Undergraduate Teaching 2023-24

Engineering Tripos Part IIA, 3E3: Modelling Risk, 2023-24

Engineering Tripos Part IIA, 3E3: Modelling Risk, 2023-24

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Dr M Herrera


Dr M Herrera

Lab Leader

Dr M Herrera

Timing and Structure

Lent term. 2 lectures/week. 16 lectures.


Basic probability theory and statistics and basic knowledge of using Excel of Microsoft.


The aims of the course are to:

  • Provide an understanding of a range of management science modelling methods involving randomness, such as statistics, decision analysis, behavioral factors, portfolio management, process analysis, queueing theory, forecasting, and regression.
  • For each of the modelling areas, students will become familiar with the types of situations in which the method is useful.


As specific objectives, by the end of the course students should be able to:

  • Understand basic concepts of probability and the rationale behind statistical reasoning.
  • Be able to calculate statistical measures like mean and variance, and interpret these in realistic situations.
  • Use confidence intervals to quantify risk.
  • Conduct hypothesis testing.
  • Be able to understand decision trees and how to apply them in decision making.
  • Identify and manage the bottleneck in a serial process, calculate the throughput of the entire system and utilisation at each step.
  • Understand and use simple formulas for queues in which arrivals occur as a Poisson process.
  • Understand the role of behavioral biases in decision making.
  • Forecast data using short range extrapolative techniques such as exponential smoothing.
  • Know how to take account of seasonality when forecasting.
  • Apply regression techniques to estimate the way in which two variables are related.
  • Be able to understand investment strategies for portfolios.
  • Be able to incorporate risk into investment and decision making.


"There are known knowns. These are things we know that we know. There are known unknowns. That is to say, there are things that we know we don't know. But there are also unknown unknowns. These are things we don't know we don't know."

- Donald Rumsfeld


Note: The content covered across all lectures and example papers will be as listed below. However, elements of the content may be re-sequenced to achieve a better flow. 

Mathematical Analysis of Deterministic and Stochastic Processes (4L)

  • Process Analysis: Identify and manage the bottleneck in a serial process, calculate the throughput of the entire system and utilisation at each step, evaluate the impact of improvements to different steps in a process.
  • Queueing theory: Poisson arrival processes, classification of queueing systems, steady state, performance measures, Little's formula, benefits and limitations of queueing theory.

Regression Analysis and Forecasting (4L)

  • Simple linear regression analysis, least squares estimates, significance of  regression, multiple regression, multi-collinearity.
  • Different methods for forecasting: moving average, exponential smoothing, modelling seasonality and trends.

Inventory Management (2L)

  • Basic concepts in inventory management: inventory management under stochastic demand.

Portfolio Management (2L)

  • Basic portfolio concepts
  • Risk and expected return on a portfolio, and the efficient frontier.

Decision Analysis (4L)

  • Events and decisions, decision trees, expected monetary value, sensitivity analysis, expected value of perfect information, expected value of sample information.
  • Behavioural Factors in Decision Making

Examples papers

In this course, we will have examples classes for all students at the same time, rather than supervisions for small groups.

  • Class 1: Process Analysis and Queuing theory.   
  • Class 2: Regression, forecasting, and inventory management.
  • Class 3: Portfolio and decision analysis.  


To be announced in lectures.

There is no Full Technical Report (FTR) associated with this module.


Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.

Examination Guidelines

Please refer to Form & conduct of the examinations.


This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.


Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.


Apply appropriate quantitative science and engineering tools to the analysis of problems.


Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.


Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.


Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.


Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.


A comprehensive understanding of the scientific principles of own specialisation and related disciplines.


A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.

Last modified: 30/10/2023 14:58