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?