Ewch i’r prif gynnwys

Operational Research Group

Our group has an impressive track-record of contributing to both the theoretical aspects of the subject area and to applications, including working on complex problems arising in healthcare planning, epidemiology, transportation, timetabling, manufacturing, green logistics and scheduling of sporting fixtures.

We now have over 20 academic staff and research students and host a thriving seminar series jointly with the Statistics research group.


  • We are a partner group within the LANCS initiative, a collaboration of four Universities with a total investment of £13m (£5.4m from EPSRC) to support the development of research capacity in OR.
  • A contributor to the EPSRC-funded National Taught-course Centre in Operational Research, NATCOR, which provides in-depth training for PhD students in OR.
  • Within the Wales Institute of Mathematical and Computational Sciences, WIMCS, the Cardiff Operational Research group leads the OR and Statistics cluster, and organises pan-Wales and UK-wide events (Professor Harper is the OR & Statistics cluster co-ordinator).
  • We help to organise meetings of the South Wales Operational Research Discussion Society (SWORDS).
  • We are a partner in the Centre for Transport Network Optimisation which develops new, highly efficient approaches for public transport network design (Dr Rhyd Lewis is our link member).
  • All of the OR staff are highly active in international collaborations, for example including strong links with the Federal University of Rio de Janeiro (Brazil), Twente University (Netherlands), University of California Davis (US), University of Toronto (Canada), University of Vienna (Austria), Karlsruhe Institute of Technology (Germany) and Monash University (Australia).

Health modelling

Professor Harper is Director of Health Modelling Centre Cymru (hmc2), which is fostering collaboration across different research areas of the mathematical and computational sciences, to create a more vibrant and effective interface between the mathematical research community, the medical research community, NHS Wales, the Welsh Government and the Health industry.

The main areas of research within the current group are:

In focus

Planning and optimisation

The planning and optimisation group is involved in the design and application of mathematical optimisation techniques to real life problems, particularly in the areas of scheduling and packing. These techniques can be used to introduce efficiency and reduce waste in the logistical operations of companies and government agencies.

One vibrant area of research in this group concerns the problem of timetabling. Universities, for example, periodically face the burden of scheduling exams and lectures so that a variety of complex, and often conflicting constraints are met. Members of the group have previously designed methods for such problems and were also involved in the organisation of the Second International Timetabling Competition in 2006-7 which allowed researchers from across the globe to design and test their algorithms on real-life problems in a competitive environment. The resources generated from this competition continue to stimulate new work by providing a useful access point into the field.

Members of the group are also active in the area of sports timetabling, where the aim is to produce schedules that are fair to all teams and that also satisfy constraints regarding pitch availability, television requirements etc. The group has previously worked with the International Rugby Board and the Welsh Rugby Union and has used metaheuristic search techniques to produce schedules for the 1999 Rugby World Cup, Welsh domestic rugby leagues, and all international rugby fixtures over a 12-year period.

The group have also published widely in the field of partitioning problems. Such problems arise regularly in industry, transportation and logistics, and include multi-dimensional packing and balancing problems, stock cutting problems, rostering problems and graph-theory. Stock cutting problems, for example, arise in areas such as the clothing and building industries, where the aim is to cut a set of predefined and possibly multi-dimensioned items from a set of equi-dimensioned “stocks” such that the wastage is minimised (thus encouraging economic savings). Previous research by the group has resulted in methods achieving state of the art results on popular benchmark problems (some of which have originated from real-world industrial processes), as well as the analysis and solving of new cutting problems provided to us by industrial partners.

Finally, the group is also investigating dynamic routing problems – that is routing problems where requirements change over time. An example is where a company receives new orders during the day and has to re-route delivery vans to the new customers while still minimising the distance travelled. High-quality solutions have been achieved using ant colony optimisation and our methods have also been applied to large scale static problems in order to divide problems into more manageable parts.

Queueing systems

There is a strong Cardiff OR tradition in the study of queueing systems, with applications of queueing theory, simulation and probability theory to practical problems. A typical research project involves both analytical insights from queueing theory and the use of computer simulation, and a number of PhD students are working in this area with particular applications to healthcare, transportation and telecommunications problems.

