The Convex Hull of Two Core Capacitated Network Design Problems
Name
OR-217-90.pdf
Size
1.64 MB
Format
Adobe PDF
Checksum (MD5)
675eadd348b16be03b294acc594c26dc
Author(s)
Magnanti, Thomas L.
Mirchandani, Prakash
Vachani, Rita
Date Issued
June 1990
Publisher
Massachusetts Institute of Technology, Operations Research Center
Series/Report no.
Operations Research Center Working Paper;OR 217-90
Abstract
The network loading problem (NLP) is a specialized capacitated network design problem in which prescribed point-to-point demand between various pairs of nodes of a network must be met by installing (loading) a capacitated facility. We can load any number of units of the facility on each of the arcs at a specified arc dependent cost. The problem is to determine the number of facilities to be loaded on the arcs that will satisfy the given demand at minimum cost. This paper studies two core subproblems of the NLP. The first problem, motivated by a Lagrangian relaxation approach for solving the problem, considers a multiple commodity, single arc capacitated network design problem. The second problem is a three node network; this specialized network arises in larger networks if we aggregate nodes. In both cases, we develop families of facets and completely characterize the convex hull of feasible solutions to the integer programming formulation of the problems. These results in turn strengthen the formulation of the NLP.
Subjects
Convex hull, Facets, Network design, Capacitated facilities.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
Persistent DSpace Link
