Resource Constrained Training
Post on 23-Feb-2016
36 Views
Preview:
DESCRIPTION
Transcript
1
Resource Constrained Training
CDR Edward DewinterLT Zachary Schwartz
MAJ Russell Gan
2
Motivation
Goal is to optimize training schedule with constrained resources that minimizes total time to complete training for two Platoons
3
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
4
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?
5
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 3Mine Countermeasures 1 0 2 2 1 0 1Mine 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
6
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….
7
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..
8
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
9
Results
• 60 days to complete. • Assuming no precedence, resource and
contiguity constraints – 50 days to complete.
10
Let’s attack the model..
• What constitutes an attack:– Terrorist actions– Natural calamities–Murphy
11
Penalties
Medical Vehicle
Demo Range
Rhino RHIB Corpsman EOD Trainer
2 4 3 2 3 3
12
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
13
Side note
• Cannot use “dual trick”• Benders does not work well with pure ILPs– Upper & lower bounds may not converge
14
Why doesn’t Benders work well for ILPs?
15
Why doesn’t Benders work well for ILPs?
16
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.
17
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
18
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
19
Interdiction Results (Relaxed)Number of
AttacksResources 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
20
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.
21
Interdiction Results (Integer)Number of
AttacksResources 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
22
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.
23
Operator Resilience Curve
10%
17%23%
38%
24
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 3Mine Countermeasures 1 0 2 2 1 0 1Mine 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
25
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
26
We want to find out..
• How many attacks can we tolerate?• Which resources are targeted the most?• What can we do about it?
27
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.
28
Questions?
top related