Queueing studies have focussed on bulk service queues and time-dependent queueing models, including research projects at Gatwick Airport, the Severn Bridge, the Channel Tunnel, and healthcare services (including the intensive care unit, operating theatres and ambulance services). Recent theoretical has made significant progress with the transient solution of queueing systems with a variety of service mechanisms (Prof. Jeff Griffiths and Dr Janet Williams) and a number of research projects have been awarded, dating back as far as 1975, to contracts and consultancies from Transport Research Laboratory, Suez Canal Authority, BP Oil Ltd, Department of Transport, Research Councils, etc. Projects have been undertaken relating to delays to pedestrians and vehicles at pedestrian crossings, accident analyses within computer controlled signal networks, facilities provided at motorway roadworks, toll systems, advantages of flared junctions at traffic signals, etc.

Research and application in simulation has involved discrete-event, system dynamics, agent-based, Monte Carlo and hybrid methods. Novel research has focussed on the use of simulation models incorporating small-world theory for modelling of disease propagation (Dr Israel Vieira), modelling consumer choice (Dr Vince Knight) and incorporating human behaviour (Prof. Paul Harper). Applications include NHS patient choice, HIV/AIDS, ambulance services, breast cancer, A&E department and critical care. Novel work on hybrid methods is exploring the feasibility and benefits of combined methodologies (such as DES and SD) and work with Social Scientists.

Probabilistic methods are being applied to modelling of telecommunication systems and opportunistic networks (Dr Dafydd Evans) which consist of mobile nodes equipped with short range wireless communications devices. Information is dispersed both by wireless transmission between the participating nodes and the movement of the nodes themselves. For example, a source node located at a railway station transmits a message to people passing nearby, who then disseminate the message across the local area. Fixed nodes are strategically placed throughout the area to act as message repositories. Dr Evans is developing probabilistic models of opportunistic networks, and using these to derive theoretical performance bounds for this type of network. Network performance statistics can involve concepts at the network level (e.g number of connected components), at the neighbourhood level (e.g. number of nodes within transmission range) or at the node level (e.g. number of messages waiting to be relayed).

Healthcare modelling

Cardiff is renowned for its long and successful tradition of research in this field. We have a large and active group of staff and postgraduate research students working on numerous health-related topics, including planning and management of healthcare services, epidemiology, and prevention, early detection and treatment of disease. Professor Harper is also Director of Health Modelling Centre Cymru (hmc2). A number of PhD students and Research Associates (post-doctoral students) are funded directly by Local Health Boards. An exciting recent initiative is the creation of a Mathematical Modelling Unit, funded by the Aneurin Bevan University Health Board with a joint lectureship and three research associates working between the OR group and the Health Board within the Aneurin Bevan Continuous Improvement team.

Research projects typically comprise of a mixture of theoretical and practical investigations, and many projects have been funded by external organisations, including various funding councils, Department of Health, NHS Information Centre, NHS Trusts and Primary Care Trusts.

Particular contributions include stochastic models for integrated healthcare resource systems (hospital bed capacities, theatre scheduling and workforce planning), stochastic facility location problems, conditional phase-type modelling, patient choice, combined data mining and simulation methodologies, modelling the cost-effectiveness of various strategies for preventing and screening for disease including breast cancer, colorectal cancer, HIV/AIDS and diabetic retinopathy, targeted screening programmes for Chlamydia, small world models for the dynamics of HIV infection, and novel research on healthcare behavioural modelling.

Several staff within the group are members of the European Working Group on Operational Research Applied to Health Services (ORAHS), and members of the Steering Group of the EPSRC funded Network in Healthcare Modelling and Simulation (MASHnet). Prof. Harper’s work on screening for Chlamydia was awarded the 2006 OR Society’s Goodeve Medal for the best paper published in the Journal of the Operational Research Society. The 2011 ORAHS international conference was be held in Cardiff (Organising team: Paul Harper, Janet Williams, Vince Knight and Israel Vieira). Recent PhD graduate Richard Wood (modelling of rehabilitation services using queueing theory and scheduling techniques) won the best PhD prize by the UK OR Society.

