The course provides a detailed exposure to the context, issues and methods used to analyse the increasingly complex problems which are found in the defence environment and to support decision making.

At a glance

  • Start dateSeptember
  • DurationMSc: 11 months full-time, Up to five years part-time. PgDip :Up to 11 months full-time, Up to four years part-time. PgCert: Up to 11 months full-time. Up to 3 years part-time
  • DeliveryContinuous assessment, written examinations, oral vivas and (MSc only) thesis.Proportions of different assessment types will vary according to programme and elective options chosen.
  • QualificationMSc, PgDip, PgCert
  • Study typeFull-time / Part-time

Who is it for?

The course is suitable for both military and civilian personnel, including those from defence industry and government departments. 10 places are normally available for the full-time cohort.

Why this course?

The course provides a detailed exposure to the context, issues and methods used to analyse the increasingly complex problems which are found in the defence environment and to support decision making. It exposes the types of analysis and allows practical experience of tools and methods which are used, ranging from judgemental analysis through mathematical techniques to models and simulations. The course includes judgemental elicitation and analysis techniques, mathematical analysis methods (including optimisation), war gaming and combat modelling, logistics modelling and simulation methods. The use and utility of all the methods are explored through practical exercises and studies.

On successful completion of the course you will:

  • Demonstrate a thorough understanding of the methods, techniques and tools for modelling defence problems and systems
  • Be able to critically assess a range of approaches and methods to help support defence analysis and decision-making.

Informed by Industry

The aim of the Industrial Advisory Panel, which is common to all components of the AMOR Postgraduate Suite, is to offer advice and input to the Course Director and the teaching team in terms of curriculum content, acquisition skills and other attributes that the practitioner community may be seeking from graduates of the course. Currently the Industrial Advisory Panel for this program has members on it from both Defence Industry (including Cassidian, BAE Systems and AWE) and the MOD.

Your teaching team

The team is joined by External Speakers from industry and defence (due to frequency of post changes it is not practical to include names).

Course details

MSc students must complete a taught phase consisting of 12 standard modules, which includes two core modules (Introduction to Operational Research Techniques and Decision Analysis), plus four advanced modules, followed by an individual thesis in a relevant topic.

Thesis topics will be related to problems of specific interest to students and sponsors or local industry wherever possible. PgDip students are required to undertake the same taught phase as the MSc, but without the individual thesis. PgCert students must complete the core module (Introduction to Operational Research Techniques) together with five other modules; up to three of these may be advanced modules.

Individual project

An individual research project on an agreed topic that allows you to demonstrate your technical expertise, independent learning abilities and critical appraisal skills.

Assessment

Continuous assessment, written examinations, oral vivas and (MSc only) thesis.Proportions of different assessment types will vary according to programme and elective options chosen.

University Disclaimer

Keeping our courses up-to-date and current requires constant innovation and change. The modules we offer reflect the needs of business and industry and the research interests of our staff and, as a result, may change or be withdrawn due to research developments, legislation changes or for a variety of other reasons. Changes may also be designed to improve the student learning experience or to respond to feedback from students, external examiners, accreditation bodies and industrial advisory panels.

To give you a taster, we have listed the core modules and some optional modules affiliated with this programme which ran in the academic year 2017–2018. There is no guarantee that these modules will run for 2018 entry. All modules are subject to change depending on your year of entry.

Compulsory modules
All the modules in the following list need to be taken as part of this course

Decision Analysis

Module Leader
  • Dr Ken McNaught
Aim
    To provide students with a good understanding of the various methods, both quantitative and qualitative, of structuring and analysing decision-making problems and the ability to identify appropriate methods to apply in practical situations.
Syllabus
    • Introduction: The role and scope of decision analysis in supporting decision making.
    • Pay-off Matrices: Structuring decision problems using a pay-off matrix to represent the value or utility of each option for each possible state of nature. Analysing the pay-off matrix under conditions of uncertainty and risk. Sensitivity/robustness of decisions to the inputs.
    • Decision Trees: Structuring and analysing decision problems using a decision tree to represent sequential decision making under conditions of risk and uncertainty. The application of Bayes' Theorem to update probabilities in the light of new information. The calculation of the value of perfect and imperfect information.
    • Bayesian Networks and Influence Diagram Decision Networks: These modern tools are examples of probabilistic graphical models which offer a powerful framework for reasoning and decision-making under risk and uncertainty. Modelling assumptions and development, example applications and software.
    • Game Theory: Classical two-person zero-sum game theory and its application to decision making under conditions of competition or conflict. Extensions of the classical theory to non zero-sum games.
    • Judgmental Methods: The elicitation and analysis of individual judgements as part of the decision making process: the strategy to task technique, the Delphi technique, the analytic hierarchy process and an associated consensus methodology.
    • Soft Systems Methods: A review and brief introduction to some of the "softer" methods used to support decision-makers. The topics covered will include Checkland's soft systems methodology, hypergames and metagames, robustness analysis and approaches to strategic decision making.
    • Multiple Criteria Decision Analysis: A review of the different approaches used in multiple criteria decision analysis where several, often conflicting, criteria are important to a decision-maker: aggregate value methods to permit trade-offs in multiple attribute decision making and mathematical programming methods in multiple objective decision making.
    • Software for Decision Analysis: Throughout the course reference will be made to the application of decision analysis software to help support the decision making process, including demonstrations and hands-on practicals.
Intended learning outcomes On successful completion of the module the student will be able to:

