Mathematics, Operational Research, Statistics and Economics (MORSE)

This module covers the skills needed to improve business process by modelling and simulation.

Computer simulation methods are among the most commonly used approaches within operational research and management science. This module teaches you the skills required to apply simulation successfully to help improve the running of a business, and it shows how companies can find good solutions by predicting the effects of changes before implementing them.

Modern simulation packages are a valuable aid in building a simulation model, and this module uses the Witness simulation package, which is widely used commercially. However, without the proper approach, the results of a simulation project can be incorrect or misleading. This module looks at each task required in a simulation project. It emphasises the practical application of simulation, with a good understanding of how a simulation model works being an essential part of this.

Students will be provided with the foundational results and language of linear algebra, which they will be able to build upon in the second half of Year Two, and the more specialised Year Three modules. This module will give students the opportunity to study vector spaces, together with their structure-preserving maps and their relationship to matrices.

They will consider the effect of changing bases on the matrix representing one of these maps, and will examine how to choose bases so that this matrix is as simple as possible. Part of their study will also involve looking at the concepts of length and angle with regard to vector spaces.

The objective of the course is to train students to use macroeconomic models to understand real-world economic phenomena. The students will learn how to interpret macroeconomic data and understand the implications of economic policies. The course will put emphasis on major issues related to economic growth, the causes of economic fluctuations, and the effectiveness of economic policy. We will investigate the link between financial openness and economic growth, and we will explain why emerging countries experience capital outflows. We will study the impact of the exchange rate regime on the effectiveness of fiscal policy, we will rationalise the increase of current account deficits in Europe after the beginning of the nineties, and we will analyse the cause(s) of cross-country differences in hours worked.

The module requires basic knowledge of basic calculus, logical thinking and problem-solving skills.

Various topics of interest to prospective managers are covered within this module, including production and demand, competition and strategic behaviour, advertising and distribution, capital budgeting and inventories, the foreign exchange market, the economics of the multinational enterprise and the politics of corporate economics. The module provides knowledge of aspects of microeconomics relevant to general management, and also emphasises techniques and tools of analysis alongside relevant theory.

The module is designed to as an introduction to aspects of the firm and its environment which are of particular relevance to management. The topics selected aim to bridge the gap between the traditional approach to managerial economics and the more modern study of the organisation.

This module describes a variety of optimisation algorithms and how business problems can be modelled using these techniques.

Optimisation is one of the primary techniques associated with management science/operational research. Sometimes called Mathematical Programming, optimisation is concerned with finding the ‘best’ solution to a problem that has a large number of possible solutions. It has a huge array of applications in many fields, and optimisation models are now used routinely in industry (especially in manufacturing, energy production and transport), in the public sector (especially defence and healthcare) and in the services (especially finance). Therefore, skills in formulating and solving optimisation problems are valuable for a variety of careers. The course is designed to enable students to apply optimisation techniques to business problems. Students should take it if they are interested in modelling real situations via mathematics. However, the goal is not mathematics for its own sake. We also want the students to have an understanding of the types of situations in which the various techniques can (or cannot) be applied.

Four main topics are covered:

• Linear programming

• Specially-structured linear programs

• Integer and mixed-integer programming

• Heuristics for large-scale problems

Probability provides the theoretical basis for statistics and is of interest in its own right.

Basic concepts from the first year probability module will be revisited and extended to these to encompass continuous random variables, with students investigating several important continuous probability distributions. Commonly used distributions are introduced and key properties proved, and examples from a variety of applications will be used to illustrate theoretical ideas.

Students will then focus on transformations of random variables and groups of two or more random variables, leading to two theoretical results about the behaviour of averages of large numbers of random variables which have important practical consequences in statistics.

Statistics is the science of understanding patterns of population behaviour from data. In the module, this topic will be approached by specifying a statistical model for the data. Statistical models usually include a number of unknown parameters, which need to be estimated.

