, Volume 26, Issue 2, pp 257–282 | Cite as

The nestedness property of location problems on the line

  • Mark Rozanov
  • Arie Tamir
Original Paper


We prove the existence of a nestedness property for a family of common convex parametric tactical serving facility location problems defined on the line. The parameter t is the length of the serving facility (closed interval). The nestedness property means that, given any two facility lengths \(t_1, t_2, 0 \le t_1<t_2\), there is an optimal solution with length \(t_1\) which lies within some optimal solution with length \(t_2\). The main idea of the proof is the representation of a serving facility as a point in \({\mathbb {R}}^2\) and the investigation of its geometrical properties. An intuitive graphical approach to the proof is given.


Location problem Convex ordered median Nestedness Extensive facility 

Mathematics Subject Classification

90C25 90C27 90C31 90C35 


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Copyright information

© Sociedad de Estadística e Investigación Operativa 2018

Authors and Affiliations

  1. 1.Sackler Faculty of Exact SciencesTel Aviv UniversityTel AvivIsrael

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