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MGTSC 352

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

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MGTSC 352

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  1. MGTSC 352 Lecture 18: 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. 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 Vancouver Toronto What’s wrong with this picture? Miami

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