Abstract
A spatial price equilibrium problem is modeled which allows piecewise linear convex flow costs, and a capacity limit on the trade flow between each supply/demand pair of regions. Alternatively, the model determines the locations of intermediate distribution centers in a market economy composed of separate regions, each with approximately linear supply and demand functions. Equilibrium prices, regional supply and demand quantities, and commodity flows are determined endogenously. The model has a quadratic programming formulation which is then reduced by exploiting the structure. The reduced model is particularly well suited to solution using successive over-relaxation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Y.C. Cheng, Iterative methods for solving linear complementarity and linear programming problems, Ph.D. Dissertation, University of Wisconsin-Madison (1981).
A.A. Cournot, (1838),Mathematical Principles of the Theory of Wealth. Translated by N.T. Bacon (MacMillan, New York, 1897).
C.W. Cryer, The solution of a quadratic programming problem using systematic overrelaxation, SIAM J. of Control 9(1971)385.
J. Eckhardt, Quadratic programming by successive overrelaxation, Kernforschungsanlage Jülich, Technical Report No. Jül-1064-MA, 1974.
S. Enke, Equilibrium among spatially separate markets: Solution by electric analogue, Econometrica 10(1951)40.
D. Erlenkotter, Facility location with price-sensitive demands: Private, public and quasipublic, Management Science 24(1977)378.
M. Florian and M. Los, A new look at static spatial price equilibrium models, Regional Science and Urban Economics 12(1982)579.
R.L. Friesz, P.T. Harker and R.L. Tobin, Alternative algorithms for the general network spatial equilibrium problem, J. of Regional Science 24(1984)475.
A.M. Geoffrion and G.W. Graves, Multicommodity distribution system design by Bender's decomposition, Management Science 20(1974)822.
F. Guder and J.G. Morris, A two-line algorithm for computing equilibrium single commodity trade flows, Wisconsin working paper 4-84-8 (1984).
C. Hildreth, A quadratic programming procedure, Naval Research Logistics Quaterly 4(1957)79.
G.G. Judge and T. Takayama, eds.,Studies in Economic Planning Over Space and Time (North-Holland, Amsterdam, 1973).
J. Krarup and P.M. Pruzan, The simple plant location problem: Survey and synthesis, Eur. J. Oper. Res. 12(1983)36.
O.L. Mangasarian,Nonlinear Programming (McGraw-Hill, New York, 1969).
O.L. Mangasarian, Solution of symmetric linear complementarity problems by iterative methods, J. of Optimization Theory and Applications 22(1977)465.
J.M. Ortega,Numerical Analysis — A Second Course (Academic Press, New York, 1972).
J. Polito, Distribution systems planning in a price responsive environment, Ph.D. Dissertation, Purdue University (1977).
P.A. Samuelson, Spatial price equilibrium and linear programming, American Economic Review 42(1952)283.
T. Takayama and G.G. Judge, Spatial equilibrium and quadratic programming, J. of Farm Economics 44(1964)67.
T. Takayama and G.G. Judge, Equilibrium among spatially separated markets: A reformulation, Econometrica 32(1964)510.
T. Takayama and G.G. Judge,Spatial and Temporal Price and Allocation Models (North-Holland, Amsterdam, 1971).
M. Von Oppen and J.T. Scott, A spatial equilibrium model for plant location and interregional trade, American J. of Agricultural Economics 58(1976)437.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Guder, F., Morris, J.G. Spatial price equilibrium, distribution center location and successive over-relaxation. Ann Oper Res 6, 111–128 (1986). https://doi.org/10.1007/BF02026819
Issue Date:
DOI: https://doi.org/10.1007/BF02026819