Head of group

Photograph of Professor Paul Harper

Yr Athro Paul Harper

Deputy Head of School, Professor of Operational Research

+44 (0)29 2087 6841

Academic staff

Iskander Aliev

Dr Iskander Aliev

Senior Lecturer

+44 (0)29 2087 5547
Photograph of Dr Maggie Chen

Dr Maggie Chen

Senior Lecturer in Financial Mathematics

+44 (0)29 2087 5523
Photograph of Tracey England

Dr Tracey England

Research Associate

+44 (0)29 2087 0986
Photograph of Dr Dafydd Evans

Dr Dafydd Evans

Lecturer in Operational Research

+44 (0)29 2087 0621
Dr Andrei Gagarin photograph

Dr Andrei Gagarin


+44 (0)29 2068 8850
Photograph of Daniel Gartner

Dr Daniel Gartner


+44 (0)29 2087 0850
Professor Owen Jones photograph

Yr Athro Owen Jones

Chair in Operational Research

029 2251 0253
Photograph of Dr Vincent Knight

Dr Vincent Knight


+44 (0)29 2087 5548
Rhyd Lewis photograph

Dr Rhyd Lewis


+44 (0)29 2087 4856

Dr Anqi Liu

Lecturer in Financial Mathematics

+44 29208 70908
Photograph of Timm Oertel

Dr Timm Oertel


+44 (0)29 2087 0849
Dr Jonathan Thompson

Dr Jonathan Thompson

Admissions Tutor

+44 (0)29 2087 5524

All seminars will commence at 12:10pm in room M/0.34, The Mathematics Building, Cardiff University, Senghennydd Road (unless otherwise stated).

Please contact Dr Timm Oertel for more details regarding Operational Research/WIMCS lectures and Dr Andrey Pepelyshev for more details regarding Statistics lectures.



21 October 2019

Tri-Dung Nguyen (University of Southampton)

To be confirmed

7 October 2019

George Loho (LSE)

To be confirmed

8 April 2019

Dr. Andreas Anastasiou (LSE)

Detecting multiple generalized change-points by isolating single ones

In this talk, we introduce a new approach, called Isolate-Detect (ID), for the consistent estimation of the number and location of multiple generalized change-points in noisy data sequences. Examples of signal changes that ID can deal with, are changes in the mean of a piecewise-constant signal and changes in the trend, accompanied by discontinuities or not, in the piecewise-linear model. The method is based on an isolation technique, which prevents the consideration of intervals that contain more than one change-point. This isolation enhances ID’s accuracy as it allows for detection in the presence of frequent changes of possibly small magnitudes. Thresholding and model selection through an information criterion are the two stopping rules described in the talk. A hybrid of both criteria leads to a general method with very good practical performance and minimal parameter choice. Applications of our method on simulated and real-life data sets show its very good performance in both accuracy and speed. The R package IDetect implementing the Isolate-Detect method is available from CRAN.

1 April 2019Stephen Disney (Cardiff University)

When the Bullwhip Effect is an Increasing Function of the Lead Time

We study the relationship between lead times and the bullwhip effect produced by the order-up-to policy. The usual conclusion in the literature is that longer lead-time increase the bullwhip effect, we show that this is not always the case. Indeed, it seems to be rather rare. We achieve this by first showing that a positive demand impulse response leads to an always increasing in the lead time bullwhip effect when the order-up-to policy is used to make supply chain inventory replenishment decisions. By using the zeros and poles of the z-transform of the demand process, we reveal when this demand impulse is positive. To make concrete our approach in a nontrivial example we study the ARMA(2,2) demand process.

22 March 2019

Martina Testori (University of Southampton)

How group composition affects cooperation in fixed networks: can psychopathic traits influence group dynamics?

