The OR Society Undergraduate Award Previous Awards

  • 2017 - Anthony Luciani, Ffion James-Hargreaves
  • 2016  - Archie Rees

Citations for The OR Society Undergraduate Award 2018

Jacob Curran-Sebastian, University of Manchester

After recently graduating from MMath Mathematics at the University of Manchester, Jacob is now preparing the work from his dissertation for publication. Besides this, he is applying for PhD positions with the intention to pursue a research career.

Lie algebraic methods for solving rime-inhomogeneous Markov chains

Markov chains appear in a wide range of contexts in mathematical biology, and have been considered, for example in epidemiology (House, 2012, 2015; Keeling & Ross, 2008) and in the modelling of ion channels (Epstein, Calderhead, Girolami, & Sivilotti, 2016; Colquhoun & Hawkes, 1981). In some cases, these processes have been assumed to be independent of time, largely for convenience. However, such assumptions need not be made, and indeed it is possible to derive a solution of the time-inhomogeneous system in cases where it is possible to exploit Lie algebraic methods to obtain matrix exponential solutions. Once these solutions have been obtained, there exist a number of numerical methods for approximating the resulting matrix exponentials (Moler & Van Loan, 2003; Higham, 2008), which can offer significant computational advantages over the standard methods for numerical integration.

Jacob Curran-Sebastian winner of 2018 Undergraduate Award with Peter Duck

Jacob Curran-Sebastian receiving his award from the Head of School, Peter Duck

Louisa James, University of South Wales

Following graduation from her BSc Mathematics course at the University of South Wales, Louisa is now applying for data analysis roles in industry linked to OR in Healthcare.

The University Timetabling problem

One common problem facing the higher education industry is that of obtaining a timetable of core events that satisfies both the students and staff in the work place as well as sustaining the policies and protocols of the establishment. This report aims to tackle this problem using a range of heuristic based methods and seeks to improve on the previous model at each stage of the analysis. T

he original problem is reduced by characterising constraints as hard and soft, and prioritising where necessary to allow for the utilisation of optimisation software. A procedure to solve this reduced problem is coded into the software to generate an optimal timetable solution. Introducing new factors and constraints into the problem and exploiting the available course data provided by the University of South Wales allows the construction of a more realistic solution. Modifying the original data set to produce a group of central events, while considering additional constraints representative of real-world limitations enables the formation of a more accurate timetable.

Further improvements to the program using local search methods and evaluating the feasibility of the problem facilitates achievement of the optimum solution, scheduling all required sessions and accomplishing the original aim of the project. The report establishes additional aspects to be considered in the future to expand on the solutions, and eventually action the findings in practice.

Louisa James winner of 2018 Undergraduate Award with Penny Holborn

Dr Penny Holborn presenting the award to Louisa James

Hristo Dobrev, University of Leicester

Following graduation, Hristo is planning to set up his own business.  He believes that what he has learned in the operational research module of his BSc Mathematics course at the University of Leicester will be invaluable in providing him with a lot more ways to optimise any future business potential.

Risk Appetite

The aim of this project was to identify the optimal level of risk that Nottingham Credit Union should accept when making loans.

No loan is without risk, so if the credit union takes no risk it will make no loans and receive no loan interest.  However, if it takes too much risk, the bad debt will outweigh the interest received on loans that do repay.  It follows that between these two extremes there lies a level of risk that maximises net income (interest received less bad debt costs incurred).

There were two main parts to the project.  The first was to find a way to identify the level of risk associated with making any particular loan.  This was done analysing all the credit union’s loans made over the previous three years to identify the factors that increased or reduced, by using logistic regression.  The second part was to examine all loan applications received to identify the risk associated with each, using the regression model, and from this to calculate the expected net income at each level of risk. Logically, the credit union should make all loans on which the expected return is greater than zero so this gives the maximum level of acceptable risk and from this the average level of bad debt can be calculated.

The calculations need to be repeated for each level of interest rate charged by the credit union, as the interest rate affects the risk/reward balance for a loan.

All aspects of the project were successfully completed.  The results indicated that the credit union’s risk appetite was marginally too low, and that it should seek to improve its profitability by taking on marginally riskier loans than had previously been the case.

Hristo Dobrev winner of 2018 Undergraduate Award with Professor Jeremy Levesley

Hristo Dobrev receiving his award from Professor Jeremy Levesley

Sam Ball, University of Liverpool

After graduating from MMath Mathematics at the University of Liverpool, Sam plans to continue learning about OR through a PhD and carry this learning through to a career in consulting or management.

Integer Linear Programs

Integer Linear Programs (ILPs) are more complicated than Linear Programs over the rational numbers (LPs) since the Simplex algorithm (with quadratic average-case complexity) can no longer be applied, and the ILP problem is known to be NP-complete. In this project, we build on ideas from LPs to look at current methods of solution for ILPs. Whereas LPs have unique shadow prices, ILPs do not; they instead have dual price functions that only have to satisfy certain realistic constraints. It turns out that the structure of these dual price functions corresponds to the choice of solution algorithm. Our discussion of these results is largely based on the work of Wolsey [1]. We also discuss applications of this result, as well as recent developments and open problems in this area.

