resource constrained training
DESCRIPTION
Resource Constrained Training. CDR Edward Dewinter LT Zachary Schwartz MAJ Russell Gan. Motivation. Goal is to optimize training schedule with constrained resources that minimizes total time to complete training for two Platoons. Background. EOD Training Unit Two, Fort Story, VA - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Resource Constrained Training](https://reader035.vdocuments.us/reader035/viewer/2022062812/568162bc550346895dd347c1/html5/thumbnails/1.jpg)
1
Resource Constrained Training
CDR Edward DewinterLT Zachary Schwartz
MAJ Russell Gan
![Page 2: Resource Constrained Training](https://reader035.vdocuments.us/reader035/viewer/2022062812/568162bc550346895dd347c1/html5/thumbnails/2.jpg)
2
Motivation
Goal is to optimize training schedule with constrained resources that minimizes total time to complete training for two Platoons
![Page 3: Resource Constrained Training](https://reader035.vdocuments.us/reader035/viewer/2022062812/568162bc550346895dd347c1/html5/thumbnails/3.jpg)
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
![Page 4: Resource Constrained Training](https://reader035.vdocuments.us/reader035/viewer/2022062812/568162bc550346895dd347c1/html5/thumbnails/4.jpg)
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?
![Page 5: Resource Constrained Training](https://reader035.vdocuments.us/reader035/viewer/2022062812/568162bc550346895dd347c1/html5/thumbnails/5.jpg)
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
![Page 6: Resource Constrained Training](https://reader035.vdocuments.us/reader035/viewer/2022062812/568162bc550346895dd347c1/html5/thumbnails/6.jpg)
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….
![Page 7: Resource Constrained Training](https://reader035.vdocuments.us/reader035/viewer/2022062812/568162bc550346895dd347c1/html5/thumbnails/7.jpg)
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..
![Page 8: Resource Constrained Training](https://reader035.vdocuments.us/reader035/viewer/2022062812/568162bc550346895dd347c1/html5/thumbnails/8.jpg)
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
![Page 9: Resource Constrained Training](https://reader035.vdocuments.us/reader035/viewer/2022062812/568162bc550346895dd347c1/html5/thumbnails/9.jpg)
9
Results
• 60 days to complete. • Assuming no precedence, resource and
contiguity constraints – 50 days to complete.
![Page 10: Resource Constrained Training](https://reader035.vdocuments.us/reader035/viewer/2022062812/568162bc550346895dd347c1/html5/thumbnails/10.jpg)
10
Let’s attack the model..
• What constitutes an attack:– Terrorist actions– Natural calamities–Murphy
![Page 11: Resource Constrained Training](https://reader035.vdocuments.us/reader035/viewer/2022062812/568162bc550346895dd347c1/html5/thumbnails/11.jpg)
11
Penalties
Medical Vehicle
Demo Range
Rhino RHIB Corpsman EOD Trainer
2 4 3 2 3 3
![Page 12: Resource Constrained Training](https://reader035.vdocuments.us/reader035/viewer/2022062812/568162bc550346895dd347c1/html5/thumbnails/12.jpg)
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
![Page 13: Resource Constrained Training](https://reader035.vdocuments.us/reader035/viewer/2022062812/568162bc550346895dd347c1/html5/thumbnails/13.jpg)
13
Side note
• Cannot use “dual trick”• Benders does not work well with pure ILPs– Upper & lower bounds may not converge
![Page 14: Resource Constrained Training](https://reader035.vdocuments.us/reader035/viewer/2022062812/568162bc550346895dd347c1/html5/thumbnails/14.jpg)
14
Why doesn’t Benders work well for ILPs?
![Page 15: Resource Constrained Training](https://reader035.vdocuments.us/reader035/viewer/2022062812/568162bc550346895dd347c1/html5/thumbnails/15.jpg)
15
Why doesn’t Benders work well for ILPs?
![Page 16: Resource Constrained Training](https://reader035.vdocuments.us/reader035/viewer/2022062812/568162bc550346895dd347c1/html5/thumbnails/16.jpg)
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.
![Page 17: Resource Constrained Training](https://reader035.vdocuments.us/reader035/viewer/2022062812/568162bc550346895dd347c1/html5/thumbnails/17.jpg)
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
![Page 18: Resource Constrained Training](https://reader035.vdocuments.us/reader035/viewer/2022062812/568162bc550346895dd347c1/html5/thumbnails/18.jpg)
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
![Page 19: Resource Constrained Training](https://reader035.vdocuments.us/reader035/viewer/2022062812/568162bc550346895dd347c1/html5/thumbnails/19.jpg)
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
![Page 20: Resource Constrained Training](https://reader035.vdocuments.us/reader035/viewer/2022062812/568162bc550346895dd347c1/html5/thumbnails/20.jpg)
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.
![Page 21: Resource Constrained Training](https://reader035.vdocuments.us/reader035/viewer/2022062812/568162bc550346895dd347c1/html5/thumbnails/21.jpg)
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
![Page 22: Resource Constrained Training](https://reader035.vdocuments.us/reader035/viewer/2022062812/568162bc550346895dd347c1/html5/thumbnails/22.jpg)
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.
![Page 23: Resource Constrained Training](https://reader035.vdocuments.us/reader035/viewer/2022062812/568162bc550346895dd347c1/html5/thumbnails/23.jpg)
23
Operator Resilience Curve
10%
17%23%
38%
![Page 24: Resource Constrained Training](https://reader035.vdocuments.us/reader035/viewer/2022062812/568162bc550346895dd347c1/html5/thumbnails/24.jpg)
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
![Page 25: Resource Constrained Training](https://reader035.vdocuments.us/reader035/viewer/2022062812/568162bc550346895dd347c1/html5/thumbnails/25.jpg)
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
![Page 26: Resource Constrained Training](https://reader035.vdocuments.us/reader035/viewer/2022062812/568162bc550346895dd347c1/html5/thumbnails/26.jpg)
26
We want to find out..
• How many attacks can we tolerate?• Which resources are targeted the most?• What can we do about it?
![Page 27: Resource Constrained Training](https://reader035.vdocuments.us/reader035/viewer/2022062812/568162bc550346895dd347c1/html5/thumbnails/27.jpg)
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.
![Page 28: Resource Constrained Training](https://reader035.vdocuments.us/reader035/viewer/2022062812/568162bc550346895dd347c1/html5/thumbnails/28.jpg)
28
Questions?