The focus will be on likelihood-based parameter estimation to demonstrate how statistical models can be used to draw conclusions from observations and experimental data, and linear regression techniques within the statistical modelling framework will also be considered.

Students will come to recognise the role, and limitations, of the linear model for understanding, exploring and making inferences concerning the relationships between variables and making predictions.

This module provides an introduction to the use and impact of information, communication and integrated technology systems on business and organisations. It focusses not on technical specifications, but rather on managerial and business implications of using these systems.

The following issues will be addressed:

• Data, Information and Decision-making
• Business Uses and Benefits of IS
• IT Selection
• Obtaining Information Systems
• Strategy and Information Systems

The course provides the business foundation for other more specialised or technical topics in Information Systems.

This module helps you improve your strategic thinking. Over the course of this module, you will learn how to use ‘games’ to model strategic situations in the real world, and how to analyse and find out solutions to these games in situations in which players are intelligent and rational. Games including “normal form games”, “extensive form games”, “Bayesian games”, “repetitive games”, and “games with correlation device” will be introduced. Opportunities for playing games with the lecturer and other students will also be provided. The module requires a basic knowledge of algebra, calculus, and economics.

Operations management is the core managerial discipline in all kinds of operation – from private-sector manufacturing through to public-sector services. It is about the human capacity to organise all the operations that underpin the modern world: transportation, the generation of energy, retailing, the production of goods, the provision of medical and educational services, and so on.

The module will introduce students to key concepts and themes of Operations Management such as operations strategy and performance objectives, operations design (e.g. layout, facility location and capacity), inventory planning and control, project management, quality management and supply chain management. These topics will be approached using a combination of qualitative and simple quantitative methods.

By the end of the course students should be able to:

• identify different kinds of operations and predict their characteristics
• apply basic planning and analysis techniques to particular cases
• understand operations problems and identify improvement strategies

Enterprise resource planning systems (ERPs) and integration solutions are essential to every modern enterprise, and this module gives you hands-on experience of SAP, a widely used enterprise technology. The module develops your understanding of how information technologies can help companies to achieve their strategic objectives, and introduces you to techniques and tools that can be used to evaluate the performance of business processes, diagnosing where problems lie and how processes can be improved.

After introductory sessions which look at the pervasive use of IT by business and at quantitative and qualitative business process analysis, you then work in small teams to compete in running a virtual dairy company, using SAP GUI as your ERP technology.

Designed as an introduction to the theory and practice of managing business projects, this module introduces project management methods in a way which links to the life cycle of a typical project – from the early project identification and definition stages, through project execution and control, to issues of implementation and change. The coverage of the early stages of the project cycle uses methods emerging from the systems movement and stresses the strategic relevance of project management. The management of the project is covered by introducing techniques for planning, scheduling and controlling projects. Attention is also given to the people management aspects of this process, including leadership, team-working and motivation.

Many organisational recruiters have identified a number of skills and knowledge they want to see from a prospective employee. Top in the priorities are spreadsheet modelling, problem structuring, statistics, and project management.

Students will be introduced to Microsoft Excel 2019 and the basics of dynamic model building, including skills such as data handling, filtering and analysis, using functions, charting, plus advanced techniques such as optimisation, simulation, and the use of Visual Basic for Applications (VBA) to automate models and construct decision support models.

The course will make extensive use of case-studies and workshop-orientated learning tasks.

This module examines the principles and practices of supply chain management, building on operations management concepts. It examines supply chain and logistics management applications in various sectors, such as retailing, pharmaceuticals, information technology, and even higher education.

Most of the time will be spent considering inter-organisational relationships from various perspectives, but it will also be necessary to understand how they relate to matters within the organisation, including functional areas such as logistics and procurement. As well as covering core principles and practices, the module also considers emerging supply chain themes such as service supply chains and sustainability.

