Operations Research (OR) is the mathematical study of resource allocation problems, decisions, games, uncertainty, scheduling and optimization. The various sub-disciplines of OR yield both analytic and computational tools that allow for mathematical modeling and efficient problem solving.

Key application areas are telecommunications, high performance computing, logistics, manufacturing, business systems, transportation, biological systems and natural resource management. The nature of research in OR is often problem specific, dealing with a wide set of methods applied to a given situation. Further, OR has a pure nature, dealing with theoretical properties of methods and models. 

At the School of Mathematics and Physics we excel in a wide variety of sub disciplines in both theoretical OR and applications. Our group sits at the intersection of applied mathematics, statistics, probability, theoretical computer science and various application domains.

Key research interests of the group include mathematical programming, computational geometry, optimal control, applied probability, stochastic mathematical biology, risk modeling, queueing theory, Monte Carlo simulation, applications to transport and logistics, applications to natural resource management and applications to conservation biology. 

Available Projects

Develop Integer Programming models and solution techniques for exact or heuristic solutions to the problems described in this paper: http://arxiv.org/abs/1508.03136

Dr Michael Forbes

Statistical analysis of and development of solution techniques for the problems in the FHCP Challenge Set

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Dr Michael Forbes

In 2007, B. Bollobas, S. Janson, and O. Riordan published an important paper titled ``The Phase Transition in Inhomogeneous Random Graphs,'' which gives properties of a very...

Dr Thomas Taimre

Random networks are often modelled without reference the particular space which they inhabit.  There is some work in this area (for example Penrose’s Random Geometric...

Dr Thomas Taimre

In many social networks, selection of friends on the basis of social status is very common. Similarly, websites may link to more popular websites in the hope of gaining more traffic. Simple models of these phenomena, where the benefits of connection vary according to some metric (for example...

Dr Thomas Taimre

Many networks from crystalline lattices to social networks display so-called self-organizing phenomena. This essentially means that global order or chaos can emerge from simple local rules.  Particular interest has been paid to these phenomena in light of residential segregation in the US...

Dr Thomas Taimre

The properties of complex networks are difficult to study without the aid of simulation, and so efficient and reliable simulation techniques for random networks are of great interest.  Two such methods are degree distributions and graph motifs.

In this project, you will investigate...

Dr Thomas Taimre

Stochastic game theory is the study of strategic interactions between actors in an environment where their payoffs are affected by the actions of all players in the past.

In this project, you will investigate in simulation simple models for stochastic network games, where the environment...

Dr Thomas Taimre

Social, economic, and infrastructure networks are crucially important to today's increasingly connected world.  In this project you will investigate how to estimate models of dynamic networks and conduct inference for these...

Dr Thomas Taimre

In this project students will implement the algorithms in the attached paper, possibly improving them by making more general use of lazy constraints.

Dr Michael Forbes

The aim of this project is to implement and improve upon the algorithms in the attached paper.  This will likely be done using Stochastic Dynamic Programming for the end game and Approximate Dynamic Programming, or similar, for the early and middle game.

Would suit someone with very...

Dr Michael Forbes

Due to the rapid advances in solution techniques in many areas of Operations Research, interesting projects can arise from applying up to date solution techniques to past papers, even very recent papers.

At an Honours level this may...

Dr Michael Forbes

This project considers the attached paper: Benders Decomposition, Branch-and-Cut, and Hybrid Algorithms for the Minimum Connected Dominating Set Problem.

The paper applies Benders Decomposition by repeatedly solving the master problem and adding Benders cuts.  This...

Dr Michael Forbes

Many real time and turn based strategy games have an initial phase of game play, before interaction with any opponents, that is almost completely focused on economic and/or military development.  This project would look to build stochastic dynamic programming models of this stage of one or...

Dr Michael Forbes

The Poisson lily-pond model is a spatial germ--grain process, whose ``germs'' are points of a Poisson process with ``grains'' growing at uniform rate from these germs, stopping when their boundaries touch.  While some results regarding the size of the largest connected...

Dr Thomas Taimre

A diffusion process on a Riemannian manifold has infinitesimal generator which is fundamentally related to the Laplace--Beltrami operator on that manifold.  For a...

Dr Thomas Taimre

The excess-phase model for interferometric signals is a simple model which well captures much of the complex behaviour observed in laser interferometers. ...

Dr Thomas Taimre

Mixture models are a powerful tool for many statistical applications, including density estimation from data.  
This project focuses on using mixture models in sequential or on-line importance sampling.  A specific application of interest is to the estimation of rare events,...

Dr Thomas Taimre

Stochastic differential equations driven by Brownian motion or L\'evy processes are well established as models for many real-world phenomena.  Just as there are efficient...

Dr Thomas Taimre

Random sums of random variables arise in many contexts of applied probability such as the probability of buffer overflow in queues, or when considering the probability of ruin for risk models.  When such quantities of interest cannot be evaluated precisely, there are many well established...

Dr Thomas Taimre

Benders Decomposition can be applied to problems with two tiers of decision variables, where the top tier are integer variables and the second tier are continuous variables.

This project would look at the application of similar approaches to problems where both tiers have integer...

Dr Michael Forbes

Approximate Dynamic Programming (ADP) is an emerging area within Operations Research.  Projects could investigate the application of ADP to a specific difficult stochastic optimisation problem, especially in a domain where the...

Dr Michael Forbes

Queueing networks are stochastic mathematical models that are often used for analyzing service, manufacturing and communication systems. One often attempts to model the situation at hand by means of a...

Dr Yoni Nazarathy