Resource Constrained Training
CDR Edward Dewinter
LT Zachary Schwartz
MAJ Russell Gan
1
Motivation
Goal is to optimize training schedule with
constrained resources that minimizes total
time to complete training for two Platoons
2
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
3
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?
4
Tasks and Resource Requirements
Tasks
First Aid 1
First Aid 2
Chemical 1
Chemical 2
Nuclear 1
Nuclear 2
Mine
Countermeasures 1
Mine
Countermeasures 2
Surf 1
Surf 2
FTX
POSTFTX
Medical
Vehicle
3
3
0
0
0
0
Demo
Range
0
0
2
2
2
2
Rhino
0
0
2
1
2
1
RHIB
0
0
0
0
0
0
Corpsman
3
3
0
0
0
0
EOD
Trainer
3
2
2
2
3
3
0
2
2
1
0
1
0
0
0
0
0
2
1
1
1
0
1
1
2
2
1
1
0
0
2
0
0
0
0
1
0
1
2
2
3
1
5
Initially.. Shortest Path Formulation
• Nodes – Tasks completed, indexed on time
tB
AB,
tA + tB
A, tA
tA
tC
AC,
tA + tC
S
tB
B, tB
LOOKS GOOD
SO FAR….
6
But..
AB,
tA + tB
1
AB,
t A + tB
+1
1
AB,
t A + tB
+2
1
AB,
tA + tB
+3
tB
Probably not the best approach..
7
Integer Program Formulation
min completion time( y )
y
subject to
Precedence Constraints
Resource Constraints
Contiguity Constraints
Task Constraints
y  0,1
y p , k ,t
1, if Platoon p does task k on time t

8
0,
otherwise

Results
• 60 days to complete.
• Assuming no precedence, resource and
contiguity constraints – 50 days to complete.
9
Let’s attack the model..
• What constitutes an attack:
– Terrorist actions
– Natural calamities
– Murphy
10
Penalties
Medical
Vehicle
Demo
Range
Rhino
RHIB
Corpsman
EOD
Trainer
2
4
3
2
3
3
11
Interdiction Model
max min completion time( y ) + penalty term( x, y )
x
y
subject to
Precedence Constraints
Resource Constraints
Contiguity Constraints
Task Constraints
Attack Constraints
x  0,1
…
y  0,1
PROBLEM!
1, if resource n is attacked at time t
xt ,n  
12
0,
otherwise

Side note
• Cannot use “dual trick”
• Benders does not work well with pure ILPs
– Upper & lower bounds may not converge
13
Why doesn’t Benders work well for
ILPs?
14
Why doesn’t Benders work well for
ILPs?
15
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.
16
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
17
Relaxed Interdiction Model
max min completion time( y ) + penalty term( x, y )
x
y
subject to
Precedence Constraints
Resource Constraints
Contiguity Constraints
Task Constraints
Attack Constraints
x  0,1
0  y 1
18
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
19
FA1
FA2
Chem
1
Chem
2
NUC
1
NUC
2
MCM
1
MCM
2
SURF
1
SURF
2
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”.
FTX
POST
FTX
This is where the bottle neck starts.
20
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
21
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.
22
Operator Resilience Curve
38%
23%
17%
10%
23
Which resources are targeted the
most?
Medical
Vehicle
Demo
Range
Rhino
RHIB
Corpsman
EOD
Trainer
2
4
3
2
3
3
Tasks
First Aid 1
First Aid 2
Chemical 1
Chemical 2
Nuclear 1
Nuclear 2
Mine
Countermeasures 1
Mine
Countermeasures 2
Surf 1
Surf 2
FTX
POSTFTX
Medical
Vehicle
3
3
0
0
0
0
Demo
Range
0
0
2
2
2
2
Rhino
0
0
2
1
2
1
RHIB
0
0
0
0
0
0
Corpsman
3
3
0
0
0
0
EOD
Trainer
3
2
2
2
3
3
0
2
2
1
0
1
0
0
0
0
0
2
1
1
1
0
1
1
2
2
1
1
0
0
2
0
0
0
0
1
0
1
2
2
3
24
1
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
25
We want to find out..
• How many attacks can we tolerate?
• Which resources are targeted the most?
• What can we do about it?
26
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.
27
Questions?
28