1. Lecture 18: MGTSC 352 Distribution Planning
Rent-A-Dent example: a transportation problem
Oil example: a minimum cost flow problem
Henderson Food Company: shortest path problem

2. Distribution Planning
Rent-a-Dent example: Transportation problem
Oil example: Minimum cost network flow problem
Henderson Food Company example: Shortest path problem

3. Transportation Problem
“arcs” / “links”
 Demand nodes
Supply nodes 

4. Minimum Cost Flow Problem (pg. 118)
Task:
Send flow from supply (-) to demand (+) nodes
Goal:
Minimize transport cost
Changing cells:
flow on each link
Constraints:
flows  arc capacities
flow in + supply  flow out + demand
flows  0
To Excel

5. Min Cost Flow: Testing Your Intuition
What if total supply < total demand, and we use flow in + supply  flow out + demand?
What if total supply > total demand, and we use flow in + supply = flow out + demand
(= instead of )?

6. Rent-a-Dent vs Oil Rent-a-Dent (transportation problem)
Every node is a supply or demand node
“Arcs” correspond to routes
Finds From-To shipments
Oil (minimum cost flow problem)
Full network
Arcs correspond to route segments
Finds flows on each segment

7. Relations
Transportation problem is a special case of the min cost flow problem
Shortest path problem is (also) a special case of min cost flow problem.
What?

8. Find the “cheapest” path from Node 1 to Node 5
Can you manipulate the problem data so as to “trick” Excel? -1 +1
to Excel

9. Quickest route from Lethbridge to Fort McMurray that...
Pg. 125
Quickest route from Lethbridge to Fort McMurray that...
..does not go through Calgary?
..goes through Rocky Mountain House?
..includes the Drumheller-Red Deer arc?
Suppose you are interested in the shortest route from Lethbridge to Fort McMurray, not the fastest route. Now what?

10. Shortest Path from Vancouver to Miami that goes through Toronto
What’s wrong with this picture?
Miami