Encyclopedia of Operations Research and Management Science

2001 Edition
| Editors: Saul I. Gass, Carl M. Harris

Network

  • Saul I. Gass
  • Carl M. Harris
Reference work entry
DOI: https://doi.org/10.1007/1-4020-0611-X_662

A network is a pair of sets (N, A), where N is a set of nodes (points, vertices) and A is a set of arcs (edges, lines, links). If i and j are nodes, then the arc joining them is denoted by the ordered pair (i, j). An arc may have a cost cij that denotes the cost per unit flow across that arc, and an upper bound flow capacity denoted by uij. For some applications, a node may be a supply node in which goods enter the network, a demand node in which goods leave the network, or a transshipment node through which goods are shipped without a gain or a loss. In most network applications, it is assumed that the flow of goods that enter a node is equal to the flow that leaves the node. This is the conservation of flow assumption.How-ever, in some applications, the amount of goods that enter a node can be more than the amount that leaves the node (e.g., due to the expansion of a liquid) or can be less than the amount that leaves a node (e.g., due to a leak or pilferage). These latter...

This is a preview of subscription content, log in to check access.

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Saul I. Gass
    • 1
  • Carl M. Harris
    • 2
  1. 1.Robert H. Smith School of BusinessUniversity of MarylandCollege PartUSA
  2. 2.School of Information Technology & EngineeringGeorge Mason UniversityFairfaxUSA