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).
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:
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.
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).
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
Lecturer in Operational Research
- +44 (0)29 2087 0621
Lecturer in Mathematics
- +44 (0)29 2068 8850
Chair in Operational Research
- 029 2251 0253
All seminars will commence at 12:10pm in room M/0.34, The Mathematics Building, Cardiff University, Senghennydd Road (unless otherwise stated).
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.
Oded Lachish (Birkbeck, University of London)
To be announced
18 February 2019
Prof. Giles Stupfler (University of Nottingham)
To be announced
21 January 2019
Stefano Coniglio (University of Southampton)
To be announced
11 December 2018
Anatoly Zhigljavsky (University of Cardiff)
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
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.