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?