Static networks have been shown to foster cooperation for specific cost-benefit ratios and numbers of connections across a series of interactions. At the same time, psychopathic traits have been discovered to predict defective behaviours in game theory scenarios. This experiment combines these two aspects to investigate how group cooperation can emerge when changing group compositions based on psychopathic traits. We implemented a modified version of the Prisoner’s Dilemma game which has been demonstrated theoretically and empirically to sustain a constant level of cooperation over rounds. A sample of 190 undergraduate students played in small groups where the percentage of psychopathic traits in each group was manipulated. Groups entirely composed of low psychopathic individuals were compared to communities with 50% high and 50% low psychopathic players, to observe the behavioural differences at the group level. Results showed a significant divergence of the mean cooperation of the two conditions, regardless of the small range of participants’ psychopathy scores. Groups with a large density of high psychopathic subjects cooperated significantly less than groups entirely composed of low psychopathic players, confirming our hypothesis that psychopathic traits affect not only individuals’ decisions but also the group behaviour. This experiment highlights how differences in group composition with respect to psychopathic traits can have a significant impact on group dynamics, and it emphasizes the importance of individual characteristics when investigating group behaviours.


Joe Paat

The proximity function for IPs

Proximity between an integer program (IP) and a linear program (LP) measures the distance between an optimal IP solution and the closest optimal LP solution. In this talk, we consider proximity as a function that depends on the right hand side vector of the IP and LP. We analyze how this proximity function is distributed and create a spectrum of probabilistic-like results regarding its value. This work uses ideas from group theory and Ehrhart theory, and it improves upon a recent result of Eisenbrand and Weismantel in the average case. This is joint work with Timm Oertel and Robert Weismantel. The proximity functions for IPs.



Prof Philip Broadbridge (La Trobe University)

Shannon entropy as a diagnostic tool for PDEs in conservation form

After normalization, an evolving real non-negative function may be viewed as a probability density. From this we may derive the corresponding evolution law for Shannon entropy. Parabolic equations, hyperbolic equations and fourth-order “diffusion” equations evolve information in quite different ways. Entropy and irreversibility can be introduced in a self-consistent manner and at an elementary level by reference to some simple evolution equations such as the linear heat equation. It is easily seen that the 2nd law of thermodynamics is equivalent to loss of Shannon information when temperature obeys a general nonlinear 2nd order diffusion equation. With the constraint of prescribed variance, this leads to the central limit theorem.

With fourth order diffusion terms, new problems arise. We know from applications such as thin film flow and surface diffusion, that fourth order diffusion terms may generate ripples and they do not satisfy the Second Law. Despite this, we can identify the class of fourth order quasilinear diffusion equations that increase the Shannon entropy.

4 March 2019

Dr. Emrah Demir (Cardiff Business School)

Creating Green Logistics Value through Operational Research

Green logistics is related to producing and dispatching goods in a sustainable way, while playing attention to environmental factors. In a green context, the objectives are not only based on economic considerations, but also aim at minimising other detrimental effects on society and on the environment. A conventional focus on planning the associated activities, particularly for the freight transportation, is to reduce expenses and, consequently, increase profitability by considering internal transportation costs. With an ever-growing concern about the environment by governments, markets, and other private entities worldwide, organizations have started to realize the importance of the environmental and social impacts associated with transportation on other parties or the society.

Efficient planning of freight transportation activities requires a comprehensive look at wide range of factors in the operation and management of transportation to achieve safe, fast, and environmentally suitable movement of goods. Over the years, the minimization of the total travelled distance has been accepted as the most important objective in the field of vehicle routing and intermodal transportation. However, the interaction of operational research with mechanical and traffic engineering shows that there exist factors which are critical to explain fuel consumption. This triggered the birth of the green vehicle routing and green intermodal studies in operational research. In recent years, the number, quality and the flexibility of the models have increased considerably. This talk will discuss green vehicle routing and green intermodal transportation problems along with models and algorithms which truly represent the characteristics of green logistics.


Oded Lachish (Birkbeck, University of London)

mart queries versus property independent queries

In the area of property testing, a central goal is to design algorithms, called tests, that decide, with high probability, whether a word over a finite alphabet is in a given property or far from the property. A property is a subset of all the possible words over the alphabet. For instance, the word can be a book, and the property can be the set of all the books that are written in English - a book is 0.1 far from being written in English if at least 0.1 of its words are not in English. The 0.1 is called the distance parameter and it can be any value in [0,1]. The input of a test is the distance parameter, the length of the input word and access to an oracle that answers queries of the sort: please give me the i'th letter in the word.