Statistical inference is the theory of the extraction of information about the unknown parameters of an underlying probability distribution from observed data. Consequently, statistical inference underpins all practical statistical applications.

This module reinforces the likelihood approach taken in second year Statistics for single parameter statistical models, and extends this to problems where the probability for the data depends on more than one unknown parameter.

Students will also consider the issue of model choice: in situations where there are multiple models under consideration for the same data, how do we make a justified choice of which model is the 'best'?

The approach taken in this course is just one approach to statistical inference: a contrasting approach is covered in the Bayesian Inference module.

Many organisational recruiters have identified particular skills and knowledge they want to see from a prospective employee. Top in the priorities are spreadsheet modelling, problem structuring, statistics, and project management. This highly practical module equips you with an advanced set of spreadsheet modelling skills, including advanced functions and programming using Visual Basic for Applications (VBA) that can be used to produce a wide range of effective decision-support models.

You will learn general concepts about spreadsheet modelling using VBA and a wide range of modelling skills which are highly relevant to management. These include structured programming, program documentation, program verification, user interface design, and general investigative modelling – including applications involving optimisation, forecasting and simulation.

Bayesian statistics provides a mechanism for making decisions in the presence of uncertainty. Using Bayes’ theorem, knowledge or rational beliefs are updated as fresh observations are collected. The purpose of the data collection exercise is expressed through a utility function, which is specific to the client or user. It defines what is to be gained or lost through taking particular actions in the current environment. Actions are continually made or not made depending on the expectation of this utility function at any point in time.

Bayesians admit probability as the sole measure of uncertainty. Thus Bayesian reasoning is based on a firm axiomatic system. In addition, since most people have an intuitive notion about probability, Bayesian analysis is readily communicated.

This module introduces you to various current techniques for forecasting future customer demand, including a range of predictive models that develop your knowledge of the best ways of forecasting in problem situations.

The aim is to ensure that you have the skills needed to develop a validated quantitative set of forecasts using both extrapolative and causal forecasting methods, and that you can apply a simple forecasting method to support demand and revenue management.

You will also learn to identify and exploit opportunities for revenue optimisation in different business contexts. You review the main methodologies used in each of these areas, discuss legal issues associated with different pricing strategies, and survey current practices in different industries. Most of the topics covered are either directly or indirectly related to pricing issues faced by firms operating in environments where they enjoy some degree of market power.

At the heart of many real-world industrial and scientific problems are increasingly large data sets that need to be analysed efficiently in order to gain novel and useful insights. The field of as data mining (also known as intelligent data analysis) brings together real large-scale datasets and algorithms from statistics, machine learning and computational intelligence that can work efficiently with real-world datasets.

he course provides an introduction to the fundamental methods and approaches from the interrelated areas of data mining, statistical/ machine learning, and intelligent data analysis. The course covers the entire data analysis process, starting from the formulation of a project objective, developing an understanding of the available data and other resources, up to the point of statistical modelling and performance assessment. The focus of the course is classification. The course content covers:

-Exploratory data analysis including visualisation and simple feature selection methods

-Classification methods like: Logistic Regression, Decision trees (Random forests), k-Nearest Neighbours, and Naive Bayes

-Performance assessment and model selection

The course uses the R programming language and more specifically the RStudio integrated programming environment.

In this module we look at how to study business operations, analyse the situation and develop appropriate information systems designs. The same techniques can be of value whether you develop them further and become an information systems professional or use them in general management or consultancy. There is an emphasis on practical application and extensive use of class exercises.

The techniques taught in this module are widely employed by analysts in the fields of information systems and general business consultancy, and the ability to analyse information requirements and design efficient and effective information systems to meet those requirements is increasingly recognised and valued by employers as an important management skill.

This course focuses on the economics of growth and development, both from a theoretical and empirical perspective. Using examples from developing countries, it explores wide-ranging, policy-relevant topics such as investments in health, education and infrastructure, microeconomics of credit markets, corruption and other determinants of economic development.

