Operational Research Group
Our group has an impressive trackrecord 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.
Networks
 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 EPSRCfunded National Taughtcourse Centre in Operational Research, NATCOR, which provides indepth 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 panWales and UKwide events (Professor Harper is the OR & Statistics cluster coordinator);
 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 20067 which allowed researchers from across the globe to design and test their algorithms on reallife 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 12year period.
The group have also published widely in the field of partitioning problems. Such problems arise regularly in industry, transportation and logistics, and include multidimensional packing and balancing problems, stock cutting problems, rostering problems and graphtheory. 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 multidimensioned items from a set of equidimensioned “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 realworld 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 reroute delivery vans to the new customers while still minimising the distance travelled. Highquality 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 timedependent 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 discreteevent, system dynamics, agentbased, Monte Carlo and hybrid methods. Novel research has focussed on the use of simulation models incorporating smallworld 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 healthrelated 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 (postdoctoral 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 phasetype modelling, patient choice, combined data mining and simulation methodologies, modelling the costeffectiveness 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
Professor Paul Harper
Deputy Head of School, Professor of Operational Research
 Email:
 harper@cardiff.ac.uk
 Telephone:
 +44 (0)29 2087 6841
Academic staff
Dr Iskander Aliev
Senior Lecturer
 Email:
 alievi@cardiff.ac.uk
 Telephone:
 +44 (0)29 2087 5547
Dr Maggie Chen
Senior Lecturer in Financial Mathematics
 Email:
 chenj60@cardiff.ac.uk
 Telephone:
 +44 (0)29 2087 5523
Dr Tracey England
Research Associate
 Email:
 englandtj@cardiff.ac.uk
 Telephone:
 +44 (0)29 2087 0986
Dr Dafydd Evans
Lecturer in Operational Research
 Email:
 evansd8@cardiff.ac.uk
 Telephone:
 +44 (0)29 2087 0621
Dr Andrei Gagarin
Lecturer in Mathematics
 Email:
 gagarina@cardiff.ac.uk
 Telephone:
 +44 (0)29 2068 8850
Dr Daniel Gartner
Lecturer
 Email:
 gartnerd@cardiff.ac.uk
 Telephone:
 +44 (0)29 2087 0850
Dr Ahmed Kheiri
Research Associate
 Email:
 kheiria@cardiff.ac.uk
 Telephone:
 +44 (0)29 2087 0936
Dr Vincent Knight
Senior Lecturer
 Email:
 knightva@cardiff.ac.uk
 Telephone:
 +44 (0)29 2087 5548
Dr Rhyd Lewis
Senior Lecturer
 Email:
 lewisr9@cardiff.ac.uk
 Telephone:
 +44 (0)29 2087 4856
Dr Timm Oertel
Lecturer
 Email:
 oertelt@cardiff.ac.uk
 Telephone:
 +44 (0)29 2087 0849
Dr Jonathan Thompson
Director of Learning and Teaching
 Email:
 thompsonjm1@cardiff.ac.uk
 Telephone:
 +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 Iskander Aliev for more details regarding Operational Research/WIMCS lectures and Dr Andrey Pepelyshev for more details regarding Statistics lectures.
Seminars
Date  Speaker  Seminar  

14 June 2017  Dmitrii Silvestrov (Stockholm)  Asymptotic Expansions for Stationary and QuasiStationary Distributions of Nonlinearly Perturbed Markov Chains and semiMarkov Processes New algorithms for computing asymptotic expansions for stationary and quasistationary distributions of nonlinearly perturbed Markov chains and semiMarkov processes are presented. The algorithms are based on special techniques of sequential phase space reduction and some kind of “operational calculus” for Laurent asymptotic expansions applied to moments of hitting times for perturbed semiMarkov processes. These algorithms have a universal character. They can be applied to nonlinearly perturbed semiMarkov processes with an arbitrary asymptotic communicative structure of the phase space. Asymptotic expansions are given in two forms, without and with explicit bounds for remainders. The algorithms are computationally effective, due to a recurrent character of the corresponding computational procedures. The related references are [12]. References [1] Gyllenberg, M., Silvestrov, D.S. (2008). QuasiStationary Phenomena in Nonlinearly Perturbed Stochastic Systems. De Gruyter Expositions in Mathematics, 44, Walter de Gruyter, Berlin, ix+579 pp. [2] Silvestrov, D., Silvestrov, S. (2016). Asymptotic expansions for stationary distributions of perturbed semiMarkov processes. In: Silvestrov, S., Rancic, M. (Eds). Engineering Mathematics II. Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization, Chapter 10. Springer Proceedings in Mathematics & Statistics 179, Springer, Cham, 151  222.  
