Afghanistan Illegal Drug Trade
LT Dan Ryan
Capt Steve Felts
Capt Bethany Kauffman
Agenda
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Problem Statement
Background
Network
Max-Flow Interdiction Model
Conclusions
Questions
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Problem Statement
• Analyze the unimpeded flow of drugs across
the global drug trade network
• Identify optimal locations to place drug
interdiction resources
• Evaluate the expected impact of these
interdiction strategies
3
M
Backstory
• Afghanistan produces 84% of the world’s heroin
and opium supplies.
• Profits from illegal drug sales fund criminal
activities detrimental to Afghan and Global
security
• Illegal drugs from Central Asia supply
consumer demands in North America and
Europe- adding to illegal drug use and
dependencies harmful to society.
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M
Backstory
• Other main beneficiaries of the trade include
international criminal organizations in Europe,
Asia, and elsewhere.
• Curtailing the illegal drug trade will reduce
violence among traffickers and reduce profits
that fund far-reaching criminal activities.
5
M
Data
-UN Office on Drugs and Crime
 World Drug Reports 2010, 2011, 2012
 Global Afghan Opium Trade, A Threat
Assessment
 Heroin: Data and Analysis
 Illicit Drug Trends in Central Asia
-Interpol
-Geopium
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Additional Notes
• Considered data from both 2002-2008 and
2009, however 2009 data did not provide
constructive results compared to the 20022008 data set, which was more robust
• Emplacing an interdiction team on an edge
represents an ‘Attack’ on the edge
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The Network
The Network
Start
The Network
End
Europe Resolution
• Divided Western Europe into 5 individual
nodes to provide further resolution to the
network: Italy, Germany, France, UK,
Netherlands
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Full Network
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Building the Model
• Design Stages:
-Max Flow Interdiction (constant penalty, 1
interdiction per arc)
-Max Flow Interdiction (non-constant penalty,
1 interdiction per arc)
-Max Flow Interdiction (non-constant penalty,
2 interdictions per arc)
-Max Flow Interdiction (non-constant penalty,
2 interdictions per arc, 2nd interdiction on an arc
half as effective as the first)
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Max Flow Interdiction Model
min max v−
𝑥,w
𝑣,𝑦
𝑠. 𝑡.
𝑑𝑖𝑗𝑦𝑖𝑗(𝑥𝑖𝑗 + 0.5 ∗ 𝑤𝑖𝑗)
𝑖,𝑗
𝑦𝑖𝑠 −
𝑦𝑠𝑖 = −𝑣
𝑦𝑖𝑡 −
𝑦𝑡𝑖 = 𝑣
𝑦𝑖𝑎 −
𝑦𝑎𝑖 = 0
𝑦𝑖𝑗 ≤ 𝑢𝑖𝑗
0 ≤ 𝑦𝑖𝑗
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Penalty Calculation
𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑡𝑦 𝑜𝑓 𝐼𝑛𝑡𝑒𝑟𝑑𝑖𝑐𝑡𝑖𝑜𝑛 = 0.1 +
1.5
𝐷𝑖𝑠𝑡𝑎𝑛𝑐 𝑒 1000
50
-Longer distance arcs have a higher probability
of interdiction, or ‘penalty’, as more drugs are
likely to be seized along longer routes.
-Penalty based on great circle distances and with
a constant of .1 (An interdiction team on an arc
guarantees interdiction of 10% of heroin across
an arc regardless of distance).
*Also calculated for 50% guaranteed interdiction
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Resiliency Curves 10% POI
250
200
Heroin Transited
10% 1 Attack
150
10% 2 Attacks
100
10% 1.5 Attacks (2nd
Attack Half as Effective as
First)
50
0
0
1
2
3
4
5
6
7
8
9
10
Number of Attacks
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10% POI: 1 Attack Per Arc
1attacks per arc
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10% POI: 2 Attacks Per Arc
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Resiliency Curves 50% POI
250
200
Heroin Transited
50% 1 Attack
150
50% 2 Attacks
100
50% 1.5 Attacks (2nd
Attack Half as Effective as
First)
50
0
0
1
2
3
4
5
6
7
8
9
10
Number of Intercepted Edges
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50% POI: 1 Attack Per Arc
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50% POI: 2 Attacks Per Arc
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Conclusions
Assuming 10% POI:
-The number of attacks performed on an edge (1,
2, or when the 2nd attack is half as effective as
the first) is almost inconsequential with less than
5 attacks.
-When multiple attacks per edge are allowed, the
benefits of each additional attack is nearly linear.
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Conclusions
Assuming 50% POI:
-The number of attacks performed on an edge (1,
2, or when the 2nd attack is half as effective as
the first) is again almost inconsequential with
less than 4 attacks.
-When multiple attacks per edge are allowed, the
benefits of each additional attack is nearly linear
up to 4 attacks as well.
-After 4 attacks, the value of each attack (or the
amount of drugs interdicted) decreases
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substantially
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Future Work
• Modeling drug traffickers best responsescreating new nodes and routes (edges)
• Increasing resolution within the model- i.e.
identifying more intermediate nodes along the
routes
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Questions
Thanks for your attention!
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