10/2/2007 1
Optimal Placement of Suicide
Bomber Detectors
Xiaofeng Nie, Rajan Batta, Colin G. Drury, Li Lin
Department of Industrial and Systems Engineering
Research Institute for Safety and Security in Transportation
The State University of New York at Buffalo
10/2/2007 2
Framework
• Introduction
• Basic Setting and Optimization Model
• Properties
• Greedy Adding Heuristic and Branch and Bound
• Base Case and Computational Analysis
• Future Work
10/2/2007 3
Introduction
• Kaplan and Kress analyze the operational effectiveness of suicide bomber (SB) detector schemes under best-case assumptions
• Two urban environments: grid and plaza
• Two kinds of intervention: instruct to flee and hit the deck
• Under some situations, intervention will not reliably result in meaningful casualty reductions
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Introduction (cont.)• Here, we consider the optimal placement of detectors to minimize the expected casualties in a threat area where the entrances and the potential targets are known
• We divide the threat area into grids
• Some grids are blocked to model physical obstructions
• The SB detector is not perfectly reliable
• Assume that the SB will travel on the shortest path from his/her chosen entrance to the selected explosive grid
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Basic Setting
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Basic Setting (cont.)
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y probabilit with gridat bomb theexplodes and
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Basic Setting (cont.)
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Basic Setting (cont.)
ratedetection ousinstantane
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Basic Setting (cont.)
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otherwise
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Events Related to the SB
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Probabilities and Casualties
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10/2/2007 14
Total Expected Casualties
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casualties expected totalThe
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withat explodes and from enters SB The
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Optimization Model
employ willedetector w ofnumber maximum theis where
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Optimization Model (cont.)
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Let
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10/2/2007 17
Properties
1 be toelements
first set the and oforder decreasingin
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grid explosive one and entrance oneonly is thereIf
solution optimal in the ,If
programnonlinear convex a is problemrelaxtion The
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10/2/2007 18
Properties (cont.)
solution optimal in the grid
in that detector one locate will we,1 and grids
other all dominates which grid one exists thereIf
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Greedy Adding Heuristic
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A Special Case
optimal is procedure GAH by thegiven solution the
then ,)( ),,( of pairs possible allfor If
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Branch and Bound
solutions optimalany geliminatin
withoutspace feasible thedecrease will
constraint adding ,by dominated is grid If
riabledecison va ingcorrespond theeliminate
can wegrids, than moreby dominated is grid a If
properties dominance some Explore
programnonlinear convex a is problem relaxation The
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Base Case
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Base Case Solutions
%43.0 error Relative
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aluefunction v optimal the,1 issolution
optimal thealgorithm, Bound andBranch theusingBy
27.976 is aluefunction v
objective ingcorrespond the83, grid and 55 grid then
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Value Bound andBranch Value Bound andBranch Value GAH
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10/2/2007 26
Computational Analysis
Procedure GAH of Efficiency
Analysis of Robustness
Analysisy Sensitivit
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Sensitivity Analysis
RateDetection ousInstantane ofEffect
RadiusDetection ofEffect
Entrances ofNumber ofEffect
Placed Detectors ofNumber ofEffect
•
•
•
•
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Effect of Number of Detectors
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Effect of Number of Entrances
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Effect of Detection Radius
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Effect of Detection Rate
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Robustness Analysis
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Efficiency of GAH Procedure
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Conclusions
• Considered how to deploy SB detectors in a threat area where the potential targets are known
• Proposed an optimization model where the objective function is the total expected casualties
• Developed two algorithms (one heuristic and one exact) and studied a base case
10/2/2007 39
Future Directions
y probabilitdetection joint heconsider t could weLater,
detectors.amony cy independen assume we work,In this
detectors of typesdifferent thesite to where
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choose tohow :detectors of kinds severalConsider
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•
10/2/2007 40
Questions?