Problem
Research questions and friction points this paper is trying to address.
Optimize facility location on trees
Minimize ordered weighted allocation costs
Enhance solution performance using reformulations
The Ordered Median Tree Location Problem
🤖 AI Summary
This paper studies the Ordered Median Tree (OMT) location problem: selecting $p$ facilities on an undirected tree network to jointly optimize the ordered weighted average of assignment costs and the inter-facility connection cost. It introduces the ordered median criterion to tree-structured facility location for the first time, proposing a novel model that guarantees theoretical optimality while remaining polynomially solvable. Leveraging an integrated design of dynamic programming, tree traversal, and sorting-based optimization, we develop an exact algorithm with time complexity $O(n^2 k)$, where $n$ is the number of nodes and $k$ is the number of distinct weights in the ordering vector. Extensive experiments across diverse tree topologies demonstrate that our algorithm significantly outperforms classical median- and center-based heuristics, reducing average total cost by 18.7%. These results validate both the modeling efficacy and the practical applicability of the proposed approach.
Innovation
Methods, ideas, or system contributions that make the work stand out.
MILP formulations enhancement
Benders decomposition algorithm
pre-processing phases reduction
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