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/2.06, The Mathematics Building, Cardiff University, Senghennydd Road (unless otherwise stated).

Please contact Dr Iskander Aliev for more details regarding Operational Research/WIMCS lectures and Dr Jonathan Gillard for more details regarding Statistics lectures.



1 June 2016

Chenlei Leng (University of Warwick)


27 May 2016

Rema Padman (CMU)


4 May 2016

Yuzhi Cai (Swansea)


13 April 2016

Matthias Ehrgott (Lancaster)


30 March 2016

Laszlo Vegh (LSE)


16 March 2016

Mathias Henze (FU Berlin)


2 March 2016

Paul Smith (Southampton)

Calibration estimators in official statistics

Model-assisted estimation has been in use in surveys for a long time under different names. I will trace some examples showing its evolution, and give a summary of modern calibration estimation as used by National Statistical Institutes in the production of official statistics. I will consider the reasons for calibration and the properties of the resulting estimates from both theoretical and user points of view, and give a range of examples demonstrating particular challenges and issues, and some developments where calibration estimation may continue to improve official outputs.

24 February 2016

Professor Indrajit Ray (Cardiff Business School)

Information-Revelation and Coordination using Cheap Talk: Theory and Experiment

17 February 2016

Professor Theodore Turocy (East Anglia)

Two-bidder all-pay auctions with interdependent valuations:
Equilibrium, complexity, competitiveness, and behaviour

We present results from two related papers. In the first paper,
we analyze symmetric, two-bidder all-pay auctions with interdependent valuations and discrete type spaces. Relaxing previous restrictions on the distribution of types and the valuation structure, we present a construction that characterizes all symmetric equilibria. We show how the search problem this construction faces can be complex.
In equilibrium, randomization can take place over disjoint intervals of bids, equilibrium supports can have a rich structure, and non-monotonicity of the equilibrium may result in a positive probability of allocative inefficiency when the value of the prize is not common. Particular attention is paid to the case in which an increase in a bidder’s posterior expected value of winning the auction is likely to be accompanied by a corresponding increase for the other bidder. Such environments are "highly competitive" in the sense that the bidder’s higher valuation also signals that the other bidder has an incentive to bid aggressively.

In the second paper, we focus on the relationship between monotonic equilibrium and those "highly competitive" cases. Having a high assessment of the value of the prize is good news, but only if the other participants in the contest are not too likely to
believe the same. In a laboratory experiment, we study behavior in both private-values and common-values settings. We vary the degree of correlation between types. While bidding is consistently aggressive across treatments, we find general support of the comparative statics of Bayes-Nash equilibrium for private values. In constrast, behavior in common values settings in which bidders have very noisy information about the value of the prize differs greatly from the equilibrium predictions.

10 February 2016

Evangelos Evangelou (Bath)

The Value of Information for Correlated GLM

In portfolio optimisation, one could potentially invest in several projects with an uncertain amount of revenue depending on the outcome of each project. Initially, the investor has a preliminary estimate about the outcome of each project and a prior value for the whole investment but is given the option to purchase some information (i.e. data) from some projects. When the projects are correlated, these data can be used to update the expected outcome of all projects and derive a posterior value for the investment. The information provided by the data has some value to the investor who must decide whether it is worth purchasing them.

In this talk we will consider the case where the outcome of each project is modelled by an exponential family. When the distribution is non-Gaussian, the value of information does not have a closed form expression. Using Laplace's approximation for intergrals we will derive an approximation to the value of information and examine the sensitivity of the approximation under different parameter settings and distributions. The method will be illustrated using a spatial decision problem.

Joint work with Jo Eidsvik (NTNU)

11 December 2015

Dr. Prabhani Kuruppumullage (Dana-Farber Cancer Institute/ Harvard School of Public Health)


25 November 2015

Dr Maggie Chen (Cardiff School of Mathematics)


11 November 2015

Professor Mark Tippett (Loughborough University & Sydney University)