Abstract
This paper deals with the facility location problems on a balancing allocation approach. Two location models are proposed, which are convex combinations of the traditional p-median and p-maxian problems together with minimizing the maximum demand level allocated to any facility. An edge deletion method with time complexity \(O(n^2)\) is represented for the balanced 2-median problem on a tree. For the balanced 2-maxian problem, it is shown the optimal solution is two end vertices of the longest path of the tree, which can be obtained in linear time.
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Fathali, J., Zaferanieh, M. The balanced 2-median and 2-maxian problems on a tree. J Comb Optim 45, 69 (2023). https://doi.org/10.1007/s10878-023-00997-9
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DOI: https://doi.org/10.1007/s10878-023-00997-9