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.

10 places are normally available for the full-time cohort.

Overview

  • Start dateSeptember
  • DurationMSc: one year full-time, up to three years part-time; PgDip: up to one year full-time, up to two years part-time; PgCert: up to one year full-time, up to two years part-time
  • DeliveryAssessment is 50% by coursework, 10% by exam and 40% thesis/dissertation
  • QualificationMSc, PgDip, PgCert
  • Study typeFull-time / Part-time
  • CampusCranfield University at Shrivenham

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 programme has members on it from both the defence industry and the MoD.

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.

Course delivery

Assessment is 50% by coursework, 10% by exam and 40% thesis/dissertation

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.

Modules

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 compulsory and elective (where applicable) modules which are currently affiliated with this course. All modules are indicative only, and may be subject to change for your year of entry.


Course modules

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

Introductory Studies

Module Leader
  • Dr John Salt
Aim

    To prepare you mathematically and organisationally to study at CDS on the Defence Simulation and Modelling and Military Operational Research Postgraduate programs.




Syllabus
    • Course Structure,
    • Intro to IT (Email, VLE, Online Access),
    • Library Introduction and Referencing,
    • Fundamental Mathematics: Probability, Statistics, Algebra, Equations (linear, polynomial, exponential and logarithmic),
    • Further Mathematics for MOR only: Matrices, Linear Systems and Solution, Differentiation, and Integration,
    • Introduction to MATLAB (MOR students only),
    • Fundamentals of Computing,
    • Spreadsheet Basics,
    • Study skills for postgraduate study.
Intended learning outcomes

On successful completion of this module you will be able to:

  • Describe the course structure and assessment procedures,
  • Demonstrate the ability to find and correctly cite research material,
  • Understand the fundamental mathematics required by the course,
  • To understand the study skills necessary to complete a postgraduate degree.

Introduction to Operational Research Techniques

Module Leader
  • Jeremy Smith
Aim
    To 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 this module you will be able to:

  • Use the basic concepts of probability and search theory,
  • Formulate problems into mathematical programming formulations including dynamic programming and linear programming and solve them,
  • Demonstrate understanding of the ideas of queuing theory by using mathematical methods to analyse queuing systems,
  • Demonstrate understanding of discrete event simulations,
  • Use a network algorithm to find the critical path through a network.

Discrete and Continuous Simulation

Aim

    The aim of the course is to provide you with a good understanding of the principles underlying both discrete event simulation (DES) and continuous simulation, focusing, in the latter case, on System Dynamics (SD) 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),
    • DES principles and types of software,
    • Developing and experimenting with DES models using an appropriate software package (currently SIMUL8),
    • System Dynamics principles,
    • Developing and experimenting with SD models using an appropriate software package (currently Vensim).
Intended learning outcomes

On successful completion of this module you will be able to:

  • Describe the origins and the main principles underlying both DES and SD,
  • Develop conceptual models of systems prior to their simulation,
  • Select appropriate probability distributions for use in stochastic simulations,
  • Develop DES and SD models of simple systems,
  • Perform appropriate experiments, policy analysis and output analysis with the completed simulation model.

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; the nature and effects of various cognitive biases affecting judgement.

    Problem Structuring Methods: a review and brief introduction to some of the ‘softer’ methods used to support decision makers. The topics covered will include the Strategic Choice Approach, scenario planning, cognitive mapping 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 this module a student should 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.
 

War Gaming and Combat Modelling

Module Leader
  • Jeremy Smith
Aim
    To provide you 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 this 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.

Statistical Analysis and Trials

Module Leader
  • Dr Trevor Ringrose
Aim

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

Syllabus
    • 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 this module you will be able to:

  • Calculate probabilities from distributions such as the binomial, Poisson and normal,
  • Perform z, t and non-parametric tests and construct z and t confidence intervals, 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
  • Jeremy Smith
Aim

    To enable you 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,
    • Cost effectiveness principles.
Intended learning outcomes

On successful completion of this module you will be able to:

  • Apply the cycle of weapon assessment studies and the measures of performance and effectiveness,
  • Evaluate the need and collection methods for data in models and the application of statistics,
  • Analyse the nature of various direct fire weapons and calculate performance measures for them,
  • Review the nature of area weapons and apply the damage function and lethal area in the analysis of their effects,
  • Explain the issues surrounding practical weapon assessment projects including force effectiveness and cost effectiveness analyses.

Intelligent Systems

Aim

    The aim of this module is to provide you with basic knowledge of intelligent systems techniques that can be applied in a variety of disciplines.



Syllabus
    • Overview of Intelligent Systems; Basic approaches to developing intelligent systems,
    • Overview of Architectures; Reasoning under uncertainty,
    • Fuzzy reasoning,
    • Bayesian networks,
    • Introduction to Artificial Neural Networks; Deep Neural Networks,
    • Hebbian learning Principle,
    • Supervised learning and unsupervised learning – perceptrons and multilayer perceptrons; basics of perceptron learning algorithm; a selection of machine learning algorithms,
    • Neural Networks for classification and prediction – discussion of case studies,
    • Review of comparable statistical techniques.
Intended learning outcomes

On successful completion of this module you will be able to:

  • Develop an application of intelligent systems using either fuzzy rule-based or Neural Network or Bayesian Belief Networks or a combination of techniques,
  • Assess the performance of developed systems,
  • Appreciate the role of data pre-processing and representation.

Logistics Modelling

Module Leader
  • Dr John Salt
Aim

    The aim of the module is to provide you 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 decision-making.

Syllabus
    • Logistics methods,
    • 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 this module you will be able to:

  • Describe the elements of a logistical system,
  • Select and apply suitable methods to solve logistical problems in stock control, transport, or ARM,
  • Present and critically evaluate the solutions so obtained.

Advanced Module 1

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

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

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

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.

Teaching team

You will be taught by Cranfield's leading experts with capability expertise, industry knowledge and collective subject research, as well as external speakers from industry and defence. The Student Academic Support lead for the MSc in Military Operational Research is Karen Crouch and the Course Director is Jonathan Searle. The teaching team includes:

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.

How to apply

Click on the ‘Apply now’ button below to start your online application.

See our Application guide for information on our application process and entry requirements.