  • Structure decision problems using a pay-off matrix and analyse the pay-off matrix under conditions of uncertainty, risk and competition
  • Structure and analyse sequential decision problems using a decision tree
  • Structure and analyse decision problems using Bayesian networks and influence diagram decision networks
  • Structure and analyse decision problems based on using expert judgments
  • Explain and apply the different approaches used in multiple criteria decision analysis
  • Explain how the different methods of representing decision problems can be used to support defence decision-making.

Introduction to Operational Research Techniques

Module Leader
  • Mr Jeremy Smith
Aim
    The module will introduce the basic philosophy of operational research and a selection of the analytical techniques used by practitioners.
Syllabus
    • Concepts of probability.
    • Mathematical programming including linear programming.
    • Queuing theory.
    • Simulation.
    • Network analysis.
    • Dynamic programming.
    • Search theory.
Intended learning outcomes On successful completion of the module the student will be able to:
  • Use the basic concepts of probability.
  • Formulate problems into the standard mathematical programming formulation.
  • Solve linear programming problems using a graphical method or the simplex algorithm.
  • Demonstrate understanding of the ideas of queuing theory by using mathematical methods to analyse queuing systems.
  • Classify simulations.
  • Design and carry out discrete event simulations.
  • Use a network algorithm to find the critical path through a network.
  • Formulate and solve dynamic programming problems.
  • Apply the basic principles of search theory.

Discrete and Continuous Simulation

Module Leader
  • Dr Ken McNaught
Aim
    To provide students with a good understanding of the principles underlying both discrete event simulation and continuous simulation focussing, in the latter case, on System Dynamics modelling.
Syllabus
    • Simulation modelling paradigms
    • Conceptual models (activity cycle diagrams, causal loop diagrams and stock/flow diagrams)
    • Input modelling (the selection and fitting of appropriate probability distributions for stochastic simulations)
    • Output analysis (methods for comparing and analysing the results of simulation experiments)
    • Discrete Event Simulation principles and types of software
    • Developing and experimenting with Discrete Event Simulation models using an appropriate software package (currently SIMUL8)
    • System Dynamics principles
    • Developing and experimenting with System Dynamics models using an appropriate software package (currently Vensim)
Intended learning outcomes On successful completion of the module the student will be able to:

  • Describe the origins and the main principles underlying both Discrete Event Simulation and System Dynamics
  • Develop conceptual models of systems prior to their simulation
  • Identify feedback loops within a System Dynamics model and understand the effects of positive and negative feedback
  • Distinguish between the different types of variables commonly used in System Dynamics models
  • Develop a System Dynamics model from an appropriate diagram
  • Select appropriate probability distributions for use in stochastic simulations
  • Develop a Discrete Event Simulation model of a simple system
  • Perform appropriate experiments, policy analysis and output analysis with the completed simulation model.

War Gaming and Combat Modelling

Module Leader
  • Mr Jeremy Smith
Aim
    To provide students with a general knowledge of the techniques used in wargaming, combat simulations and analytical battle models.
Syllabus
    • Introduction: An introduction to the methods used in combat modelling and their application in support of defence decision-making and training
    • Combat Simulation: The basic principles of discrete event Monte Carlo simulations of combat illustrated through the use of a simple engagement model. Extension of the concepts to allow more realistic representation of the battlefield. Aggregated models of combat
    • Lanchester's Equations: The deterministic and stochastic Lanchester equations for direct and indirect fire as used for both homogeneous and heterogeneous forces. The application of Lanchester's equations in current models of combat
    • War Gaming/lnteractive Simulation: The underlying principles of war gaming and the interactive simulation of combat as used for the assessment, testing and training of military forces and their equipment. The synthetic battlefield. Synthetic Environments: constructive, virtual and live simulations of combat. Manual Combat Wargames. Other gaming techniques.
    • War Gaming and Combat Modelling Practicals: The practical application of war gaming and combat modelling with issues such as: data and scenarios, terrain modelling, combat algorithms (attrition and movement), the representation of human factors, measures of effectiveness, the verification and validation of combat models, automated forces, simulation for training and distributed simulation.
Intended learning outcomes On successful completion of the module you will be able to:

