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Lower Bounds for the Hub Location Problem
Morton O'Kelly, Darko Skorin-Kapov and Jadranka Skorin-Kapov
Vol. 41, No. 4 (Apr., 1995), pp. 713-721
Published by: INFORMS
Stable URL: http://www.jstor.org/stable/2632890
Page Count: 9
You can always find the topics here!Topics: Objective functions, Heuristics, Fixed costs, Underestimates, Optimal solutions, Tabu search, Datasets, Triangle inequalities, Integers, Cost functions
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We present a new lower bound for the Hub Location Problem (HLP) where distances satisfy the triangle inequality. Our lower bound is based on a linearization of the problem and its modification obtained by incorporating the knowledge of a known heuristic solution. A lower bound was computed for some standard data sets from the literature ranging between 10 and 25 nodes, with 2, 3, and 4 hubs, and for different values for the parameter a, representing the discount for the flow between hubs. The novel approach of using a known heuristic solution to derive a lower bound in all cases reduced the difference between the upper and lower bound. This difference measures the quality of the best known heuristic solution in percentages above the best lower bound. As a result of this research, for smaller problems (all instances with 10 and 15 nodes) the average difference is reduced to 3.3%. For larger sets (20 and 25 nodes) the average difference is reduced to 5.9%.
Management Science © 1995 INFORMS