The Impact of Mathematics on Defence Policy

IMA Mathematics 2012

‘The Impact of Mathematics on Defence Policy’

James Moffat, Senior Fellow, Dstl

©Crown Copyright 2012. Published with the permission of the Defence Science and Technology Laboratory on behalf of the Controller of HMSO

© Dstl 2011Dstl is part of the Ministry of Defence

• Life is just Chemistry (James Watson)• Chemistry is just Physics (Neils Bohr)• Physics is just Mathematics (Paul Dirac)

1 May 2023


Crown Copyright Dstl 2011

Strategic Defence & Security Review


The Strategic Defence & Security Review - SDSR

• SDSR background• Analysis supporting policy• Some observations


National Security Strategy

Strategic Defence and Security Review


• Strategic Context• Britain’s Distinctive Role• National Security Risk Assessment• ‘Adaptable Britain’

– Retain a broad spectrum of security and defence capabilities– Strengthen relationships with key allies– Coordinate and integrate whole of Government response

National Security Strategy

Our Key Customers


1 May 2023

SDSR Support

PR11

“Detail”

Synthesis

ImplementationCSR

Policy Choices

Capability Choices

SDSR White Paper “Headlines”

20 Oct 2010

Work strands

Ideas

Jan 2011

Advice and analysis to support work

strands

Synthesising work strand ideas.

Force structure risk assessment

Advice to mitigate risks and support implementation

General Election May 2010


• A range of mixes of defence capabilities and costs were rapidly analysed in near real time direct with key decision-makers

• This enabled best choices to be made within financial constraints

• Negotiations with Treasury reduced savings target from 10-20% to 7.5%

Key Impacts of Analysis


Homeland Influence Intervention Stabilisation

Matching Resource to Aspiration

Increasing

Levels of

Ambition

Policy Choices – Prioritise capabilities to achieve affordability


Force Structure Cost - Projected defence budget in 2020

Steady State 2 Annual CompoundedEquipment Procurement (Aerospace) 0.0% 0%

#Equipment Procurement (Other) 0.0% 0%

COO1 1 1

Equipment (Running Cost) 0.0% 0%

COO2 1 1 Personnel 0.0% 0%

Other 0.0% 0%

COO3 1 1

Annual CompoundedOverhead Deflator 0.0% 0% 100

Top Herrick

3rd Standing Commitments 1

Harmony 2 TRUE 2nd COO 3

DPA data is available. 31 Base Overheads 1

Force Structure Cost Visualisation ToolUNCLASSIFIED

Overheads

Standing Commitments

Defence Planning Assumptions (DPAs) Cost Pressures

Strategy Management

Graph Legend Order TablesGraph

0

20

40

60

80

now 0 0 0 0 futureC

ost

Overheads COO Standing Commitments

Flat Real Flat Cash -14%

NoneSmall ScaleMedium Scale

Non-Enduring

NoneSmall ScaleMedium Scale

Non-Enduring

NoneSmall Scale

Non-Enduring

1 in x 1 in y

Auto-updateUpdate Graph

R

R

R

R

R

R

R

Enduring

Enduring

Enduring

Available?

Reset all DPAs

High Level SummaryR

Overheads

COO

Standing Commitments

Medium Scale

‘Fast Analysis’: Policy Assumptions, Costs and Capabilities


• will be sized and shaped to conduct Standing Commitments plus:• an enduring stabilisation operation • one non-enduring complex intervention• one non-enduring simple intervention

Chosen by National Security Council from 3 affordable

postures developed by fast analysis

Set at 2 interventions after analysis showed

that 3 were unaffordable and

unlikely historically

Analysis helped inform the development of Defence Planning Assumptions


Analysis supported the development of Future Force 2020


• Scenario-based analysis generated insights into force requirements

• Force structure analysis highlighted differences between ‘ideal’ force and 2015 post-Afghanistan force

• Generated three coherent force structures for 10% and 20% savings levels

• Tested forces emerging from Senior Decision Maker discussion

• Informed VCDS Senior Judgement Panel debates on the value of major force elements

Analysis supported the development of Future Force 2020


Output Evolution

• Increasing number of levels of information– From Whole Force Structure, Capability Packages / Areas, down to Force Elements

• Increasing range of tailored communication methods– Including; handouts, interactive briefings, supported desk level discussions, memos

• Increasing amount of interaction – From set handout or brief to interactive briefs holding a depth of information as required.