  • Critically appraise the full range of wargames and combat simulations and apply them to defence problems
  • Use the deterministic and stochastic Lanchester equations to represent combat between both homogeneous and heterogeneous forces
  • Use interactive computer based representations of military operations
  • Explain how the different methods of representing the operations of military forces are used in the training, testing and assessment of those forces and their equipment.

Logistics Modelling

Module Leader
  • Mr Mark Lewis
Aim
    The module will provide students with a good understanding of the principles and techniques of Logistics Modelling. The emphasis is on the development and application of quantitative models to support logistical analysis.
Syllabus
    • Logistics methodologies
    • Modelling distribution networks with linear programming approaches
    • Inventory control
    • Reliability, availability and maintenance modelling
    • Simulation of logistics systems.
Intended learning outcomes On successful completion of the module the student will be able to:

  • Describe the most important logistical methodologies such as Just In Time (JIT), Integrated Logistic Support (ILS) and Material Requirement Planning (MRP)
  • Describe the similarities and differences between commercial and military logistics systems
  • Perform simple reliability and replacement calculations
  • Calculate the optimum level of spare parts to hold in some simple settings
  • Derive and apply the Economic Order Quantity formula in inventory control
  • Describe various inventory control systems and understand their strengths and weaknesses
  • Perform a Pareto analysis of an organisation’s stockholding
  • Formulate and solve simple shortest-path, assignment, transportation and trans-shipment problems
  • Perform a set of MRP calculations
  • Describe the role of simulation in designing logistical systems.

Statistical Analysis and Trials

Module Leader
  • Dr Trevor Ringrose.
Aim

    To give students an introduction to probability distributions, the design of experiments and the analysis of data.

Syllabus

    Pre-course reading including topics marked*

    • Principles of data collection, organisation, analysis and interpretation*
    • Graphing and summarising data, exploratory data analysis*
    • Probability*
    • Probability distributions
    • Confidence intervals and significance tests for large and small samples
    • Tests of consistency and goodness of fit
    • Non-parametric methods
    • Introduction to experimental/trials design
    • Regression and analysis of variance for the analysis of experimental data
    • Statistical aspects of simulation modelling.
Intended learning outcomes

On successful completion of the module the student will be able to:

  • Calculate probabilities from distributions such as the binomial, Poisson and normal
  • Perform z and t tests and construct z and t confidence intervals, and know when they are appropriate
  • Perform simple non-parametric tests and know when they are appropriate
  • Appreciate the basic principles of experimental design, such as randomisation and factorial designs
  • Analyse data using simple linear regression and one and two-way analysis of variance, and assess when these are appropriate
  • Set up a simple Markov chain.

Weapon System Performance Assessment

Module Leader
  • Mr Jeremy Smith
Aim

    To enable students to understand the application of operational research techniques to the assessment of weapon systems.

Syllabus
    • Concepts of performance and effectiveness measures
    • Dispersion of fire
    • Accuracy, consistency and precision
    • Calculation of Single Shot Kill Probability for direct fire weapons
    • Modelling of area effect weapons (eg shells, grenades) including using the damage function
    • Modelling of minefields and calculation of stopping power
    • Assessment of direct fire systems examples
    • Methods for modelling of land, sea and air targets
    • Approaches to the analysis of various other weapon systems
    • Force effectiveness comparisons
    • Practical exercises to illustrate the theories
Intended learning outcomes On successful completion of the module the student will be able to:

  • Describe the cycle of weapon assessment studies and the measures of performance and effectiveness
  • Demonstrate the application of statistics to weapon delivery errors
  • Discuss the nature of direct fire weapons and demonstrate how to calculate their performance
  • Review the nature of area weapons and demonstrate the use of the damage function and lethal area in the analysis of their effects
  • Use a technique for the analysis of anti-tank minefields
  • Appreciate the different emphasis in the study of guided weapon systems
  • Review the special nature of other weapon systems and the ideas involved in their assessment
  • Evaluate the need and collection methods for data in models
  • Explain the issues surrounding practical weapon assessment projects including force effectiveness and cost effectiveness analyses.

