Joe Ashpari John Crain

2 U.S. Potato Transport

3 Background Johnny Joe’s Inc  An emerging potato chip conglomerate  Potato chip plants in several cities throughout the U.S  Various suppliers of potatoes in U.S. and Canada  Largest Overhead: Cost of Shipping from supplier to plants  Doritos is rumored to be considering aggressive options to sabotage our continued growth

4 Overview  Potato flow as a Min-Cost Flow Model  Demand drives the flow  Goal: Clear the demand at minimum cost, satisfying all upper/lower bound constraints  Key modifications to the basic model Split the Supply nodes to allow the attacker to interdict the supply nodes Add cost for Unsatisfied Demand in the objective function we are minimizing Interdiction represented by total flow out of a supply node being attacked  Measure of Effectiveness: Total Shipping Cost

Supply/Demand Facilities Potato Suppliers  Boise, ID  Spokane, WA  Bakersfield, CA  Colorado Springs, CO  Baker City, OR  Bangor, ME  Chippewa Falls, WI  Minot, ND  Billings, MT  Calgary, Canada Potato Chip Plants  Atlanta, GA  Boston, MA  Chicago, IL  Dallas, TX  Richmond, VA  Detroit, MI  Los Angeles, CA  New York, NY  Philadelphia, PA  St. Louis, MO 5

Nodes 6 Supply Demand

Arcs 7 Supply Demand

Abstract Network 8 Supply Demand

Graphical Model 9 S1b Supply Demand S2b S10b D1 D2 D10 (c ij, 0, ∞) S10a S2a S1a -560,000+25, , , , ,000 (0, 0, ∞)

Mathematical Model 10 i: nodes (alias j, a) c ij = shipping cost in $ per cwt (centum weight) to ship from node i to node j d ij = delay cost in $ per cwt for a delay between i and j s j = shortage cost at node j per cwt of potatoes UD j = unsatisfied demand at node j in cwt potatoes b(j) = supply/demand at node j u ij = capacity from node i to node j OBJ: min s.t.

Estimating Costs 1.How much does it cost to truck potatoes? 2.What does the cost depend on? What are the units of the cost?

Max weight: 11,000 lbs Lets use ~ 10,000 lbs max weight for a truck C ij = =

Question Arises 1.What quantity of potatoes represent the demand for our problem?

Lets use roughly 1% of Total Potato Demand for each Demand Node

16 Scenarios  Baseline (no attacks)  Attack Case 1: Aggressive bidding to drive up the costs  Attack Case 2: Complete buyout of selected suppliers

17 Baseline (no attacks)  All demand satisfied  Total Cost = $ M Supply Demand

18 Baseline (no attacks)  Optimal Flow FromToFlow, Y ij (cwt) BakersfieldLos Angeles52,000 Colorado SpringsDallas23,600 BangorBoston32,410 BangorNew York53,200 BangorPhiladelphia19,780 BangorRichmond14,500 Chippewa FallsChicago36,000 Chippewa FallsDetroit10,050 Chippewa FallsSt. Louis15,180 Chippewa FallsAtlanta25,000

19 Attack Case 1  Delay parameter set to $40 per cwt (roughly 50% of the maximum shipping cost per cwt)  In model, Number of Interdictions ranged from 1 to 9

Attack Case 1: 1 Interdiction 20 Supply Demand

Attack Case 1: 2 Interdictions 21 Supply Demand

Attack Case 1: 3 Interdictions 22 Supply Demand

Attack Case 1: 4 Interdictions 23 Supply Demand

Attack Case 1: 5 Interdictions 24 Supply Demand

Attack Case 1: 6 Interdictions 25 Supply Demand

Attack Case 1: 7 Interdictions 26 Supply Demand

Attack Case 1: 8 Interdictions 27 Supply Demand

Attack Case 1: 9 Interdictions 28 Supply Demand

29 Attack Case 1 Results  Interdiction locations are nested  Total cost increases by a similar amount for each additional interdiction (no large spikes)  Not very interesting results

30 Attack Case 1: Operator Resilience Curve

31 Attack Case 2  Delay parameter set to nC  In model, number of interdictions ranged from 1 to 9

Attack Case 2: 1 Interdiction 32 Supply Demand

Attack Case 2: 2 Interdictions 33 Supply Demand

Attack Case 2: 3 Interdictions 34 Supply Demand

Attack Case 2: 4 Interdictions 35 Supply Demand

Attack Case 2: 5 Interdictions 36 Supply Demand

Attack Case 2: 6 Interdictions 37 Supply Demand

Attack Case 2: 7 Interdictions 38 Supply Demand

Attack Case 2: 8 Interdictions 39 Supply Demand

Attack Case 2: 9 Interdictions 40 Supply Demand

41 Attack Case 2 Results  Similar increases in total cost up to 4 interdictions  At 8 interdictions and beyond, we are unable to satisfy our demand  Going from 7 to 8 interdictions, the interdiction locations are not nested  Spike in total cost from 7 to 8 interdictions and 8 to 9 interdictions

42 Attack Case 2: Operator Resilience Curve

43 Summary & Conclusion  Foster the relationships with 4 key suppliers: Bangor, Chippewa Falls, Bakersfield, and Billings  Bangor and Chippewa Falls – close geographic proximity to largest demand facilities; offer great value in terms of shipping costs  Bakersfield and Billings –Sufficient availability of supply; able to meet demands in a constrained (interdicted) scenario  Building strong relationships with these 4 suppliers makes us resilient to either of the attack cases

Future Work To further minimize costs, we can look at supply lines for the following produce: 1. Piggyback transportation: Same Refrigeration Requirements: Potatoes (late crop) Cucumbers Eggplants Ginger (not with eggplants) Grapefruit, Florida and Texas Pumpkin and squashes, winter Watermelons 2. Railcar Usage in Addition to Trucking Cheaper costs, more possible routes. 3. Implement Capacity constraints into model

References  mgmt.wsu.edu/AgbusResearch/docs/eb1925.pdf  ed%20Truck&rpfile=content/rental_details_reefer.html ed%20Truck&rpfile=content/rental_details_reefer.html  TELPRDC TELPRDC  TELDEV TELDEV 

46 Questions?