Skip to main content
Log in

Continuous location of an assembly station

  • Original Paper
  • Published:
TOP Aims and scope Submit manuscript

Abstract

Demand existing at client points in the plane for several products should be met. Products have to be assembled from different components obtainable at given prices at various sources with known production capacities. The optimal design of the resulting supply chain must be determined, including the location of a central assembly station in the plane, so as to minimize the total operational cost comprising buying and transport of components as well as transport of final products. This problem leads to a difficult nonlinear and non-convex optimization problem for which a locally convergent algorithm is proposed. Some computational results are presented.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Balas E, Zemel E (1980) An algorithm for large zero–one knapsack problems. Oper Res 28:1130–1154

    Article  Google Scholar 

  • Blanquero R, Carrizosa E (2009) Continuous location problems and Big Triangle Small Triangle: constructing better bounds. J Glob Optim 45(3):389–402

    Article  Google Scholar 

  • Carrizosa E, Rodríguez-Chía AM (1997) Weber problems with alternative transportation systems. Eur J Oper Res 97:87–93

    Article  Google Scholar 

  • Cooper L (1964) Heuristic methods for location–allocation problems. SIAM Rev 6:37–52

    Article  Google Scholar 

  • Drezner Z, Nickel S (2009) Solving the ordered one-median problem in the plane. Eur J Oper Res 195(1):46–61

    Article  Google Scholar 

  • Drezner Z, Suzuki A (2004) The big triangle small triangle method for the solution of non-convex facility location problems. Oper Res 52(1):128–135

    Article  Google Scholar 

  • Drezner Z, Klamroth K, Schöbel A, Wesolowsky GO (2003) The Weber problem. In: Drezner Z, Hamacher H (eds) Facility location: applications and theory. Springer, Berlin, pp 1–36

    Google Scholar 

  • Drezner Z, Drezner T, Wesolowsky GO (2009) Location with acceleration-deceleration distance. Eur J Oper Res 198(1):157–164

    Article  Google Scholar 

  • Eilon S, Watson-Gandy CDT, Christofides N (1971) Distribution management. Hafner, New York

    Google Scholar 

  • Gugat M, Pfeiffer B (2007) Weber problems with mixed distances and regional demand. Math Methods Oper Res 66:419–449

    Article  Google Scholar 

  • Kaufman L, Plastria F (1988) The Weber problem with supply surplus. Belg J Oper Res Stat Comput Sci 28:15–31

    Google Scholar 

  • Kellerer H, Pferschy U, Pisinger D (2004) Knapsack problems. Springer, Berlin

    Book  Google Scholar 

  • Kuhn HW (1973) A note on Fermat’s problem. Math Program 4:98–107

    Article  Google Scholar 

  • Martello S, Toth P (1990) Knapsack problems—algorithms and computer implementations. Wiley, Chichester

    Google Scholar 

  • Plastria F (1992) GBSSS: the generalized big square small square method for planar single facility location. Eur J Oper Res 62(2):163–174

    Article  Google Scholar 

  • Plastria F (1995) Continuous location problems. In: Drezner Z (ed) Facility location: a survey of applications and methods. Springer, Berlin, pp 229–266, chap 11

    Google Scholar 

  • Plastria F (2011) The Weiszfeld algorithm: proof, amendments and extensions. In: Eiselt HA, Marianov V (eds) Foundations of location analysis. International series in operations research and management science, vol. 155. Springer, Berlin, pp 357–390. ISBN 978-1-4419-7571-3

    Chapter  Google Scholar 

  • Plastria F, Elosmani M (2008) On the convergence of the Weiszfeld algorithm for continuous single facility location-allocation problems. Top 16(2):388–406

    Article  Google Scholar 

  • Schöbel A, Scholz D (2009) The theoretical and empirical rate of convergence for geometric branch-and-bound methods. Working paper, Institut für Numerische und Angewandte Mathematik—Arbeitsgruppe Optimierung, Universität Göttingen, Germany

  • Weber A (1909) Über den Standort der Industrien. Tübingen. English translation by Friedrich CJ (1929) Theory of the location of industries. University of Chicago Press

  • Weiszfeld E (1937) Sur le point pour lequel la somme des distances de n points donnés est minimum. Tohoku Math J (First Ser) 43:355–386

    Google Scholar 

  • Weiszfeld E, Plastria F (2009) On the point for which the sum of the distances to n given points is minimum (translated and annotated by F. Plastria). Ann Oper Res 167(1):7–41

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Frank Plastria.

Additional information

The research of the second author was partially supported by a grant of the Algerian Ministry of Higher Education for research at VUB-Belgium, and by the VUB project GOA62. A preliminary version of this paper was presented at the EWGLA 17 meeting in Elche, Nov 2008.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Plastria, F., Elosmani, M. Continuous location of an assembly station. TOP 21, 323–340 (2013). https://doi.org/10.1007/s11750-011-0185-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11750-011-0185-9

Keywords

Mathematics Subject Classification (2000)

Navigation