Chapter 7
Network Flow Models
Shortest Route Problem
• Given distances between nodes, find
the shortest route between any pair of
nodes.
Example: p.282 (291)
Solution Methods
• Dijkstra algorithm:
– Introduced in book.
– Not required for this course
• Using QM:
– Required for this course
– Data input format -
Discussion
• What if the ‘cost’, instead of ‘distance’,
between two nodes are given, and we
want to find the ‘lowest-cost route’ from a
starting node to a destination node?
• What if the cost from a to b is different
from the cost from b to a? (QM does not
handle this situation.)
Minimal Spanning Tree
Problem
• Given costs (distances) between
nodes, find a network (actually a
“tree”) that covers all the nodes with
minimum total cost.
• Applications:
Example: p.290 (299)
Solution Method: Using QM.
Shortest Route vs. Minimal
Spanning
• The minimal spanning tree problem is to
identify a set of connected arcs that cover
all nodes.
• The shortest route problem is to identify a
route from a particular node to another,
which typically does not pass through
every node.
Maximal Flow Problem
• Given flow-capacities between nodes,
find the maximum amount of flows
that can go from the origin node to
the destination node through the
network.
• Applications:
Example: p.294 (303)
Solution Method: Using QM.
Network Flow Problem Solving
• Given a problem, we need to tell what
‘problem’ it is (shortest route, minimal
spanning tree, or maximal flow); then use
the corresponding module in QM to solve
it.