Lecture 14 - Network

# Lecture 14 - Network - 540:311DETERMINISTICMODELSIN...

This preview shows pages 1–11. Sign up to view the full content.

540:311 DETERMINISTIC MODELS IN OPERATIONS RESEARCH Lecture 14: Chapter 8.1‐8.3 Class Mee±ng: Mon April 18 th 10:20‐11:40am Prof. W. Art Chaovalitwongse

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
DescripCon Many important op@miza@on problems can be analyzed by means of graphical or network representa@on. The following network models will be discussed: 8.2 Shortest path problems 8.3 Maximum ﬂow problems 8.5 Minimum cost network ﬂow problems 8.6 Minimum spanning tree problems
8.1 Basic Defni@ons A graph or network is defned by two sets oF symbols: • Nodes: A set oF points or ver@ces ( V ) are called nodes oF a graph or network. • Arcs: An arc consists oF an ordered pair oF ver@ces and represents a possible direc@on oF mo@on that may occur between ver@ces. 1 2 Nodes 1 2 Arc

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Nota@on and Terminology Network terminology. Node set N = {1, 2, 3, 4} = V Vertices Network G = (N, A) = (V,E) Arc Set A = {(1,2), (1,3), (3,2), (3,4), (2,4)} E Edges 2 3 4 1 a b c d e An Undirected Graph or Undirected Network 2 3 4 1 a b c d e A Directed Graph or Directed Network In an undirected graph, (i,j) = (j,i)
Chain: A sequence of arcs such that every arc has exactly one vertex in common with the previous arc is called a chain. 1 2 Common vertex between two arcs Path: A path is a chain in which the terminal node of each arc is iden@cal to the ini@al node of next arc. For example in the ±gure below (1,2)‐(2,3)‐(4,3) is a chain but not a path; (1,2)‐(2,3)‐(3,4) is a chain and a path, which represents a way to travel from node 1 to node 4. 2 3 1 4

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Some Good Applica@ons Transporta@on Transporta@on of goods over transporta@on networks Scheduling of ﬂeets of airplanes: @me/space networks Manufacturing Scheduling of goods for manufacturing Flow of manufactured items within inventory systems Communica@ons Design and expansion of communica@on systems Flow of informa@on across networks Personnel Assignment Assignment of crews to airline schedules Assignment of drivers to vehicles
Communica@on Networks

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Example: Communica@on Network Modeling Given the topology and traﬃc matrix in an IP network, which link weights should be used such that the cost is minimized? Input: graph G(R,L) R is the set of routers L is the set of unidirec@onal links C l is the capacity of link l Input: traﬃc matrix M i,j is traﬃc load from router i to j Output: se‘ng of the link weights w l is weight on unidirec@onal link l P i,j,l is frac@on of traﬃc from i to j traversing link l
Supply Chain Networks

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
8.2 Shortest Path Problems Assume that each arc in the network has a length associated with it. Suppose we start with a par@cular node. The problem of Fnding the shortest path from node 1 to any other node in the network is called a shortest path problem. 2 3 4 5 6 2 4 2 1 3 4 2 3 2 1 Consider a network G = (N, A) in which there is an origin node s and a destination node t.
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 09/20/2011 for the course ENG 300 taught by Professor Albin during the Fall '11 term at Rutgers.

### Page1 / 45

Lecture 14 - Network - 540:311DETERMINISTICMODELSIN...

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online