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Agenda
• 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
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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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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.
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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 2002-2008 data set, which was more robust
• Emplacing an interdiction team on an edge represents an ‘Attack’ on the edge
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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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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
min𝑥, w
max𝑣 ,𝑦
v −∑( 𝑖 , 𝑗 )
𝑑𝑖𝑗𝑦𝑖𝑗 (𝑥𝑖𝑗+0.5∗𝑤𝑖𝑗)
𝑠 . 𝑡 . ∑ 𝑦𝑖𝑠−∑ 𝑦𝑠𝑖=−𝑣 ∑ 𝑦𝑖𝑡−∑ 𝑦𝑡𝑖=𝑣 ∑ 𝑦𝑖𝑎−∑ 𝑦𝑎𝑖=0 𝑦𝑖𝑗≤𝑢𝑖𝑗 0≤ 𝑦𝑖𝑗
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Penalty Calculation
-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
0 1 2 3 4 5 6 7 8 9 100
50
100
150
200
250
10% 1 Attack10% 2 Attacks10% 1.5 Attacks (2nd Attack Half as Effective as First)
Number of Attacks
Hero
in T
rans
ited
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Resiliency Curves 50% POI
0 1 2 3 4 5 6 7 8 9 100
50
100
150
200
250
50% 1 Attack
50% 2 Attacks
50% 1.5 Attacks (2nd Attack Half as Effective as First)
Number of Intercepted Edges
Her
oin
Tran
site
d
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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 substantially
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Future Work
• Modeling drug traffickers best responses- creating new nodes and routes (edges)
• Increasing resolution within the model- i.e. identifying more intermediate nodes along the routes