Download presentation
Presentation is loading. Please wait.
Published bySarah McCormick Modified over 9 years ago
1
Joe Ashpari John Crain
2
2 U.S. Potato Transport
3
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
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 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
6
Nodes 6 Supply Demand
7
Arcs 7 Supply Demand
8
Abstract Network 8 Supply Demand
9
Graphical Model 9 S1b Supply Demand S2b S10b D1 D2 D10 (c ij, 0, ∞) S10a S2a S1a -560,000+25,000 +32,410 +14,500 -400,000 -245,000 (0, 0, ∞)
10
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.
11
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?
13
Max weight: 11,000 lbs Lets use ~ 10,000 lbs max weight for a truck C ij = =
14
Question Arises 1.What quantity of potatoes represent the demand for our problem?
15
Lets use roughly 1% of Total Potato Demand for each Demand Node
16
16 Scenarios Baseline (no attacks) Attack Case 1: Aggressive bidding to drive up the costs Attack Case 2: Complete buyout of selected suppliers
17
17 Baseline (no attacks) All demand satisfied Total Cost = $ 3.275 M Supply Demand
18
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
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
20
Attack Case 1: 1 Interdiction 20 Supply Demand
21
Attack Case 1: 2 Interdictions 21 Supply Demand
22
Attack Case 1: 3 Interdictions 22 Supply Demand
23
Attack Case 1: 4 Interdictions 23 Supply Demand
24
Attack Case 1: 5 Interdictions 24 Supply Demand
25
Attack Case 1: 6 Interdictions 25 Supply Demand
26
Attack Case 1: 7 Interdictions 26 Supply Demand
27
Attack Case 1: 8 Interdictions 27 Supply Demand
28
Attack Case 1: 9 Interdictions 28 Supply Demand
29
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
30 Attack Case 1: Operator Resilience Curve
31
31 Attack Case 2 Delay parameter set to nC In model, number of interdictions ranged from 1 to 9
32
Attack Case 2: 1 Interdiction 32 Supply Demand
33
Attack Case 2: 2 Interdictions 33 Supply Demand
34
Attack Case 2: 3 Interdictions 34 Supply Demand
35
Attack Case 2: 4 Interdictions 35 Supply Demand
36
Attack Case 2: 5 Interdictions 36 Supply Demand
37
Attack Case 2: 6 Interdictions 37 Supply Demand
38
Attack Case 2: 7 Interdictions 38 Supply Demand
39
Attack Case 2: 8 Interdictions 39 Supply Demand
40
Attack Case 2: 9 Interdictions 40 Supply Demand
41
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
42 Attack Case 2: Operator Resilience Curve
43
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
44
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
45
References http://www.agribusiness- mgmt.wsu.edu/AgbusResearch/docs/eb1925.pdf http://canada.ryder.com/printerfriendly.jsp?title=Refrigerat ed%20Truck&rpfile=content/rental_details_reefer.html http://canada.ryder.com/printerfriendly.jsp?title=Refrigerat ed%20Truck&rpfile=content/rental_details_reefer.html http://www.ams.usda.gov/AMSv1.0/getfile?dDocName=S TELPRDC5093083 http://www.ams.usda.gov/AMSv1.0/getfile?dDocName=S TELPRDC5093083 http://www.ams.usda.gov/AMSv1.0/getfile?dDocName=S TELDEV3021003 http://www.ams.usda.gov/AMSv1.0/getfile?dDocName=S TELDEV3021003 http://www.ers.usda.gov/Publications/
46
46 Questions?
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.