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Network design arc set with variable upper bounds
Author(s) -
Atamtürk Alper,
Günlük Oktay
Publication year - 2007
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.20162
Subject(s) - mathematics , arc (geometry) , set (abstract data type) , variable (mathematics) , network planning and design , knapsack problem , integer (computer science) , upper and lower bounds , flow (mathematics) , relaxation (psychology) , combinatorics , discrete mathematics , mathematical optimization , computer science , geometry , mathematical analysis , psychology , computer network , social psychology , programming language
In this paper we study the network design arc set with variable upper bounds. This set appears as a common substructure of many network design problems and is a relaxation of several fundamental mixed‐integer sets studied earlier independently. In particular, the splittable flow arc set, the unsplittable flow arc set, the single node fixed‐charge flow set, and the binary knapsack set are facial restrictions of the network design arc set with variable upper bounds. Here we describe families of strong valid inequalities that cut off all fractional extreme points of the continuous relaxation of the network design arc set with variable upper bounds. Interestingly, some of these inequalities are also new even for the aforementioned restrictions studied earlier. © 2007 Wiley Periodicals, Inc. NETWORKS, Vol. 50(1), 17–28 2007