Impact of possible Policy

ChoicesCapability Audit

Risks

Impact of PR11

Measures

Cost Effectivenes

s of Force Elements

Post SDSR Post SDSR with PR11 Measures

Epoch 1 Epoch 2 Epoch 1 Epoch 2

ABCDEFGHIJKLMNO

Capability Packages

Force Structure

2010 2015 2020RISK 1RISK 2RISK 3


Whew!

Presented to Parliament

by the Prime Minister

by Command of Her Majesty

October 2010


Output Evolution






Risks

Impact of PR11

Measures

Cost Effectivenes

s of Force Elements



ABCDEFGHIJKLMNO

Capability Packages

Force Structure

2010 2015 2020RISK 1RISK 2RISK 3



StratBoi Introduction

• StratBoi provides evidence to inform Senior Decision Makers on adjusting the balance of funding between capability areas

– Has been providing independent, auditable and coherent evidence, since 2009

– Draws from the breadth of MOD’s analysis programme

Given what the UK Defence wants to be able to do…

What is the most cost effective mix of capabilities to do this?



StratBoi Analysis - Method SCENARIOS

CAMPAIGNS

EFFECTS

TASKS

SYSTEM OPTIONS

ENABLER OPTIONS

OPTIMISATION

‘OPTIMUM’ FORCE POOL

SYSTEM AVAILABILITY

CONCURRENCY REQUIREMENTS

COSTS




CAMPAIGNS

EFFECTS

TASKS

SYSTEM OPTIONS

ENABLER OPTIONS

OPTIMISATION


SYSTEM AVAILABILITY


COSTS

Defence Policy




CAMPAIGNS

EFFECTS

TASKS

SYSTEM OPTIONS

ENABLER OPTIONS

OPTIMISATION


SYSTEM AVAILABILITY


COSTS

Tasks




CAMPAIGNS

EFFECTS

TASKS

SYSTEM OPTIONS

ENABLER OPTIONS

OPTIMISATION


SYSTEM AVAILABILITY


COSTS

Constraints




CAMPAIGNS

EFFECTS

TASKS

SYSTEM OPTIONS

ENABLER OPTIONS

OPTIMISATION


SYSTEM AVAILABILITY


COSTS

System Option Costs




CAMPAIGNS

EFFECTS

TASKS

SYSTEM OPTIONS

ENABLER OPTIONS

OPTIMISATION


SYSTEM AVAILABILITY


COSTS

Sufficient Force Structure

at Minimum Cost




CAMPAIGNS

EFFECTS

TASKS

SYSTEM OPTIONS

ENABLER OPTIONS

OPTIMISATION


SYSTEM AVAILABILITY


COSTS

Defence Policy Iteration


1 May 2023

At the heart of StratBoi is a Mixed Integer Linear Programme

• The Linear Programme generates cost-effective force mixes• Approach

– Provide a clear and auditable relationship between Policy, Capabilities and the Force Structure

– Minimise total cost subject to constraints on task effectiveness– Iterate



Example Output: Comparison by Domain


Output Evolution






Risks

Impact of PR11

Measures

Cost Effectivenes

s of Force Elements



ABCDEFGHIJKLMNO

Capability Packages

Force Structure

2010 2015 2020RISK 1RISK 2RISK 3

Some Personal Reflections

Not necessarily reflecting the views of either Dstl or MoD

1 May 2023


Analysis Interventions

1 May 2023

Messes Problems Puzzles

Interventions

Solution(s)

Typically, problem structuring support, SME workshops etc

Typically via the production of models, methods and other

repeatable approaches

1 2

http://www.google.co.uk/imgres?imgurl=http://us.cdn2.123rf.com/168nwm/prawny/prawny0601/prawny060100111/309436-man-with-a-key-to-the-door-but-which-door.jpg&imgrefurl=http://www.123rf.com/photo_309440_holding-the-key--businessman-holding-the-key-to-the-door-or-problem.html&usg=__vsqwpLZnbvSUTgrYeti1M4uGDP8=&h=127&w=168&sz=6&hl=en&start=83&zoom=1&itbs=1&tbnid=6FW-lMro8vRv3M:&tbnh=75&tbnw=99&prev=/search?q=key+to+the+door&start=80&hl=en&sa=N&biw=1260&bih=891&ndsp=20&tbm=isch&prmd=ivns&ei=8tQ_TqWPBZPE8QPWgrDcCw


Traditional war fighting analysis is well covered

Abridged extract


Cyber is a newly emerging analysis area, and a key future requirement

Abridged extract


1 May 2023

Questions?

Data & Analytics

The Impact of Mathematics on Defence Policy