This applied module is an introduction to the economics of health and health care and will develop your awareness of the main policy issues in this field. It provides a comprehensive set of economic tools for critically appraising fundamental issues in the economics of health while offering a broad overview of the UK’s National Health Service and other health care systems around the world. The emphasis is on the use and interpretation of microeconomic models and the latest empirical evidence.

This module builds on basic microeconomics concepts to explore competition between firms and the evolution of market structure. It focuses on understanding the way firms make decisions and the effects of those decisions on market outcomes like prices, quantities, the type of products offered, and social welfare. The module first introduces basic concepts in Industrial Organisation to study imperfect competition and the determinants of market power. It then proceeds to analyse important topics in competition policy, such as cartels and merger policy.

The module requires an understanding of intermediate microeconomics (especially production/cost theory), basic concepts of game theory, and basic calculus.

This module develops your understanding of concepts and theories of international trade and factor flows, with particular reference to the way in which such material can inform policymaking. Topics covered include the Ricardian model, the Heckscher-Ohlin model, international trade under imperfect competition, outsourcing and offshoring, trade models based on heterogeneous firms and multinational firms, and trade policy under perfect and imperfect competition. Throughout the module we emphasise the applicability of the models learned, and their relevance to real-world events. Examples include the relationship between labour productivity and wages, opinions toward free trade, and the impact of immigration.

Focusing on the microeconomics of labour and personnel, this module covers topics such as the economics of migration, wage determination, job search and labour market discrimination.

There is a particular emphasis on principal agent problems in human resources and the design of incentives within firms.

Economics theory is used to analyse the operation of labour markers and assess the empirical evidence. Areas covered include:

• the firm's demand for labour
• labour supply at an individual and aggregate level
• causes of wage rigidity
• the economic impact of trade unions
• inflation and unemployment

Using the classical problem of data classification as a running example, this module covers mathematical representation and visualisation of multivariate data; dimensionality reduction; linear discriminant analysis; and Support Vector Machines. While studying these theoretical aspects, students will also gain experience of applying them using R.

An appreciation for multivariate statistical analysis will be developed during the module, as will an ability to represent and visualise high-dimensional data. Students will also gain the ability to evaluate larger statistical models, apply statistical computer packages to analyse large data sets, and extract and evaluate meaning from data.

This module formally introduces students to the discipline of financial mathematics, providing them with an understanding of some of the maths that is used in the financial and business sectors.

Students will begin to encounter financial terminology and will study both European and American option pricing. The module will cover these in relation to discrete and continuous financial models, which include binomial, finite market and Black-Scholes models.

Students will also explore mathematical topics, some of which may be familiar, specifically in relation to finance. These include:

• Conditional expectation
• Filtrations
• Martingales
• Stopping times
• Brownian motion
• Black-Scholes formula

Throughout the module, students will learn key financial maths skills, such as constructing binomial tree models; determining associated risk-neutral probability; performing calculations with the Black-Scholes formula; and proving various steps in the derivation of the Black-Scholes formula. They will also be able to describe basic concepts of investment strategy analysis, and perform price calculations for stocks with and without dividend payments.

In addition, to these subject specific skills and knowledge, students will gain an appreciation for how mathematics can be used to model the real-world; improve their written and oral communication skills; and develop their critical thinking.

The aim is to introduce students to the study designs and statistical methods commonly used in health investigations, such as measuring disease, causality and confounding.

Students will develop a firm understanding of the key analytical methods and procedures used in studies of disease aetiology, appreciate the effect of censoring in the statistical analyses, and use appropriate statistical techniques for time to event data.

They will look at both observational and experimental designs and consider various health outcomes, studying a number of published articles to gain an understanding of the problems they are investigating as well as the mathematical and statistical concepts underpinning inference.

