Annals of Operations Research

, Volume 18, Issue 1, pp 267–276 | Cite as

Existence theory for spatially competitive network facility location models

  • Terry L. Friesz
  • Roger L. Tobin
  • Tan Miller
Section IV Discrete And Network Location Problems


Models for locating a firm's production facilities while simultaneously determining production levels at these facilities and shipping patterns so as to maximize the firm's profits are presented. In these models, existing firms, are assumed to act in accordance with an appropriate model of spatial equilibrium. A proof of existence of a solution to the combined location-equilibrium problem is provided.


Shipping Production Level Location Model Facility Location Production Facility 
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]
    S. Dafermos and A. Nagurney, Sensitivity analysis for the general spatial economic equilibrium problem, Operations Research 32(5) (1984) 1069.Google Scholar
  2. [2]
    D. Erlenkotter, Facility location with price-sensitive demands: private, public and quasi-public, Management Science 24(4) (1977) 378.Google Scholar
  3. [3]
    T.L. Friesz, P.T. Harker and R.L. Tobin, Alternative algorithms for the general network spatial price equilibrium problem, Journal of Regional Science 24(4) (1984) 475.Google Scholar
  4. [4]
    T.L. Friesz, T. Miller and R.L. Tobin, Algorithms for spatially competitive network facility location, Environment and Planning B 15 (1988) forthcoming.Google Scholar
  5. [5]
    T.L. Friesz, R.L. Tobin, T.E. Smith and P.T. Harker, A nonlinear complementarity formulation and solution procedure for the general derived demand network equilibrium problem, Journal of Regional Science 23(3) (1983) 337.Google Scholar
  6. [6]
    P. Hanjoul and J.P. Thisse, The location of a firm on a network, in:Applied Decision Analysis and Economic Behaviour, ed. A.J. Hughes Hallett (Martinus Nishoff Publishers, 1984) p. 289.Google Scholar
  7. [7]
    P. Hansen and J.-F. Thisse, Multiplant location for profit maximization, Environment and Planning A 9(1) (1977) 63.Google Scholar
  8. [8]
    P.T. Harker, A variational inequality approach for the determination of oligopolistic market equilibrium, Mathematical Programming 30 (1984) 105.MathSciNetGoogle Scholar
  9. [9]
    P.T. Harker, Alternative models of spatial competition, Operations Research 34(3) (1986) 410.Google Scholar
  10. [10]
    P.T. Harker and J.S. Pang, Existence of optimal solutions to mathematical programs with equilibrium constraints, Working Paper 87-05-03, Dept. of Decision Sciences, The Wharton School, University of Pennsylvania, 1987.Google Scholar
  11. [11]
    D. Kinderlehrer and G. Stampacchia,An Introduction to Variational Inequalities and their Applications (Academic Press, 1980).Google Scholar
  12. [12]
    J.M. Ortega and W.C. Rheinboldt,Iterative Solution of Nonlinear Equations in Several Variables (Academic Press, 1970).Google Scholar
  13. [13]
    C. Revelle, The maximum capture or sphere of influence location problem: Hotelling revisited on a network, Journal of Regional Science 26(2) (1986) 343.Google Scholar
  14. [14]
    P.A. Samuelson, Spatial price equilibrium and linear programming, American Economic Review 42 (1952) 283.Google Scholar
  15. [15]
    H.D. Sherali, A.L. Soyster and F.H. Murphy, Stackelberg-Nash-Cournot equilibria: characterizations and computations, Operations Research 31(2) (1983) 253.Google Scholar
  16. [16]
    T. Takayama and G.C. Judge,Spatial and Temporal Price and Allocation Models (North-Holland, 1971).Google Scholar
  17. [17]
    R.L. Tobin and T.L. Friesz, Spatial competition facility location models: definition, formulation and solution approach, Annals of Operations Research: Location Theory and Applications 6(1) (1986) 49.Google Scholar
  18. [18]
    J.L. Wagner and L.M. Falkson, The optimal nodal location of public facilities with price-sensitive demand, Geographical Analysis 7 (1975) 69.Google Scholar

Copyright information

© J.C. Baltzer A.G. Scientific Publishing Company 1989

Authors and Affiliations

  • Terry L. Friesz
    • 1
  • Roger L. Tobin
    • 2
  • Tan Miller
    • 3
  1. 1.University of PennsylvaniaPhiladelphiaU.S.A.
  2. 2.GTE LaboratoriesWalthamU.S.A.
  3. 3.American Olean Tile Co.LansdaleU.S.A.

Personalised recommendations