

  • Wesolowsky GO, Truscott WG (1975) The multiperiod location–allocation problem with relocation of facilities. Manag Sci 22:57–65

    Google Scholar 

  • Won Y (2000) New p-median approach to cell formation with alternative process plans. Int J Prod Res 38:229–240

    Google Scholar 

Download references

Acknowledgments

This research has been possible thanks to grants by the Spanish Ministry of Science and Education, BEC2006-12291, the Chilean CONICYT–FONDECYT 1070741, and support from the Instituto Milenio “Complex Engineering Systems,” through grants ICM-MIDEPLAN P-05-004-F and CONICYT FBO16.

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile

    Vladimir Marianov

  2. Department of Economics and Business, Pompeu Fabra University, Barcelona, Spain

    Daniel Serra

Authors
  1. Vladimir Marianov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Daniel Serra
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vladimir Marianov .

Editor information

Editors and Affiliations

  1. Faculty of Business Administration, University of New Brunswick, Fredericton,, New Brunswick, Canada

    H. A. Eiselt

  2. Depto. Ingenieria Electrica, Pontificia Universidad Católica de Chile, Av. Vicuna Mackenna 4860, Macul, Santiago, Chile

    Vladimir Marianov

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Marianov, V., Serra, D. (2011). Median Problems in Networks. In: Eiselt, H., Marianov, V. (eds) Foundations of Location Analysis. International Series in Operations Research & Management Science, vol 155. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7572-0_3

Download citation

Publish with us

Policies and ethics

Search

Navigation