Multicommodity Supply and Transportation Networks with Resource Constraints

The Generalized Multicommodity Flow Problem

by Richard D. Wollmer

Download

Full Document

FormatFile SizeNotes
PDF file 0.7 MB

Use Adobe Acrobat Reader version 10 or higher for the best experience.

Purchase

Purchase Print Copy

 FormatList Price Price
Add to Cart Paperback32 pages $20.00 $16.00 20% Web Discount

A method for treating multicommodity network flows in which limited resources are shared among several arcs instead of only one. Applications include solving practical problems of vehicle scheduling, military interdiction, and two-way traffic flow. This study extends the previous solution methods for networks with individual arc capacity constraints to cover joint constraints. This formulation can handle one or more joint capacity constraints in a multicommodity network; with some adjustment in the objective function, it can maximize a linear combination of commodity flows and find a feasible routing to meet flow requirements. An arc subset-chain incidence matrix is formulated and solved by a simplex multiplier method. Alternatively, a node-arc incidence matrix can be solved by the Dantzig-Wolfe decomposition algorithm. The procedures turn out to be identical. This approach can solve several times as many problems as the individual arc constraint method, yet surprisingly little change is required in some of the solution algorithms.

This report is part of the RAND Corporation Research memorandum series. The Research Memorandum was a product of the RAND Corporation from 1948 to 1973 that represented working papers meant to report current results of RAND research to appropriate audiences.

Permission is given to duplicate this electronic document for personal use only, as long as it is unaltered and complete. Copies may not be duplicated for commercial purposes. Unauthorized posting of RAND PDFs to a non-RAND Web site is prohibited. RAND PDFs are protected under copyright law. For information on reprint and linking permissions, please visit the RAND Permissions page.

The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.