10 May 2017  Martin Kunc (Warwick)  TBA  
19 April 2017  Martin Lotz (University of Manchester)  Randomized dimension reduction in optimization and topological data analysis This talk reviews some recent and current work on extracting information from random projections of data. We first discuss a phase transition phenomenon in convex optimization: the probability that convex regularization succeeds in recovering a signal from few random measurements jumps sharply from zero to one as the number of measurements exceeds a certain threshold. After explaining the geometric and probabilistic ideas behind this phenomenon, we show how they can also be applied to problems in other fields such as topological data analysis.  
22 March 2017  James Woodcock (Cambridge)  Modelling active transport and health: state of the science and future directions The last decade have seen a growth of studies modelling how a shift to active transport can affect population health. Results have generally shown the potential for substantial benefits but uncertainties remain around impacts for different subgroups and on the generalisability of the results to lower and middle income settings. Correspondingly as the science matures there is a move to more rigorous methods and use of new data. In this talk I will consider how research is addressing these issues with a focus on how we model population physical activity exposures and risks, and how we estimate changes in injury risk with changes in active travel volume. 
Past seminars
Date  Speaker  Seminar 

15 February 2017  Alexander Stewart (UCL)  Evolution and the dynamics of social behavior Abstract: Understanding the dynamics of social behavior is very much a puzzle for our time. On the one hand, this puzzle is critical to understanding how human behavior is changing as we update and expand our social networks in unprecedented ways. On the other hand, these complex dynamics can (perhaps) be understood, due to recent expansion in empirical data and computational power. An evolutionary perspective is vital to this effort, providing a framework for understanding how and when behavioral change will spread through a population. However, in order to provide this perspective we must develop mechanistic models of behavioral changes at the individual level that explain the emergence of social phenomena, such as social norms or collective identities, at the level of groups and populations. I will discuss ongoing attempts to model some of the complex social behaviors found in humans such as cooperation, using evolutionary game theory, and some insights this approach yields about the emergence and stability of social norms. I will then briefly discuss how these game theoretic models can be connected to experiments to test qualitative predictions about human social behaviour. 
30 November 2016  Ivan Papić (Osijek University)  Heavytailed fractional Pearson diffusions Heavytailed fractional Pearson diffusions are a class of subdiffusions with marginal heavytailed Pearson distributions: reciprocal gamma, FisherSnedecor and Student distributions. They are governed by the timefractional diffusion equations with polynomial coefficients depending on the parameters of the corresponding Pearson distribution. We present the spectral representation of transition densities of fractional FisherSnedecor and reciprocal  gamma diffusions, which depend heavily on the structure of the spectrum of the infinitesimal generator of the corresponding nonfractional Pearson diffusion. Also, we present the strong solutions of the Cauchy problems associated with heavytailed fractional Pearson diffusions and the correlation structure of these diffusions.