Intelligent Systems

Module Leader
  • Dr Venkat Sastry
Aim
    To provide students with basic knowledge of intelligent systems techniques that can be applied in a variety of disciplines.
Syllabus
    • Review of intelligent systems
    • Problem spaces and architectures
    • Classical inference techniques
    • Review of search algorithms
    • Reasoning under uncertainty
    • Fuzzy reasoning
    • Bayesian networks
    • Rule based programming.
Intended learning outcomes

On successful completion of the module the student will be able to:

  • Develop a simple application using rule based programming
  • Develop simple applications using fuzzy inference and Bayesian network techniques
  • Assess available architectures and techniques for a practical problem under consideration.

Advanced Module 1

Module Leader
Aim

    The aim of this module is to allow students to conduct an in-depth study in an area of particular personal interest or relevance to them, in the context of their degree.


Syllabus

    A self-study ‘mini-project’ conducted over two weeks, on an individually selected and agreed topic, which must follow on from one or more already completed standard taught modules in that degree.

    Part-time students will typically complete their work over a 10-week period, one such block of 10 weeks being offered in each academic term.



Intended learning outcomes On successful completion of the module a diligent student will be able, within the individual topic agreed, to:

  • Plan, organise and undertake an individual, open-ended research activity with appropriate supervision
  • Demonstrate an ability to acquire, organise, discuss, assess and apply relevant knowledge
  • Demonstrate an ability to gather and critically appraise data and to utilise it within the appropriate context
  • Critically apply appropriate methods, tools, techniques, processes and knowledge to the topic selected
  • Communicate findings in the form of both a written deliverable and an oral presentation.


Advanced Module 2

Module Leader
Aim

    The aim of this module is to allow students to conduct an in-depth study in an area of particular personal interest or relevance to them, in the context of their degree.


Syllabus

    A self-study ‘mini-project’ conducted over two weeks, on an individually selected and agreed topic, which must follow on from one or more already completed standard taught modules in that degree.

    Part-time students will typically complete their work over a 10-week period, one such block of 10 weeks being offered in each academic term.



Intended learning outcomes On successful completion of the module a diligent student will be able, within the individual topic agreed, to:

  • Plan, organise and undertake an individual, open-ended research activity with appropriate supervision
  • Demonstrate an ability to acquire, organise, discuss, assess and apply relevant knowledge
  • Demonstrate an ability to gather and critically appraise data and to utilise it within the appropriate context
  • Critically apply appropriate methods, tools, techniques, processes and knowledge to the topic selected
  • Communicate findings in the form of both a written deliverable and an oral presentation.


Advanced Module 3

Module Leader
Aim

    The aim of this module is to allow students to conduct an in-depth study in an area of particular personal interest or relevance to them, in the context of their degree.


Syllabus

    A self-study ‘mini-project’ conducted over two weeks, on an individually selected and agreed topic, which must follow on from one or more already completed standard taught modules in that degree.

    Part-time students will typically complete their work over a 10-week period, one such block of 10 weeks being offered in each academic term.



Intended learning outcomes On successful completion of the module a diligent student will be able, within the individual topic agreed, to:

  • Plan, organise and undertake an individual, open-ended research activity with appropriate supervision
  • Demonstrate an ability to acquire, organise, discuss, assess and apply relevant knowledge
  • Demonstrate an ability to gather and critically appraise data and to utilise it within the appropriate context
  • Critically apply appropriate methods, tools, techniques, processes and knowledge to the topic selected
  • Communicate findings in the form of both a written deliverable and an oral presentation.


Advanced Module 4

Module Leader
Aim

    The aim of this module is to allow students to conduct an in-depth study in an area of particular personal interest or relevance to them, in the context of their degree.


Syllabus

    A self-study ‘mini-project’ conducted over two weeks, on an individually selected and agreed topic, which must follow on from one more already completed standard taught modules in that degree.

    Part-time students will typically complete their work over a 10-week period. One such block of 10 weeks being offered in each academic term.


Intended learning outcomes On successful completion of the module a diligent student will be able, within the individual topic agreed, to:
  • Plan, organise and undertake an individual, open-ended research activity with appropriate supervision.
  • Demonstrate an ability to acquire, organise, discuss, assess and apply relevant knowledge.
  • Demonstrate an ability to gather and critically appraise data and to utilise it within the appropriate context.
  • Critically apply appropriate methods, tools, techniques, processes and knowledge to the topic selected.
  • Communicate findings in the form of both a written deliverable and an oral presentation.

