Post on 05-Jan-2016
description
Joe Ashpari
John Crain
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U.S. Potato Transport
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Background
Johnny Joe’s IncAn emerging potato chip conglomeratePotato chip plants in several cities throughout the U.SVarious suppliers of potatoes in U.S. and CanadaLargest Overhead: Cost of Shipping from supplier to plantsDoritos is rumored to be considering aggressive options to sabotage our continued growth
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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
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Nodes
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Supply Demand
Arcs
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Supply Demand
Abstract Network
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Supply Demand
Graphical Model
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S1b
Supply Demand
S2b
S10b
D1
D2
D10
(cij, 0, ∞)
S10a
S2a
S1a-560,000 +25,000
+32,410
+14,500-400,000
-245,000
(0, 0, ∞)
Mathematical Model
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i: nodes (alias j, a)cij = shipping cost in $ per cwt (centum weight) to ship from node i to node jdij = delay cost in $ per cwt for a delay between i and jsj = shortage cost at node j per cwt of potatoesUDj = unsatisfied demand at node j in cwt potatoesb(j) = supply/demand at node juij = capacity from node i to node j
OBJ: min
s.t.
( , ) | ( ) 0
( )ij ij ij ij j ji j E j b j
c d X Y s UD
( , ) ( , )
( ),ia aii a E a i E
y y b a a V
0 , ( , )ij ijy u i j E
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
1_ 100 _2.54 * * * ( )
* 10,000 _ 1_ _
0.0254 * ( )_ *
ij
ij
Dollars Truck lbsDist mi
Truck Miles lbs cwt Potatoes
DollarsDist mi
cwt Potatoes Miles
Cij =
=
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
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Scenarios
Baseline (no attacks) Attack Case 1: Aggressive bidding to drive up
the costs Attack Case 2: Complete buyout of selected
suppliers
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Baseline (no attacks)
All demand satisfied Total Cost = $ 3.275 M
Supply Demand
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Baseline (no attacks)
Optimal FlowFrom To Flow, Yij (cwt)
Bakersfield Los Angeles 52,000
Colorado Springs Dallas 23,600
Bangor Boston 32,410
Bangor New York 53,200
Bangor Philadelphia 19,780
Bangor Richmond 14,500
Chippewa Falls Chicago 36,000
Chippewa Falls Detroit 10,050
Chippewa Falls St. Louis 15,180
Chippewa Falls Atlanta 25,000
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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
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Supply Demand
Attack Case 1: 2 Interdictions
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Supply Demand
Attack Case 1: 3 Interdictions
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Supply Demand
Attack Case 1: 4 Interdictions
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Supply Demand
Attack Case 1: 5 Interdictions
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Supply Demand
Attack Case 1: 6 Interdictions
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Supply Demand
Attack Case 1: 7 Interdictions
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Supply Demand
Attack Case 1: 8 Interdictions
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Supply Demand
Attack Case 1: 9 Interdictions
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Supply Demand
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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
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Attack Case 1: Operator Resilience Curve
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Attack Case 2
Delay parameter set to nC
In model, number of interdictions ranged from 1 to 9
Attack Case 2: 1 Interdiction
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Supply Demand
Attack Case 2: 2 Interdictions
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Supply Demand
Attack Case 2: 3 Interdictions
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Supply Demand
Attack Case 2: 4 Interdictions
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Supply Demand
Attack Case 2: 5 Interdictions
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Supply Demand
Attack Case 2: 6 Interdictions
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Supply Demand
Attack Case 2: 7 Interdictions
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Supply Demand
Attack Case 2: 8 Interdictions
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Supply Demand
Attack Case 2: 9 Interdictions
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Supply Demand
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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
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Attack Case 2: Operator Resilience Curve
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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
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/
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Questions?