16 November 2016  Joerg Kalcsics (University of Edinburgh)  Structural Properties of Voronoi Diagrams in Facility Location Problems with Continuous Demand Authors: Igor Averbakh, Oded Berman, Jörg Kalcsics, Dmitry Krass In most facility location models customer demand is assumed to be discrete and aggregated to a relatively small number of points. However, in many urban applications the number of potential customers can be in the millions and representing every customer residence as a separate demand point is usually infeasible. Thus, it may be more accurate to represent customer demand as spatially distributed over some region. We consider the conditional market share problem where locations of n facilities are fixed and we seek to find the optimal location for the (n+1)st facility with the objective of maximizing its market share. We assume that demand is uniformly distributed over a convex polygon, facilities can be located anywhere in the polygon, and customers obtain service from the closest open facility under rectilinear distances. Once the locations of all facilities are specified, the market area of a facility is given by its Voronoi cell in the Voronoi diagram generated by the facilities. The main difficulty when optimizing the location of the new facility is that it is generally impossible to represent the objective function in closed form; in fact, the representation depends on the structure of the Voronoi diagram, i.e., the position and the geometry of the cell boundaries. Unfortunately, this structure can change drastically with the location of the new facility. In this talk we derive structural properties of Voronoi diagrams for the rectilinear distances and show how to use them to identify regions where the resulting Voronoi diagram is "structurally identical" for every point in a region. Given such regions, we can derive a parametric representation of the objective function which is valid for any location in the region. This, in turn, allows us to optimize the location of the new facility over this region using classical nonlinear programming techniques. While the optimization techniques are specific to the particular model being considered, the structural results we derive, as well as our general approach, are quite universal, and can be applied to many other location models as well. 
2 November 2016  Laszlo Vegh (LSE)  Rescaled coordinate descent methods for Linear Programming Simple coordinate descent methods such as von Neumann's algorithm or Perceptron, both developed in the 50s, can be used to solve linear programming feasibility problems. Their convergence rate depends on the condition measure of the problem at hand, and is typically not polynomial. Recent work of Chubanov (2012, 2014), related to prior work of Betke (2004), has gathered renewed interest in the application of these methods in order to obtain polynomial time algorithms for linear programming. We present two algorithms that fit into this line of research. Both our algorithms alternate between coordinate descent steps and rescaling steps, so that either the descent step leads to a substantial improvement in terms of the convergence, or we can infer that the problem is ill conditioned and rescale in order to improve the condition measure. In particular, both algorithms are based on the analysis of a geometrical invariant of the LP problem, used as a proxy for the condition measure, that appears to be novel in the literature. This is joint work with Daniel Dadush (CWI) and Giacomo Zambelli (LSE). 
19 October 2016  Oleg Klesov (National University of Ukraine)  Generalized renewal processes and Pseudoregularly varying functions. 
13 July 2016  Lenny Fukshansky (Claremont McKenna)  Lattices from Abelian groups, spherical designs, and packing density maxima Abstract: Lattices are fundamentally important in discrete geometry, cryptography, discrete optimization and computer science. The lattice sphere packing problem asks for a lattice that maximizes the packing density function among all lattices in a given dimension. A systematic approach to this problem involves understanding what properties a lattice should have to be a strong candidate for such a maximum. I will discuss such properties, including a connection to spherical designs, which are certain highly symmetric point configurations on spheres. I will then exhibit a construction of a family of lattices from finite Abelian groups, which have interesting geometric properties and produce local maxima for the packing density function in infinitely many dimensions. This is joint work with A. Böttcher, S. R. Garcia and H. Maharaj. 
1 June 2016  Chenlei Leng (University of Warwick)  Distributed sparse regression by decorrelating features An attractive approach for downscaling a Big Data problem is to first partition the dataset into subsets and then fit using distributed algorithms. Feature space partitioning can be effective for analysing datasets with a large number of features, but suffers from the failure of not taking correlations into account if done naively. In this paper, we propose a new embarrassingly parallel framework named DECO for distributed variable selection and parameter estimation. The trick is to apply a simple decorrelation step before performing sparse regression on each subset. The theoretical and computational attractiveness of DECO will be illustrated. This is joint work with Xiangyu Wang and David Dunson. 
25 May 2016  Murad Taqqu (Boston University, USA)  A unified approach to selfnormalized block sampling The inference procedure for the mean of a stationary time series is usually quite different under various model assumptions because the partial sum process behaves differently depending on whether the time series is short or longrange dependent, or whether it has a light or heavytailed marginal distribution. We develop an asymptotic theory for the selfnormalized block sampling, and prove that the corresponding block sampling method can provide a unified inference approach for the aforementioned different situations in the sense that it does not require the a priori estimation of auxiliary parameters. This is joint work with Shuyang Bai and Ting Zhang. 