Fees and funding

European Union students applying for university places in the 2017 to 2018 academic year and the 2018 to 2019 academic year will still have access to student funding support. Please see the UK Government’s announcement (21 April 2017).

Cranfield University welcomes applications from students from all over the world for our postgraduate programmes. The Home/EU student fees listed continue to apply to EU students.

MSc Full-time £19,000
MSc Part-time £19,000 *
PgDip Full-time £15,300
PgDip Part-time £15,300 *
PgCert Full-time £7,650
PgCert Part-time £7,650 *
  • * Fees can be paid in full up front, or in equal annual instalments, up to a maximum of two payments per year; first payment on or before registration and the second payment six months after the course start date. Students who complete their course before the initial end date will be invoiced the outstanding fee balance and must pay in full prior to graduation.

Fee notes:

  • The fees outlined apply to all students whose initial date of registration falls on or between 1 August 2018 and 31 July 2019.
  • All students pay the tuition fee set by the University for the full duration of their registration period agreed at their initial registration.
  • For self-funded applicants a non-refundable £500 deposit is payable on offer acceptance and will be deducted from your overall tuition fee.
  • Additional fees for extensions to the agreed registration period may be charged and can be found below.
  • Fee eligibility at the Home/EU rate is determined with reference to UK Government regulations. As a guiding principle, EU nationals (including UK) who are ordinarily resident in the EU pay Home/EU tuition fees, all other students (including those from the Channel Islands and Isle of Man) pay Overseas fees.

For further information regarding tuition fees, please refer to our fee notes.



MSc Full-time £19,000
MSc Part-time £19,000 *
PgDip Full-time £15,300
PgDip Part-time £15,300 *
PgCert Full-time £7,650
PgCert Part-time £7,650 *
  • * Fees can be paid in full up front, or in equal annual instalments, up to a maximum of two payments per year; first payment on or before registration and the second payment six months after the course start date. Students who complete their course before the initial end date will be invoiced the outstanding fee balance and must pay in full prior to graduation.

Fee notes:

  • The fees outlined apply to all students whose initial date of registration falls on or between 1 August 2018 and 31 July 2019.
  • All students pay the tuition fee set by the University for the full duration of their registration period agreed at their initial registration.
  • For self-funded applicants a non-refundable £500 deposit is payable on offer acceptance and will be deducted from your overall tuition fee.
  • Additional fees for extensions to the agreed registration period may be charged and can be found below.
  • Fee eligibility at the Home/EU rate is determined with reference to UK Government regulations. As a guiding principle, EU nationals (including UK) who are ordinarily resident in the EU pay Home/EU tuition fees, all other students (including those from the Channel Islands and Isle of Man) pay Overseas fees.

For further information regarding tuition fees, please refer to our fee notes.



Funding Opportunities

Please contact studentfunding@cranfield.ac.uk for more information on funding.

Entry requirements

A first or second class Honours degree or equivalent in science, engineering or mathematics. Alternatively, a lesser qualification together with appropriate work experience may be acceptable.

English Language

If you are an international student you will need to provide evidence that you have achieved a satisfactory test result in an English qualification. The minimum standard expected from a number of accepted courses are as follows:

In addition to these minimum scores you are also expected to achieve a balanced score across all elements of the test. We reserve the right to reject any test score if any one element of the test score is too low.

We can only accept tests taken within two years of your registration date (with the exception of Cambridge English tests which have no expiry date).

Students requiring a Tier 4 (General) visa must ensure they can meet the English language requirements set out by UK Visas and Immigration (UKVI) and we recommend booking a IELTS for UKVI test.

Security clearance for Shrivenham

Some Cranfield University courses are delivered at the Defence Academy of the United Kingdom, Shrivenham which is a Ministry of Defence (MOD) site. All applicants to courses that are wholly or partially delivered at Shrivenham must complete the BPSS (HMG Baseline Personnel Security Standard V4 April 2014) prior to registration on the course or must already hold a security clearance to this level or higher.

Please visit our security clearance page for further information.



Your career

The course equips you for appointments within the armed forces or government, or in the defence related activities of commercial organisations, or further research leading to a PhD.

Applying

Applicants may be invited to attend an interview. Applicants based outside of the UK may be interviewed either by telephone or video conference.

Apply now