The quality of a test is measured by it query complexity, which is the maximum number of queries it uses as a function of the input word length and the distance parameter, ideally this number does not depend on the input length. Tests that achieve this ideal for specific properties have been discovered for numerous properties. In general, tests that achieve the ideal for different properties differ in the manner in which they select their queries. That is, the choice of queries depends on the property.

In this talk, we will see that for the price of a significant increase in the number of queries it is possible to get rid of this dependency. We will also give scenarios in which this trade-off is beneficial.

18 February 2019 (Time 13:10 - 14:00)

Prof. Giles Stupfler (University of Nottingham)

Asymmetric least squares techniques for extreme risk estimation

Financial and actuarial risk assessment is typically based on the computation of a single quantile (or Value-at-Risk). One drawback of quantiles is that they only take into account the frequency of an extreme event, and in particular do not give an idea of what the typical magnitude of such an event would be. Another issue is that they do not induce a coherent risk measure, which is a serious concern in actuarial and financial applications. In this talk, I will explain how, starting from the formulation of a quantile as the solution of an optimisation problem, one may come up with two alternative families of risk measures, called expectiles and extremiles. I will give a broad overview of their properties, as well as of their estimation at extreme levels in heavy-tailed models, and explain why they constitute sensible alternatives for risk assessment using some real data applications. This is based on joint work with Abdelaati Daouia, Irène Gijbels and Stéphane Girard.

21 January 2019

Stefano Coniglio (University of Southampton)

Bilevel programming and the computation of pessimistic single-leader-multi-follower equilibria in Stackelberg games

We give a very broad overview of bilevel programming problems and their relationship with Stackelberg games, with focus on two classical limitations of this paradigm: the presence of a single follower and the assumption of optimism.
We then investigate the problem of computing an equilibrium in Stackelberg games with two or more noncooperating followers who react to the strategy chosen by the leader by playing a Nash Equilibrium, focusing, in particular, on the pessimistic case where, if the follower's game (parameterized by the leader's strategy) admits more Nash equilibria, the followers choose one which minimizes the leader's utility.

We then address the case where the followers are restricted to pure strategies, illustrate some hardness and inapproximability results, and the concentrate on exact solution algorithms.

After proposing a single-level (but undecidable) reformulation for the problem, we propose an exact implicit enumeration algorithm capable of computing the supremum of the problem as well as an alpha-approximate strategy, for any nonnegative alpha.

Experimental results are presented and illustrated, showing the viability of our approach.

11 December 2018

Anatoly Zhigljavsky (University of Cardiff)

Multivariate dispersion

3 December 2018

Dr Ilaria Prosdocimi  (University of Bath)

Detecting coherent changes in flood risk in Great Britain

Flooding is a natural hazard which has affected the UK throughout history, with significant costs for both the development and maintenance of flood protection schemes and for the recovery of the areas affected by flooding. The recent large repeated floods in Northern England and other parts of the country raise the question of whether the risk of flooding is changing, possibly as a result of climate change, so that different strategies would be needed for the effective management of flood risk. To assess whether any change in flood risk can be identified, one would typically investigate the presence of some changing patterns in peak flow records for each station across the country. Nevertheless, the coherent detection of any clear pattern in the data is hindered by the limited sample size of the peak flow records, which typically cover about 45 years. We investigate the use of multi-level hierarchical models to better use the information available at all stations in a unique model which can detect the presence of any sizeable change in the peak flow behaviour at a larger scale. Further, we also investigate the possibility of attributing any detected change
to naturally varying climatological variables.


Prof Benjamin Gess (Max Planck Institute)

Random dynamical systems for stochastic PDE with nonlinear noise

In this talk we will revisit the problem of generation of random dynamical systems by solutions to stochastic PDE. Despite being at the heart of a dynamical system approach to stochastic dynamics in infinite dimensions, most known results are restricted to stochastic PDE driven by affine linear noise, which can be treated via transformation arguments. In contrast, in this talk we will address instances of stochastic PDE with nonlinear noise, with particular emphasis on porous media equations driven by conservative noise. This class of stochastic PDE arises in particular in the analysis of stochastic mean curvature motion, mean field games with common noise and is linked to fluctuations in non-equilibrium statistical mechanics.

Past events

Past Seminars 2017-18

Past Seminars 2016-17

Past Seminars 2015-16