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\(\epsilon\)-approximations for multidimensional weighted location problems. (English) Zbl 0575.90021

This paper considers the multidimensional weighted minimax location problem, namely, finding a facility location that minimizes the maximal weighted distance to n points. General distance norms are used. An \(\epsilon\)-approximate solution is obtained by applying a variant of the Russian method for the solution of Linear Programming. The algorithm has a time complexity of O(n log \(\epsilon)\) for fixed dimensionality k. Computational results are presented.

MSC:

90B05 Inventory, storage, reservoirs
90C90 Applications of mathematical programming
90C05 Linear programming
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