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An aggregation approach to solving the network p ‐median problem with link demands
Author(s) -
Zhao Peiwu,
Batta Rajan
Publication year - 2000
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/1097-0037(200012)36:4<233::aid-net4>3.0.co;2-i
Subject(s) - link (geometry) , heuristics , mathematical optimization , computer science , construct (python library) , aggregate (composite) , mathematics , computer network , materials science , composite material , programming language
This paper considers the p ‐median problem on a general network with link demands. We construct the network in such a way that only transportation intersections are taken to be nodes and, therefore, both continuous and discrete link demands are allowed in our model. For such a model, we show that a nodal solution can be used to approximate the true optimal solution and an error bound which involves only the demands on a single link is given for the error caused by such an approximation. Based on nodal solutions, we demonstrate that a model with continuous link demands can be transformed into an equivalent discrete link demand model. Further, we propose a method to aggregate demands on each link in solving the p ‐median problem on a general network without introducing any aggregation errors to the problem solution. The implementation of the proposed approach with some heuristics is discussed. © 2000 John Wiley & Sons, Inc.