[1] L. A. Wolsey. Integer Programming Duality: Price Functions and Sensitivity Analysis. Mathematical Programming 20.1, 1980.

Citations for The OR Society Undergraduate Award 2017

Anthony Luciani, University of Leicester

After graduating from BSc Mathematics, Anthony will be studying a Masters in Financial Mathematics and Computation at the University of Leicester and working on a long-term project regarding cryptocurrency trading with a friend.

Optimising a Mining Strategy For New Crofton Cooperative Colliery (NCCC)

New Crofton Cooperative Colliery is planning to sink a new coal mine near Wakefield in Yorkshire. The proposed method of working – room and pillar – is understood on a theoretical basis using a presentation written by Dr Hirschi, but NCCC would like to understand more about how it will work in practice and whether it is the most efficient method. The purpose of this project is to develop a simulation model in a suitable software package that can be used to demonstrate to NCCC its proposed method of operation and possible alternatives to it. The dissertation outlines the benefits of the proposed methods, and contains a simulation creator tool which allows people with no specialist simulation knowledge to measure the optimality of their own strategy against the methods of others.

Anthony Luciani winner of 2017 Undergraduate Award with Professor Alex Clark

Anthony Luciani with Professor Alex Clark

Ffion James-Hargreaves, University of South Wales

Following Graduation from BSc Mathematics at the University of South Wales, Ffion has accepted a job at the Office for National Statistics based in Newport, South Wales as a Statistical Officer working in the National Accounts Coordination Division.

Investigating the impact of alcohol related attendances at A&E

This research investigates the impact of alcohol related attendances on the demand and capacity of the emergency services, specifically the Accident and Emergency departments within the Aneurin Bevan University Health Board.

Alcohol misuse is a major problem in modern society, resulting in both physical and mental harm, causing a large number of Accident and Emergency (A&E) attendances, which are therefore creating a significant burden on the department. The current operation of alcohol-related attendances, by most A&E departments, could be further improved. The remainder of this research examines the current literature published around areas of the subject, such that known methods can be implemented, i.e. statistical analysis and simulation.

Overall, there has been a decrease of 40.71% of attendances over the time frame of April 2010 to March 2016, yet men still encompass 61% of these. According to a Chi-Squared Goodness of Fit test, paired with the Kruskal-Wallis and the post-hoc Stepdown Bonferroni, there were no differences between the number of male and female attendances year on year, explaining that the ratio of males to females stays constant, although total alcohol-related attendances are decreasing in general. After performing further statistical analysis, it was seen that the Royal Gwent General Hospital and Nevill Hall General District Hospital handled the greatest number of attendances and were also found to have the largest number of patients arriving via Air Ambulance/Helicopter.

Then, when simulating an A&E department using the simulation software, Simul8, it was shown that having one doctor assigned to each specific triage category (1 through 5 and 6), was a viable solution to decreasing the impact of alcohol-related attendances on the A&E department. This was seen when 100% of patients left the system in less than the specified time frame, at four hours.

This should, in turn, strengthen the role of A&E departments and overall, may result in a decrease in the number of cases of alcohol-related incidences.

Ffion James-Hargreaves winner of 2017 Undergraduate Award with Dr Penny Holborn

Ffion James-Hargreaves with Dr Penny Holborn

Citation for The OR Society Undergraduate Award 2016

Archie Rees, University of South Wales

When asked about his future plans, Archie said “after my degree in BSc Mathematics I wish to pursue a career in the analytics and statistics industry. In particular, my time doing the project reaffirmed my desire to have a career analysing sports statistics, as I thoroughly enjoyed focusing on the NFL, making decisions based on both the statistics and figures attained and the actual football and setup of the national football league.”

The best of the best: An investigation into the efficiency of NFL franchises

This project investigates the efficiencies of NFL franchises for the 2014 and 2015 Regular Seasons. After investigating the strengths and weaknesses of several benchmarking methods, an adapted CCR formulation of DEA is used. The approach is applied to the 2014 and 2015 seasons, and it is found that there is a range of efficiencies for the NFL franchises for both the 2014 and 2015 season, however on average the 2015 season (74.79%) has slightly higher efficiencies than 2014 (71.06%), although this difference is not significantly different. The Seattle Seahawks were the only franchise to be 100% efficient in both seasons.

The analysis is carried out using normalised data with regards to offensive and defensive salaries (as inputs) and winning percentage, passing touchdowns (taken as a differential of touchdowns scored and touchdowns conceded) and rushing touchdowns (also as a differential). The approach also allows for the identification of areas of inefficiency, which are analysed for the 2014 season.

The models and results are then contrasted with other work in the area, namely ‘Is Winning Everything?’ (Einolf, 2004). The main contrasts between the two papers is their attitude towards injuries and how they affect efficiency, and the formulation of DEA, as ‘Is Winning Everything’ uses the BCC formulation of DEA to include the concept of diminishing returns, where the CCR formulation used in this paper that assumes a constant rate of return from inputs.