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 ­ Springer-Verlag 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 branch-and-cut 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-

Source: Atamtürk, Alper - Department of Industrial Engineering and Operations Research, University of California at Berkeley

Collections: Engineering