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Joe Ashpari John Crain

Johnny Joe's Inc. is emerging as a significant player in the potato chip industry with manufacturing plants across major U.S. cities and a network of suppliers in the U.S. and Canada. However, the rising costs of shipping threaten our growth, especially with rumors of Doritos potentially sabotaging our supply. This analysis employs a Min-Cost Flow Model to manage potato supply and demand, focusing on minimizing shipping costs while accounting for potential disruptions. Strategies include strengthening supplier relationships and exploring alternatives like rail transportation.

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Joe Ashpari John Crain

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  1. 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

  5. Supply/Demand Facilities Potato Suppliers 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 • Boise, ID • Spokane, WA • Bakersfield, CA • Colorado Springs, CO • Baker City, OR • Bangor, ME • Chippewa Falls, WI • Minot, ND • Billings, MT • Calgary, Canada

  6. Nodes Supply Demand

  7. Arcs Supply Demand

  8. Abstract Network Supply Demand

  9. Graphical Model Supply Demand (0, 0, ∞) (cij, 0, ∞) S1a S1b D1 -560,000 +25,000 S2b S2a D2 -245,000 +32,410 S10a S10b D10 +14,500 -400,000

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

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

  12. Max weight: 11,000 lbs Lets use ~ 10,000 lbs max weight for a truck Cij = =

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

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

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

  16. Baseline (no attacks) • All demand satisfied • Total Cost = $ 3.275 M Supply Demand

  17. Baseline (no attacks) • Optimal Flow

  18. 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

  19. Attack Case 1: 1 Interdiction Supply Demand

  20. Attack Case 1: 2 Interdictions Supply Demand

  21. Attack Case 1: 3 Interdictions Supply Demand

  22. Attack Case 1: 4 Interdictions Supply Demand

  23. Attack Case 1: 5 Interdictions Supply Demand

  24. Attack Case 1: 6 Interdictions Supply Demand

  25. Attack Case 1: 7 Interdictions Supply Demand

  26. Attack Case 1: 8 Interdictions Supply Demand

  27. Attack Case 1: 9 Interdictions Supply Demand

  28. 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

  29. Attack Case 1: Operator Resilience Curve

  30. Attack Case 2 • Delay parameter set to nC • In model, number of interdictions ranged from 1 to 9

  31. Attack Case 2: 1 Interdiction Supply Demand

  32. Attack Case 2: 2 Interdictions Supply Demand

  33. Attack Case 2: 3 Interdictions Supply Demand

  34. Attack Case 2: 4 Interdictions Supply Demand

  35. Attack Case 2: 5 Interdictions Supply Demand

  36. Attack Case 2: 6 Interdictions Supply Demand

  37. Attack Case 2: 7 Interdictions Supply Demand

  38. Attack Case 2: 8 Interdictions Supply Demand

  39. Attack Case 2: 9 Interdictions Supply Demand

  40. 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

  41. Attack Case 2: Operator Resilience Curve

  42. 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

  43. 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

  44. References • http://www.agribusiness-mgmt.wsu.edu/AgbusResearch/docs/eb1925.pdf • http://canada.ryder.com/printerfriendly.jsp?title=Refrigerated%20Truck&rpfile=content/rental_details_reefer.html • http://www.ams.usda.gov/AMSv1.0/getfile?dDocName=STELPRDC5093083 • http://www.ams.usda.gov/AMSv1.0/getfile?dDocName=STELDEV3021003 • http://www.ers.usda.gov/Publications/

  45. Questions?

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