Policymakers at Central Banks lie in a unique position to influence economic activity. This module examines the role of monetary policy in influencing the expectations and behaviour of agents in the economy and the implications this has for outcomes such as inflation, GDP and household welfare. Students will focus on applications of monetary theory to central banks problems and the recent objectives of the Bank of England Monetary Policy Committee. Topics include Central Bank independence, inflation targeting and the zero lower bound on interest rates, money creation and quantitative easing, and the macroeconomics of pandemics.

Central to this module is the Crossbay Contracting Game, a management game designed by the module convenor and his colleagues at HCS Ltd.

Three (health service) organisations are involved in a contract negotiation, and you will be part of the management team of one of these organisations. The contract concerns funding requirements for core activities over the coming financial year.

The main aim is to reach an agreement that is satisfactory to all three parties – but you must of course ensure that your own organisation is likely to come out of it well. Much of your time will be spent analysing the emerging situation and negotiating with the other parties.

Alongside this 'management' task there is also a modelling task. Teams are provided with a decision support system they can use to analyse the emerging situation and help them decide which strategies are cost-effective for their organisation.

This module presents an overview of the interactions between the government, firms, and citizens, using a mix of theory and empirical work. Sometimes, markets are not efficient, and government intervention is necessary. Sometimes, markets are efficient, but equity concerns create the need for government. There is often a tension between the socially optimal policy and the outcome of the democratic process.

Some questions we study in this module:

• What is the role of government in the economy?
• Is it fair to redistribute money through taxation?
• Are some taxes better than others?
• How to deal with pollution, discriminations, and other inefficiencies of the market?
• How to make multinational companies pay taxes?
• Is there such a thing as an ideal voting system?

The concept of generalised linear models (GLMs), which have a range of applications in the biomedical, natural and social sciences, and can be used to relate a response variable to one or more explanatory variables, will be explored. The response variable may be classified as quantitative (continuous or discrete, i.e. countable) or categorical (two categories, i.e. binary, or more than categories, i.e. ordinal or nominal).

Students will come to understand the effect of censoring in the statistical analyses and will use appropriate statistical techniques for lifetime data. They will also become familiar with the programme R, which they will have the opportunity to use in weekly workshops.

Important examples of stochastic processes, and how these processes can be analysed, will be the focus of this module.

As an introduction to stochastic processes, students will look at the random walk process. Historically this is an important process, and was initially motivated as a model for how the wealth of a gambler varies over time (initial analyses focused on whether there are betting strategies for a gambler that would ensure they won).

The focus will then be on the most important class of stochastic processes, Markov processes (of which the random walk is a simple example). Students will discover how to analyse Markov processes, and how they are used to model queues and populations.

Issues and problems in the complex world of management do not necessarily arise in a well-structured form. People often do not know what they want or what is possible. They may also disagree about what they are trying to achieve and the means for arriving at their goals. Much thinking needs to be done in order to define an appropriate framework within which a useful analysis or project can be carried out.

Various approaches have been developed in recent years to assist in this task, often referred to as problem-structuring methods (PSMs). These very practically oriented methodologies typically involve the management team to help facilitate the structuring of complex situations. They place emphasis on dialogue to think through strategic problems, identify the salient issues, formulate goals and negotiate action plans. This module introduces you to several PSMs and some of the process skills needed to use them.

Modern statistics is characterised by computer-intensive methods for data analysis and development of new theory for their justification. In this module students will become familiar with topics from classical statistics as well as some from emerging areas.

Time series data will be explored through a wide variety of sequences of observations arising in environmental, economic, engineering and scientific contexts. Time series and volatility modelling will also be studied, and the techniques for the analysis of such data will be discussed, with emphasis on financial application.

Another area the module will focus on is some of the techniques developed for the analysis of multivariates, such as principal components analysis and cluster analysis.

Lastly,students will spend time looking at Change-Point Methods, which include traditional as well as some recently developed techniques for the detection of change in trend and variance.