# Interns 2012

Below you can find details of the summer 2012 interns including a description of their research project. Click here to view the weekly blog written by 2012 interns. **Jamie-Leigh Chapman University of York, MSci Mathematics (2009-2013)Supervisor: Jamie Fairbrother**

**Often we have to make decisions in the face of uncertainty. A shop manager has to decide what stock to order without knowing the exact demand for each item. An investment banker has to choose a portfolio without knowing how the values of different assets will evolve. Taking this uncertainty into account allows us to make good robust decisions. This project uses stochastic programming as a tool to investigate such decision-making processes.**

*Scenario Generation for Stochastic Programming*

**View Jamie-Leigh's presentation and poster.**

**William Cook**

University of Cambridge, BA Mathematics with Physics (2010-2013)

Supervisor: Terry James

University of Cambridge, BA Mathematics with Physics (2010-2013)

Supervisor: Terry James

**It is without question that surveillance is very much a part of the modern world. A growing interest in the need for surveillance has been matched by technological advances in the area. Surveillance cameras, either static or as part of an unmanned aerial vehicle have the ability to feed real-time information to a control centre. Here the subject under surveillance can be properly assessed in terms of their identity or possible intentions in a biometric fashion. This project explores an aspect of the emerging operational research field of Homeland Security. More specifically this project will consider the challenge of modelling the defensive surveillance of public areas which are subject to attack by terrorist subjects.**

*Modelling anti-terrorist surveillance systems from a queueing perspective*

**View William's presentation and poster.**

**Josephine Evans**

**University of Cambridge, BA Mathematics (2010-present)**

Supervisor: Tim Park

The advent of smart phones has opened up new possibilities for the collection of data. These phones contain sensors such as accelerometers, gyroscopes and GPS making them a cheap and easy way for companies to collect time series data. This data is often multivariate and nonstationary and often the main challenge is deciding which channels to focus the analysis on rather than the choice of analysis method itself. This project uses principal components analysis to identify which channel to focus on when analysing a multivariate time series.

Supervisor: Tim Park

*Spectral Analysis of Multivariate Time Series*

**View Josephine's presentation and poster.**

**Matthew Ludkin**

**University of Birmingham, MSci Mathematics (2009-2013)**

Supervisor: Mark Bell

One of the most widely used dynamic modelling methods in Operational Research for understanding and improving organisational systems is discrete event simulation (DES); an application of this method is in modelling maintenance processes. In a large organisation there are often many additional interactions that affect the maintenance operations. When this is the case, there are occasions where modelling the system using DES alone is not sufficient therefore System Dynamics (SD) may be utilised. In Operational Research these two approaches have traditionally been separated but in recent years there has been an emergence of using hybrid models that contain both techniques, as the limitations of each have been said to complement one another. This project initially involves building DES and SD models separately before finally combining the two models to create hybrid models of maintenance processes.

Supervisor: Mark Bell

*Hybrid simulation models for maintenance processes*

**View Matthew's presentation and poster.**

**Helen Mossop**

**Newcastle University, MMathStat Mathematics and Statistics (2009-2013)**

Supervisor: Shreena Patel

Supervisor: Shreena Patel

**Simple probability models are often inadequate for describing the data we encounter in reality because of heterogeneity in the population we are attempting to model. One way to overcome this is to use a mixture model which represents the population as consisting of several sub-populations (or clusters), each of which can be modelled by a standard parametric distribution. This project concerns a population of customers each of whom have an (unobservable) maximum price which they are willing to pay for a product, called a referral price. We wish to cluster customers to capture differences in their price-sensitivity by assuming that referral prices are generated by a mixture of normal distributions. Standard clustering techniques will be adapted in order to estimate how likely a customer is to accept future quotes.**

*Clustering customers to estimate willingness-to-pay*

**View Helen's presentation and poster.**

**Gwern Owain**

**Cardiff University, BSc Mathematics (2010-2013)**

Supervisor: Jak Marshall

Supervisor: Jak Marshall

**Queues occur naturally in business and computer science applications. So ubiquitous are queues in various situations that being able to model their behaviour is an essential skill for any practitioner or researcher of operations research. Often it is of benefit to simultaneously manage the flow of work in and out of multiple queues given limitations of service resources. This project introduces the rich theory of queueing systems and presents an opportunity to explore efficient ways of coping with random demands on a system with multiple parallel queues with cost structures imposed on them.**

*Resource Allocation problems in queueing theory*

**View Gwern's presentation and poster.**

**Stephen Page**

University of Cambridge, BA Mathematics (2010-present)

Supervisor: Saeideh Dehghan-Nasiri

University of Cambridge, BA Mathematics (2010-present)

Supervisor: Saeideh Dehghan-Nasiri

**The travelling salesman problem is a very well-known optimization problem. This project studies aspects of this problem with additional time window restrictions on the service time of customers and uses a real road network graph. Small scale versions of the problem may be solved using exact optimization techniques. This project looks at solving the problem using exact solution methods and developing and applying a dynamic programming algorithm that provides a lower bound for the problems of a larger scale.**

*Prize-Collecting Steiner Travelling Salesman Problem with Time Windows*

**View Stephen's presentation and poster.**

**Paul Sharkey**

University College Dublin, BSc Mathematical Science (2009-2013)

Supervisor: Ross Towe

Wave height is of inherent interest to oil companies with offshore operations. Through determining the distribution of wave heights, this information can be used to minimise the risk and consequently the cost of future offshore operations. A current consideration is also whether climate change will have an impact on the distribution of wave heights. This project considers extreme value theory for modelling wave heights in the North Sea.

University College Dublin, BSc Mathematical Science (2009-2013)

Supervisor: Ross Towe

*Modelling the North Sea wave climate*

**View Paul's presentation and poster.**

**Faye Williamson**

**Lancaster University, MSci Mathematics (2010-2013)**

Supervisor: Dan Suen

Supervisor: Dan Suen

**Analysing healthcare systems has been an important concern of healthcare modellers for many years. Understanding patient flows and the number of patients in healthcare systems is an important tool when trying to improve hospital efficiency and, among other things, reduce patient waiting times. This project seeks to highlight similarities between healthcare models and the types of systems multigrade population models are applied to using data from a healthcare case.**

*Semi-Markov processes in a healthcare setting*

**View Faye's presentation and poster.**

**Elena Zanini**

University of Edinburgh, BSc Applied Mathematics (2009-2013)

Supervisor: Chris Nemeth

University of Edinburgh, BSc Applied Mathematics (2009-2013)

Supervisor: Chris Nemeth

**There exist numerous problems in statistics, engineering, signal processing, etc. which require the estimation of a hidden process. One such example can be found in target tracking, where the aim is to estimate the state of a target (e.g. position, velocity) given only partial, noisy observations (e.g. bearing measurements only). The process of estimating a target's state given only partial, noisy observations is known as filtering. This project involve gaining an understanding of particle filtering techniques and reviewing the current literature before using particle filtering methods to assess various models.**

*Parameter Estimation with Particle Filtering Algorithms*

**View Elena's presentation and poster.**