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Optimization and Operational Research PhD

Awards: PhD

Study modes: Full-time, Part-time

Funding opportunities

Research profile

The work in the Operational Research and Optimization research group is in three main areas: the mathematical and computing aspects of optimization, combinatorial optimization, and energy systems.

The core technology in optimization is the solution of large sparse linear and quadratic problems, and we provide world-class expertise in the two main solution methods for these: the simplex method and the interior point method. In combinatorial optimization, we provide expertise for modelling real-world problems using integer linear programming formulations and for deriving efficient exact and heuristic algorithms to solve them.

Specialist expertise in energy includes optimization of system planning and optimization, security of supply risk analysis, and decision support for public policy. We also have interests in PDE-constrained optimization, global optimization, decomposition methods, parallel computing, industrial applications of optimization and stochastic optimization.

Specific topics which could yield PhD projects include:

  • Algorithms for linear and nonlinear nonconvex smooth optimization problems
  • Optimization methods for linear, integer linear, quadratic and nonlinear programming
  • Decomposition methods for large-scale nonlinear nonconvex constrained optimization
  • Bundle methods
  • Warm starts for interior point methods
  • Pooling problems
  • Applications of optimization in logistics
  • Parameter uncertainty in queueing theory and revenue management.
  • Facility location and vehicle routing

Training and support

Being part of the Operational Research and Optimization group will give you the opportunity to meet and confer with academics worldwide. You will be a member of the Edinburgh Research Group in Optimization (ERGO) which, through its regular seminar series, attracts local and international researchers interested in the development of operational research and optimization. As a group, we are currently collaborating with researchers in Denmark, the Netherlands, Canada, USA, Italy, Norway, China, France, Spain, Germany and Turkey, and are invited to give addresses and organise workshops at major optimization, OR and energy conferences.

Facilities

You will enjoy excellent facilities, ranging from one of the world’s major supercomputing hubs to libraries for research at the leading level, including the new Noreen and Kenneth Murray Library at King’s Buildings.

Students have access to more than 1,400 computers in suites distributed across our University’s sites, many of which are open 24 hours a day. In addition, if you are a research student, you will have access to dedicated desk space with monitors and a laptop computer.

We provide all our mathematics postgraduates with access to software packages such as:

  • Maple
  • Matlab
  • Mathematica

Research students are allocated parallel computing time on ‘Eddie’, the Edinburgh Compute and Data Facility. You can also request use of the BlueGene/Q supercomputer facility for your research.

VIDEO: Operational Research (OR) MSc Graduates

Entry requirements

These entry requirements are for the 2025/26 academic year and requirements for future academic years may differ. Entry requirements for the 2026/27 academic year will be published on 1 Oct 2025.

A UK first class honours degree, or its international equivalent, in an appropriate subject; or a UK 2:1 honours degree plus a UK masters degree, or their international equivalents; or relevant qualifications and experience.

International qualifications

Check whether your international qualifications meet our general entry requirements:

English language requirements

Regardless of your nationality or country of residence, you must demonstrate a level of English language competency which will enable you to succeed in your studies.

English language tests

We accept the following English language qualifications at the grades specified:

  • IELTS Academic: total 6.5 with at least 6.0 in each component. We do not accept IELTS One Skill Retake to meet our English language requirements.
  • TOEFL-iBT (including Home Edition): total 92 with at least 20 in each component. We do not accept TOEFL MyBest Score to meet our English language requirements.
  • C1 Advanced (CAE) / C2 Proficiency (CPE): total 176 with at least 169 in each component.
  • Trinity ISE: ISE II with distinctions in all four components.
  • PTE Academic: total 65 with at least 59 in each component. We do not accept PTE Academic Online.
  • Oxford ELLT: 7 overall with at least 6 in each component.

Your English language qualification must be no more than three and a half years old from the start date of the programme you are applying to study, unless you are using IELTS, TOEFL, Trinity ISE or PTE, in which case it must be no more than two years old.

Degrees taught and assessed in English

We also accept an undergraduate or postgraduate degree that has been taught and assessed in English in a majority English speaking country, as defined by UK Visas and Immigration:

We also accept a degree that has been taught and assessed in English from a university on our list of approved universities in non-majority English speaking countries (non-MESC).

If you are not a national of a majority English speaking country, then your degree must be no more than five years old at the beginning of your programme of study.

Find out more about our language requirements:

Academic Technology Approval Scheme

If you are not an EU, EEA or Swiss national, you may need an Academic Technology Approval Scheme clearance certificate in order to study this programme.

Fees and costs

Tuition fees

AwardTitleDurationStudy mode
PhDOptimization and Operational Research4 YearsFull-timeTuition fees
PhDOptimization and Operational Research8 YearsPart-timeTuition fees
PhDOptimization and Operational Research with Internship4 YearsFull-timeTuition fees
PhDOptimization and Operational Research with Internship8 YearsPart-timeTuition fees

Scholarships and funding

Most PhD students in Mathematics receive full scholarships to cover their tuition fees and living costs.

Others may use a combination of the following funding to pay their tuition fees and living costs:

  • scholarships
  • borrowing money
    • taking out a loan
    • family support
  • personal savings
  • income from work
  • employer sponsorship

Explore sources of funding for postgraduate study

Featured funding

UK government postgraduate loans

If you live in the UK, you may be able to apply for a postgraduate loan from one of the UK's governments.

The type and amount of financial support you are eligible for will depend on:

  • your programme
  • the duration of your studies
  • your tuition fee status

Programmes studied on a part-time intermittent basis are not eligible.

Other funding opportunities

Search for scholarships and funding opportunities:

Further information

  • School of Mathematics
  • James Clerk Maxwell Building
  • Peter Guthrie Tait Road
  • The King's Buildings Campus
  • Edinburgh
  • EH9 3FD

Application deadlines

We strongly recommend you submit your completed application as early as possible, particularly if you are also applying for funding or will require a visa. We may consider late applications if we have places available. All applications received by 20 January 2025 will receive full consideration for funding. Later applications will be considered until all positions are filled.

How to apply

You must submit two references with your application.

Find out more about the general application process for postgraduate programmes:

Further information

  • School of Mathematics
  • James Clerk Maxwell Building
  • Peter Guthrie Tait Road
  • The King's Buildings Campus
  • Edinburgh
  • EH9 3FD