Modeling Attacks to Chesapeake Bay ShippingLT Sarah WatsonLT Matt Yokeley

Project Overview

• What is this project about?

• The goal of this project

• The scope of this project

Background

• Terrorism continues to threaten international cargo

• There is a larger threat to sea born attack than air born

• Long term effects of shipping attacks

= + $

The Network

• Chesapeake Bayo Covers 64,299 square miles

o More than 150 rivers feed into it

• Abstractiono One “dummy” start node

o Three supply ports

o Ends at Chesapeake Lighthouse

o 55 arcs

The Model

• Built using Max-flow

Subject to:

The Dual

• The dual gave us optimal attack points

Subject to:

• Iterated through attacks to find optimal subsequent

attacks

ProcessSelect max number of

attackers (x= 1-4)

Determine plan of attack

Remove attacked arcs

from list

Find number of CG vessels required to prevent complete

network shutdown

0 1 2 3 4 5 6 7 8 9 1040000

50000

60000

70000

80000

90000

100000

110000

120000

130000

140000

0

1

2

3

4

Flow of Goods Goods Stopped by TerroristArcs Attacked

Number of Coast Guard VesselsT

ota

l G

oods

(tons

x 1

000)

Num

ber

of

Arc

s

Analysis of One Attacker

• Maximum flow of network = 180,235.3

tons

Attackable arcsOptimal arc for terrorist to attackDefended arcs

At this point the entire path out of Hampton Roads is protected

from attack

0 2 4 6 8 100

20000

40000

60000

80000

100000

120000

140000

160000

180000

200000

0

1

2

3

4

Flow of Goods Goods Stopped by TerroristArcs Attacked

Number of Coast Guard VesselsT

ota

l G

oods

(tons

x 1

000)

Num

ber

of

Arc

s

Analysis of Two Attackers

• Maximum flow of network = 180,235.3

tons

Attackable arcsOptimal arc for terrorist to attackDefended arcs

0 3 6 9 120

20000

40000

60000

80000

100000

120000

140000

160000

180000

200000

0

1

2

3

4

Flow of Goods Goods Stopped by TerroristArcs Attacked

Number of Coast Guard VesselsT

ota

l G

oods

(tons

x 1

000)

Num

ber

of

Arc

s

Analysis of Three Attackers

• Maximum flow of network = 180,235.3

tons

Attackable arcsOptimal arc for terrorist to attackDefended arcs

0 3 6 9 12 160

20000

40000

60000

80000

100000

120000

140000

160000

180000

200000

0

1

2

3

4

Flow of Goods Goods Stopped by TerroristArcs Attacked

Number of Coast Guard VesselsT

ota

l G

oods

(tons

x 1

000)

Num

ber

of

Arc

s

Analysis of Four Attackers

• Maximum flow of network = 180,235.3

tons

Attackable arcsOptimal arc for terrorist to attackDefended arcs

The terrorist is able to employ this extra attack as

a “reserve” to keep the network down

Conclusions

• It’s possible to shut down all cargo flow by only attacking two arcs

• Attacker/defender ratio is not one-to-one

• Compounding increase in goods near the bay entrance causes it to

be the major point of concern

• What’s next?o Model distance from CG stations to attack points

o Use probabilities of attack on arcs

o Assign priorities to arcs base d on cargo

Questions??