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AN ALGORITHM FOR THE SPATIAL PRICE EQUILIBRIUM PROBLEM ON A GENERAL NETWORK IN THE SPACE OF THE PATH FLOWS *
Author(s) -
DrissiKaïtouni Omar,
Florian Michael
Publication year - 1991
Publication title -
journal of regional science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.171
H-Index - 79
eISSN - 1467-9787
pISSN - 0022-4146
DOI - 10.1111/j.1467-9787.1991.tb00141.x
Subject(s) - path (computing) , mathematical optimization , computer science , equivalence (formal languages) , a priori and a posteriori , space (punctuation) , flow network , simple (philosophy) , algorithm , mathematics , philosophy , epistemology , discrete mathematics , programming language , operating system
. The spatial price equilibrium on a general network may be formulated as a nonlinear‐cost mathematical programming problem with simple constraints, when the decision variables are the path flows. The solution of this problem is difficult due to the very large number of variables (paths) and the impracticality of generating all the paths from all the origins to all the destinations. In this paper, we develop a Gauss‐Seidel‐Newton Projection algorithm and combine it with a restriction strategy. That makes it unnecessary to generate a priori all the paths. This algorithm may be further improved by exploiting the equivalence between the spatial price equilibrium on a general network and the network equilibrium. Computational results that we present in this paper demonstrate the efficiency of the proposed solution algorithms.