Rectilinear minimax hub location problems |
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| Authors: | M E O’Kelly |
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| Institution: | (1) Department of Geography, The Ohio State University, Columbus, USA |
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| Abstract: | The minimax hub location problem sites a facility to minimize the maximum weighted interaction cost between pairs of fixed nodes. In this paper, distances are represented by a rectilinear norm and may be suited to factory layout or street
network problems. The problem is already well known (in 2-D) as the round trip location problem and is extended to 3-D in
this paper. One rationale for the solution method is based on an extension of the geometric arguments used to solve the minimax
single facility location problem. Suppose a budget is provided for interactions, and that each interaction must be accomplished
for no more than this cost. The algorithm uses a bi-section search for the feasible budget until it finds the expenditure
needed to provide for these flows. The extension in the present paper is that the nodes are permitted to be on different layers
(levels). This 3-D version of the problem appears to be a new variant of the hub model. The models and solution techniques
developed in the paper are illustrated using a small 55 node problem. Because of a relatively efficient implementation of
the bi-section search, the algorithm in 2-D and 3-D is also applied successfully to a 550 node problem.
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| Keywords: | Transportation Logistics Hub location Minimax 3D network models |
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