TY - JOUR

T1 - The nestedness property of the convex ordered median location problem on a tree

AU - Rozanov, Mark

AU - Tamir, Arie

N1 - Publisher Copyright:
© 2020 Elsevier B.V.

PY - 2020/5

Y1 - 2020/5

N2 - This paper deals with the problem of locating an extensive facility of restricted length within a given tree network. Topologically, the selected extensive facility is a subtree. The nestedness property means that a solution of a problem with a shorter length constraint is part of a solution of the same problem with a longer length constraint. We prove the existence of a nestedness property for a common family of convex ordered median (COM) objective functions. We start with the proof of the nestedness property for a rooted tree problem, where the extended facility is a subtree of some tree network rooted at a specified node, and proceed to prove the nestedness property for the general location model on a tree.

AB - This paper deals with the problem of locating an extensive facility of restricted length within a given tree network. Topologically, the selected extensive facility is a subtree. The nestedness property means that a solution of a problem with a shorter length constraint is part of a solution of the same problem with a longer length constraint. We prove the existence of a nestedness property for a common family of convex ordered median (COM) objective functions. We start with the proof of the nestedness property for a rooted tree problem, where the extended facility is a subtree of some tree network rooted at a specified node, and proceed to prove the nestedness property for the general location model on a tree.

KW - Convex ordered median

KW - Extensive facility

KW - Graph optimization

KW - Location theory

KW - Nestedness

UR - http://www.scopus.com/inward/record.url?scp=85083899782&partnerID=8YFLogxK

U2 - 10.1016/j.disopt.2020.100581

DO - 10.1016/j.disopt.2020.100581

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AN - SCOPUS:85083899782

SN - 1572-5286

VL - 36

JO - Discrete Optimization

JF - Discrete Optimization

M1 - 100581

ER -