Project code



School of Mathematics and Physics

Start dates

October, February and April

Application deadline

Applications accepted all year round

Applications are invited for a self-funded, 3-year full-time or 6-year part time PhD project.

The PhD will be based in the School of Mathematics and Physics, and will be supervised by Professor Dylan Jones.

The work on this project will involve:

  • Developing goal programming models for enhanced clustering 
  •  Using clustering to improve goal programming based decision making
  •  Applying the developed methodology to decision problems from application areas such as healthcare, transportation and logistics or renewable energy and sustainability.

Goal programming is an established technique within the Operational Research topic of Multiple Criteria Decision Making. It is used in order to formulate and provide solutions to decision problems with multiple conflicting objectives and potentially multiple decision makers to satisfy. Members of the CORL have used goal programming to model and solve decision problems within many fields include healthcare planning, logistics of offshore wind farms and mapping of Arctic search and rescue needs. Recently, these have included use of clustering to help analyse the results. 

Clustering methods belong to the field of data analytics and machine learning and have hence received considerable theoretical and application-based interest in recent years. The quality of a clustering solution can be measured by many different metrics, some of which are problem dependent. Clustering can hence be posed as a multi-criteria problem, and there is a growing body of literature applying multiple objective methodologies to the clustering problem, however there is little research that utilises the technique of goal programming for this purpose. 

This project therefore explores the synergies between goal programming and clustering in two principal directions. Firstly, the use of clustering to improve the modelling power of goal programming will be investigated. Means of clustering by decision variables, stakeholders goals and parameters will be investigated, including the use of recent goal programming variants. A clustering based goal programming methodology will hence be developed and tested on applications arising from the CORL research centre. Secondly, the use of goal programming to aid the constrained clustering technique will be investigated, with goals pertaining to common clustering performance metrics and an emphasis on the trade-off between balance between clusters versus efficiency of the overall clustering solution. The resulting goal programming based clustering method will be evaluated on established test sets.

Entry requirements

You'll need a good first degree from an internationally recognised university or a Master’s degree in an appropriate subject. In exceptional cases, we may consider equivalent professional experience and/or qualifications. English language proficiency at a minimum of IELTS band 6.5 with no component score below 6.0.

We particularly welcome applications from students with an understanding of Operational Research (e.g. industrial engineering, computer science, mathematics and other relevant disciplines). Students must be competent in, or willing to learn, optimisation and data analytics computer software.

How to apply

We encourage you to contact Prof Dylan Jones ( to discuss your interest before you apply, quoting the project code.

When you are ready to apply, please follow the 'Apply now' link on the Operational Research and Logistics PhD subject area page and select the link for the relevant intake. Make sure you submit a personal statement, proof of your degrees and grades, details of two referees, proof of your English language proficiency and an up-to-date CV. Our ‘How to Apply’ page offers further guidance on the PhD application process. 

When applying please quote project code:SMAP7490423