The m-centre problem is a fundamental model for equitable facility location. Its minimax nature distinguishes it from median models, prioritising worst-case service. Despite its NP-hardness, effective heuristics and exact algorithms for small instances enable practical use in emergency services, telecommunications, and logistics. Future research should focus on robust and dynamic m-centre models to handle real-time uncertainties.
Minimising maximum response time saves lives. The m-centre model locates ambulance depots such that the farthest neighbourhood is within a critical threshold (e.g., 8 minutes). The city of Barcelona used an m-centre model to reduce worst-case response time by 22%. m centres
Distribution centres are placed to minimise the maximum delivery time to any retail outlet, protecting against disruptions in the worst-case scenario. The m-centre problem is a fundamental model for
As cities grow smarter and networks densify, the m-centre will remain an indispensable tool for designers who ask not merely for efficiency, but for fairness in the farthest corner of the service region. Future research should focus on robust and dynamic
m-centre, minimax facility location, covering problems, NP-hard, computational geometry, location analysis.
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