Research Group on Optimisation
Optimisation is concerned with methods for finding the ‘best’ option when one is faced with a huge range of possible options. More formally, it deals with maximising (or minimising) a function of some decision variables, subject to various constraints.
Optimisation problems arise in a variety of contexts, having numerous applications not only in Operational Research, Operations Management and Quantitative Finance, but also in Mathematics, Physics, Statistics, Computer Science, Engineering, Computational Biology and even Sports! Optimisation is a truly multi-disciplinary field.
Current Research Activities
- Professor Kevin Glazebrook, Dr Christopher Kirkbride and Dr Peter Jacko work on optimal policies for stochastic resource-allocation problems. The classical approach to solving such problems, stochastic dynamic programming, becomes computationally infeasible once the system reaches a certain level of complexity. Current research focuses on alternative methods, based for example on Lagrangian relaxation, to develop near-optimal policies.
- Professor Konstantinos G Zografos, Professor Richard Eglese and Dr Burak Boyaci are mainly interested in developing models and algorithms for practical problems which arise in the context of logistics, such as vehicle routing, facility location or airline scheduling problems. They are particularly interested in applications in which environmental considerations are an important factor.
- Professor Adam Letchford and Dr Trivikram Dokka work on exact solution methods and bounding procedures for hard optimisation problems. They work mainly on discrete (aka combinatorial) problems, but also occasionally on continuous (aka global) problems. The solution methods are typically based on linear, quadratic or semidefinite programming.
- Professor Matthias Ehrgott works mainly on multi-objective combinatorial optimisation problems, and in particular on algorithms for producing complete and non-redundant sets of pareto-optimal solutions. He also has an interest in applications of optimisation to both medicine and transportation.
- Professor Stein W Wallace's principal interest is in decision making under uncertainty. He has worked with a broad range of applications, including portfolio management, energy, telecommunications and project scheduling. He has worked on algorithmic and modelling issues in stochastic programming.
- Professor Mike Wright researches into the development, analysis and implementation of metaheuristic techniques for solving complex real-life combinatorial problems with several objectives. Applications include problems arising in sport such as timetabling cricket fixtures. He is also interested in other applications of OR in Sports, including the analysis of tactical decisions in sports using dynamic programming.
For more details, see the respective staff web pages.
Potential research projects
Whilst the group is always willing to discuss the ideas of potential PhD students or external collaborators, there are also several ongoing research projects that you may want to get involved in. These are listed below. On the following pages further details of each project are given.
- Cutting Plane Methods for Combinatorial Optimisation
- Cliques and Colourings
- Lagrangian Heuristics for Optimisation Problems
- Two-Stage Stochastic Mixed-Integer Programming
- Development of a Bi-objective Branch and Bound Algorithm
- Efficient Algorithms for Data Envelopment Analysis
- Metaheuristic Search Techniques - design, analysis and implementation
- The analysis of tactical decisions within sports
- Stochastic models for dynamic resource allocation
- Novel approaches to the optimal control of complex random systems
- Management of multi-location inventory systems
- Dynamic routing of customers in queueing systems
- Management of the outsourcing of warranty repair work
- Developing and Solving Itinerary Planning Models in Large Scale Intermodal Freight Transport Networks
- Modelling and Solving Vehicle Routing and Scheduling Problems with Environmental and Societal Considerations
- Models and Algorithms for Supporting Strategic Tactical and Operational Decisions for Station Based Electric Vehicle Sharing Systems
- Optimising Airport Slot Allocation Considering Network-Wide Interactions
Current and past PhD student members are listed here.
If you would like to apply for a PhD, please see our PhD admissions page.