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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?