Operational Research

Research themes

Operational Research
Our main research areas are Computational Optimisation, Game Theory, Healthcare Modelling, Revenue Management, Stochastic Programming and Simulation and Transportation and Supply Chain.

Computational optimisation

Computational optimisation is widely used in science, engineering, economics, and industry. Researchers in our group develop cutting-edge theories and algorithms that push the limits in optimisation. 

Much of the work is supported by various outside organisations and carried out with their collaboration. Recent examples include the European Space Agency, EPSRC, Boeing Defense, ThyssenKrupp, Alcatel-Lucent, Bell Labs, Qualcomm and the Brussels Capital-Region. 

Our current research interests include: 

  • decision making under uncertainty
  • optimisation in data dimension reduction and visualization
  • multi-objective and bi-level optimisation
  • discrete optimisation
  • non-smooth optimisation
  • optimisation methods in game theory
  • optimisation in finance

Game theory

Game theory is a mathematical discipline that studies settings involving multiple decision makers or players. Two major branches of game theory are cooperative game theory and non-cooperative game theory. This depends on whether players are collaborating or competing against each other. In cooperative game theory, players can form coalitions to jointly achieve some objectives. These are associated with some payoff values, representing the costs and profits.

Our research group focuses on how payoffs are shared among players in a fair and stable way and on how coalitions are formed. We develop computational optimisation techniques for computing solutions of large games. We also study stochastic games in which the characteristic function is uncertain.

We are also interested in Stackelberg games where the players take turns according to a hierarchy and in the bilevel programming aspect that the corresponding equilibrium finding problem entails. Recent applications include:

  • supply chain coordination
  • multi-agent systems optimisation in finance
  • computation of leader-follower Nash equilibria

Revenue management

Revenue management is the process of setting prices to maximise a company's revenue. Airlines are the most well-known users of revenue management, but its use is growing in other industries such as online advertising and fashion retailing. With the widespread availability of the internet, consumers can easily access pricing information. A consequent of this is that price competition has become a much more important factor in a consumer's choice of which product to buy.

Examples of projects include investigating the impact of price competition on the optimal prices charged for time-limited products such as airline tickets and hotel rooms. We also look at customer choice modelling for vehicle routing and ferry fares.

Stochastic programming and simulation

Stochastic programming and processes represent an important part of our research. The optimisation side of our work includes developing and or investigating new mathematical models. These models capture the uncertainty and other features such as competition, equilibrium and hierarchical relationships between decision makers.

The simulation aspect of our work is on construction of stochastic simulation models. These are for the analysis of:

  • airline ticket pricing
  • revenue management models
  • epidemiological models, especially TB and HIV
  • healthcare modelling
  • Markov combat models
  • models of fire service emergency cover

Transportation and supply chain

We apply exact and heuristic techniques to tackle a wide range of transportation, supply chain and logistics problems. These include:

  • traveling salesman and vehicle routing problems
  • production planning and scheduling
  • inventory control

Methods implemented include:

  • mathematical programming
  • stochastic processes
  • exact and heuristic algorithms for combinatorial optimisation
  • artificial intelligence
  • game theory
  • Laplace transforms

These methods were applied to address production planning for:

  • heat and power co-generation
  • vehicle routing optimisation
  • enhancing efficiency of supply chains