Economies of Scale in Hub & Spoke Network Design Models: We Have It All Wrong

  • Alf Kimms


The hub & spoke network design problem is a strategic logistics planning problem with applications for airlines, telecommunication companies, computer networks, postal services, and trucking companies, for example. Basically, the problem in all these applications is that for a given set V = 1,... , n of nodes (airports, computers, post offices, depots, ...) goods must be transported between possibly every pair of nodes. Direct connections between every pair of nodes would result in n(n − 1) linkages which is impractically high and economically non-profitable. Consider, for instance, an airline that serves several airports worldwide. Offering nonstop flights between every pair of airports would require a huge amount of planes and crews and many empty seats on board could be observed for many connections. In such settings, it turns out to be reasonable to install one or more so-called hub locations where direct links are then available to hub nodes as indicated in figure 1 where nodes 3, 6, and 9 are assumed to be hubs. Transporting goods from, say, node 1 to node 11, can then be done via hubs 3 and 6.


Fixed Cost Network Design Problem Piecewise Linear Approximation Quantity Discount Trucking Company 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Bryan DL (1998) Extensions to the hub location problem: Formulations and numerical examples. Geographical Analysis 30:315–330CrossRefGoogle Scholar
  2. [2]
    Bryan DL, O’Kelly ME (1999) Hub-and-spoke networks in air transportation: An analytical review. Journal of Regional Science 39:275–295CrossRefGoogle Scholar
  3. [3]
    Campbell JF (1994a) A survey of network hub location. Studies in Locational Analysis 6:31–49Google Scholar
  4. [4]
    Campbell JF (1994b) Integer programming formulations of discrete hub location problems. European Journal of Operational Research 72:387–405CrossRefGoogle Scholar
  5. [5]
    Campbell JF, Ernst AT, Krishnamoorthy M (2002) Hub location problems. In: Drezner Z, Hamacher HW (eds.) Facility Location — Applications and Theory. Springer, Berlin, pp. 373–407Google Scholar
  6. [6]
    Campbell JF, Ernst AT, Krishnamoorthy M (2004a) Hub arc location problems: Part I — introduction and results. Management Science, to appearGoogle Scholar
  7. [7]
    Campbell JF, Ernst AT, Krishnamoorthy M (2004b) Hub arc location problems: Part II — formulations and optimal algorithms. Management Science, to appearGoogle Scholar
  8. [8]
    Cánovas L, García S, Marín A (2004) Localización de Concentradores. In: Pelegrín B (ed.) Avances en Localización de Servicios y sus Aplicaciones. Servicio de Publicaciones de la Universidad de Murcia, pp. 35–58Google Scholar
  9. [9]
    Cánovas L, Landete M, Marín A (2005) New formulations for the uncapacitated multiple allocation hub location problem. European Journal of Operational Research, to appearGoogle Scholar
  10. [10]
    Ebner G (1997) Controlling komplexer Logistiknetzwerke. GVB Schriftenreihe 34, NürnbergGoogle Scholar
  11. [11]
    Ernst AT, Hamacher H, Jiang H, Krishnamoorthy M, Woeginger G (2002) Uncapacitated single and multiple allocation p-hub center problems. Working Paper, CSIRO Mathematical and Information Sciences, ClaytonGoogle Scholar
  12. [12]
    Ernst AT, Krishnamoorthy M (1999) Solution algorithms for the capacitated single allocation hub location problem. Annals of Operations Research 86:141–159CrossRefGoogle Scholar
  13. [13]
    Garfinkel RS, Sundararaghavan PS, Noon C, Smith DR (1996) Optimal use of hub facilities: A two-hub model with fixed arc costs. Sociedad de Estadística e Investigación Operativa, Top 4:331–343Google Scholar
  14. [14]
    Gavish B (1992) Topological design of computer communication networks — the overall design problem. European Journal of Operational Research 58:149–172CrossRefGoogle Scholar
  15. [15]
    Kara BY, Tansel BÇ (2000) On the single-assignment p-hub center problem. European Journal of Operational Research 125:648–655CrossRefGoogle Scholar
  16. [16]
    Klincewicz JG (1998) Hub location in backbone/tributary network design: A review. Location Science 6:307–335CrossRefGoogle Scholar
  17. [17]
    Klincewicz JG (2002) Enumeration and search procedures for a hub location problem with economies of scale. Annals of Operations Research 110:107–122CrossRefGoogle Scholar
  18. [18]
    Mayer G (2001) Strategische Logistikplanung von Hub&Spoke-Systemen. Deutscher Universitäts-Verlag, WiesbadenGoogle Scholar
  19. [19]
    O’Kelly ME (1986) The location of interacting hub facilities. Transportation Science 20:92–106CrossRefGoogle Scholar
  20. [20]
    O’Kelly ME (1987) A quadratic integer program for the location of interacting hub facilities. European Journal of Operational Research 32:393–404CrossRefGoogle Scholar
  21. [21]
    O’Kelly ME, Bryan DL (1998) Hub location with flow economies of scale. Transportation Research Part B 32:605–616CrossRefGoogle Scholar
  22. [22]
    O’Kelly ME, Miller HJ (1994) The hub network design problem — a review and synthesis. Journal of Transport Geography 2:31–40CrossRefGoogle Scholar
  23. [23]
    Podnar H, Skorin-Kapov J, Skorin-Kapov D (2002) Network cost minimization using threshold based discounting. European Journal of Operational Research 137:371–386CrossRefGoogle Scholar
  24. [24]
    Skorin-Kapov D, Skorin-Kapov J, O’Kelly M (1996) Tight linear programming relaxations of uncapacitated p-hub median problems. European Journal of Operational Research 94:582–593CrossRefGoogle Scholar
  25. [25]
    Stadtler H (2004) A general quantity discount and supplier selection mixed integer programming model. Working Paper, University of HamburgGoogle Scholar
  26. [26]
    Wagner B (2003) An exact solution procedure for a cluster hub location problem. Working Paper, TU DarmstadtGoogle Scholar
  27. [27]
    Wagner B (2005) Design von Hub&Spoke-Netzwerken in der Logistik — modellbasierte Lösungsansatze. Ph.D. dissertation, TU Darmstadt, in preparationGoogle Scholar
  28. [28]
    Wlček H (1998) Gestaltung der Güterverkehrsnetze von Sammelgutspeditionen. GVB Schriftenreihe 37, NürnbergGoogle Scholar

Copyright information

© Deutscher Universitäts-Verlag/GWV Fachverlage GmbH, Wiesbaden 2006

Authors and Affiliations

  • Alf Kimms
    • 1
  1. 1.Lehrstuhl für Allgemeine Betriebswirtschaftslehre, insbesondere Produktion und LogistikTU Bergakademie FreibergFreiberg

Personalised recommendations