4 May 2016  Yuzhi Cai (Swansea)  Density forecasting with TGARCH models for financial returns This talk presents a novel density forecasting method based on a threshold GARCH (TGARCH) model and an associated value at risk (VaR) model for financial returns. Without estimating the TGARCH model directly, we proposed a Bayesian approach based on a working likelihood to the estimation of the VaR model. This estimation method allows a model that has multiple thresholds to be dealt with easily. As a result, the forecasting method allows us to obtain multiplestep ahead density forecasts for financial returns without using any information on the distribution of the innovation term of a TGARCH model. Since our method produces density forecasts, it also enables us to study the effect of the past financial returns on the entire distribution of the current return. Hence, any predictive quantity of interest can be obtained as byproducts of our method. Compared with other models, much improved density forecasts have been obtained from our method. 
13 April 2016  Matthias Ehrgott (Lancaster)  Generating deliverable treatment plans and beam angle optimisation in the presence of multiple objectives in radiotherapy treatment planning External radiation therapy is one of the major forms of treatment of cancer. Planning a radiation treatment for a patient involves making tradeoffs between the main goals of radiotherapy, namely to irradiate the tumour according to some prescription to affect tumour control and to avoid damage to surrounding healthy tissue. This conflict permeates all aspects of treatment planning from the selection of beam angles to the optimisation of fluence maps to the sequencing of the gantry for treatment delivery. In this talk I will first describe a matheuristic approach to incorporate multiobjective fluence optimisation in the beam angle optimisation problem. The second part of the talk will cover a column generation approach to the multiobjective fluence map optimisation problem, which achieves a reduction of the number of apertures and total fluence required to deliver a Paretooptimal treatment. 
16 March 2016  Mathias Henze (FU Berlin)  Tight asymptotic estimates for the quantitative discrete Hellynumber of the integral lattice Given a discrete subset $S$ of $\mathbb{R}^n$, let $c(S,k)$ be the smallest number $t$ such that for every finite system of linear inequalities that has exactly $k$ solutions in $S$, there exists a subsystem of at most $t$ inequalities that still has exactly $k$ solutions in $S$. This number was introduced for $S=\mathbb{Z}^n$ by Aliev et al.~(2014) in order to study a quantitative version of Doignon's integer variant of the classical Helly theorem. K. Clarkson was the fi rst to notice that using Doignon's theorem one can obtain a probabilistic algorithm for integer linear programming. Following this approach, the quantitative version has been applied to finding the l best integer feasible points of an integer program. The initial estimate $c(\mathbb{Z}^n,k)\in O(k)$ by Aliev et al.~was recently improved to a sublinear bound by Chestnut et al., who also determined the asymptotic growth of $c(\mathbb{Z}^2,k)$ to be $k^\frac13$. Via the theory of Hellynumbers of set families we show that $c(S,k)$ admits a variety of different interpretations, for example, by the maximum number of vertices of a polytope containing $k$ nonvertex points of $S$, or by the maximum number of facets of an inclusionmaximal polyhedron containing $k$ points of $S$ in its interior. Based on these interpretations, we show that for the integral lattice the asymptotic behavior of $c(\mathbb{Z}^n,k)$ is given by $\Theta(k^\frac{n1}{n+1})$, and we determine $c(\mathbb{Z}^n,k)$ for small values of $k$ exactly. For general discrete sets $S$ we derive an upper bound of $c(S,k)\in O(k\cdot h(S))$, where $h(S)$ is the Hellynumber of $S$. This is joint work with G. Averkov, B. Gonz\'{a}lez Merino, I. Paschke, and S. Weltge. 
2 March 2016  Paul Smith (Southampton)  Calibration estimators in official statistics Modelassisted 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)  InformationRevelation and Coordination using Cheap Talk: Theory and Experiment 
17 February 2016  Professor Theodore Turocy (East Anglia)  Twobidder allpay auctions with interdependent valuations: We present results from two related papers. In the first paper, 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 
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 nonGaussian, 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) 