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Resource Constrained Training
CDR Edward Dewinter
LT Zachary Schwartz
MAJ Russell Gan
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Motivation
Goal is to optimize training schedule with constrained resources that minimizes total time to complete training for two Platoons
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Background
• EOD Training Unit Two, Fort Story, VA• Train EOD Platoons prior to deployment• Ideal plan is to train two Platoons at the same
time
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Ultimately we want to find out..
• How many attacks on the resources can we tolerate?
• Which resources are targeted the most?• What can we do about it?
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Tasks and Resource Requirements
TasksMedical Vehicle
Demo Range Rhino RHIB Corpsman
EOD Trainer
First Aid 1 3 0 0 0 3 3First Aid 2 3 0 0 0 3 2Chemical 1 0 2 2 0 0 2Chemical 2 0 2 1 0 0 2Nuclear 1 0 2 2 0 0 3Nuclear 2 0 2 1 0 0 3
Mine Countermeasures 1 0 2 2 1 0 1
Mine Countermeasures 2 0 2 1 1 0 1Surf 1 0 1 1 0 0 2Surf 2 0 1 2 0 0 2FTX 0 1 2 2 1 3POSTFTX 0 0 1 0 0 1
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Initially.. Shortest Path Formulation
• Nodes – Tasks completed, indexed on time
S
A, tA
B, tB
AB, tA + tB
AC, tA + tC
tA
tB
tB
tC
LOOKS GOOD SO FAR….
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But..
AB, tA + tB
tB
AB, tA + tB
+1
AB, tA + tB
+2
AB, tA + tB
+3
1 1 1
Probably not the best approach..
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Integer Program Formulation
min ( )
subject to
Precedence Constraints
Resource Constraints
Contiguity Constraints
Task Constraints
ycompletion time y
0,1
y, ,
1, if Platoon does task on time
0, otherwise p k t
p k ty
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Results
• 60 days to complete. • Assuming no precedence, resource and
contiguity constraints – 50 days to complete.
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Let’s attack the model..
• What constitutes an attack:– Terrorist actions– Natural calamities–Murphy
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Penalties
Medical Vehicle
Demo Range
Rhino RHIB Corpsman EOD Trainer
2 4 3 2 3 3
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Interdiction Modelmax min ( ) + ( , )
subject to
Precedence Constraints
Resource Constraints
Contiguity Constraints
Task Constraints
yxcompletion time y penalty term x y
Attack Constraints
0,1
0,1
x
y
…
PROBLEM!
,
1, if resource is attacked at time
0, otherwise t n
n tx
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Side note
• Cannot use “dual trick”• Benders does not work well with pure ILPs– Upper & lower bounds may not converge
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Why doesn’t Benders work well for ILPs?
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Why doesn’t Benders work well for ILPs?
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Side note
• Cannot use “dual trick”• Benders does not work well with pure ILPs– Upper & lower bounds may not converge
• But, if a valid Benders cut is generated at every iteration, then the algorithm converges to optimality.
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New Plan• Solve relaxed interdiction problem using Benders• Hard code interdiction results into ILP
subproblem
Limitations• Attacker placed at a disadvantage
– Optimal attack in the relaxed version is suboptimal to the original problem
– In relaxed version, attacker considers options which do not actually exist to the operator in the original problem
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Relaxed Interdiction Modelmax min ( ) + ( , )
subject to
Precedence Constraints
Resource Constraints
Contiguity Constraints
Task Constraints
yxcompletion time y penalty term x y
Attack Constraints
0,1
0 1
x
y
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Interdiction Results (Relaxed)
Number of Attacks
Resources Attacked Resultant Completion Time
0 NIL 60 days
1 EOD Trainer (Day 3) 60 days
2 EOD Trainer (Day 3)EOD Trainer (Day 4)
60 days
3 EOD Trainer (Day 4)EOD Trainer (Day 5)EOD Trainer (Day 6)
60 days
4 Demo Range (Day 4)EOD Trainer (Day 5)EOD Trainer (Day 6)EOD Trainer (Day 7)
60 days
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FA1 FA2
Chem1
Chem 2
NUC1
NUC2
MCM1
MCM2
SURF 1
SURF 2
FTX POSTFTX
Attacking early would pose less of a problem to the operator.Could easily schedule tasks that do not require that resource to “fill the gap”.
This is where the bottle neck starts.
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Interdiction Results (Integer)
Number of Attacks
Resources Attacked Resultant Completion Time
0 NIL 60 days
1 EOD Trainer (Day 32) 66 days
2 Demo Range (Day 55)Rhino (Day 60)
70 days
3 EOD Trainer (Day 33)EOD Trainer (Day 50)EOD Trainer (Day 60)
74 days
4 Demo Range (Day 3)Demo Range (Day 23)Demo Range (Day 46)Demo Range (Day 55)
83 days
* 0 tolerance was used throughout for both B&B and Benders
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Randomly Generated Attacks
• Done for 1 attack scenario:– 100 random attacks generated–Worst case – 65 days– Benders on ILP still provides more realistic
outputs
• Attacking all resources on the same day would be suboptimal to attacker.
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Operator Resilience Curve
10%
17%
23%
38%
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Which resources are targeted the most?
TasksMedical Vehicle
Demo Range Rhino RHIB Corpsman
EOD Trainer
First Aid 1 3 0 0 0 3 3First Aid 2 3 0 0 0 3 2Chemical 1 0 2 2 0 0 2Chemical 2 0 2 1 0 0 2Nuclear 1 0 2 2 0 0 3Nuclear 2 0 2 1 0 0 3
Mine Countermeasures 1 0 2 2 1 0 1
Mine Countermeasures 2 0 2 1 1 0 1Surf 1 0 1 1 0 0 2Surf 2 0 1 2 0 0 2FTX 0 1 2 2 1 3POSTFTX 0 0 1 0 0 1
Medical Vehicle
Demo Range
Rhino RHIB Corpsman EOD Trainer
2 4 3 2 3 3
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What can we do about it?
• Relieve bottleneck– Adjust FTX lesson plan
• Create redundancy–More EOD Trainers–More demo ranges– Leverage on simulation instead of L/F ranges
• Improve security of resources– Housing Rhino’s close to base security
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We want to find out..
• How many attacks can we tolerate?• Which resources are targeted the most?• What can we do about it?
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Future Research
• Expand the model to include all EOD training pipelines.
• Applying model to other types of training programs subject to similar constraints.
• Develop algorithm to solve max-min ILP problems exactly.
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Questions?