 
Summary: Digital Object Identifier (DOI) 10.1007/s101070100269
Math. Program., Ser. A 92: 315333 (2002)
Alper Atamtürk · Deepak Rajan
On splittable and unsplittable flow capacitated network
design arcset polyhedra
Received: August 8, 2000 / Accepted: October 25, 2001
Published online December 6, 2001 SpringerVerlag 2001
Abstract. We study the polyhedra of splittable and unsplittable single arcset relaxations of multicommodity
flow capacitated network design problems. We investigate the optimization problems over these sets and the
separation and lifting problems of valid inequalities for them. In particular, we give a lineartime separation
algorithm for the residual capacity inequalities [19] and show that the separation problem of cstrong in
equalities [7] is N Phard, but can be solved over the subspace of fractional variables only. We introduce two
classes of inequalities for the unsplittable flow problems. We present a summary of computational experiments
with a branchandcut algorithm for multicommodity flow capacitated network design problems to test the
effectiveness of the results presented here empirically.
1. Introduction
Given a network, a set of origindestinationvertex pairs (commodities)and demand data
for the commodities, the multicommodity capacitated network design problem is to in
stall integer multiples of some capacity unit on the arcs of the network and route the flow
of commodities so that the sum of capacity installation and flow routing costs is mini
