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A decomposition framework for mathematical programming problems, Mathematics, Computer Science, Operations Research – PhD (Funded)

  • Full or part time
  • Application Deadline
    Friday, November 15, 2019
  • Competition Funded PhD Project (Students Worldwide)
    Competition Funded PhD Project (Students Worldwide)

Project Description

Academic Supervisors:
Dr Stephen J. Maher, Department of Mathematics, College of Engineering, Mathematics and Physical Sciences, University of Exeter.

Department of Mathematics, Streatham, Exeter

Project Description:

Mathematical optimisation problems arising from real-world applications typically consist of many interconnecting components, i.e. a fleet of vehicles at a delivery depot, crew and aircraft in airline operations and the numerous, semi-autonomous power stations supplying the electricity grid. These interconnections introduce structure that can be exploited through the use of decomposition techniques. A popular decomposition technique used to exploit such structure is Benders’ decomposition.

Recently, a general Benders’ decomposition framework has been made available within the mathematical and constraint programming solver SCIP ( This framework provides the functionality to solve many real-world optimisation problems, specifically mixed integer programs and convex quadratic programs. However, there are still many problem classes that are not fully supported, such as convex and non-convex mixed integer non-linear problems. The goal of this project is to extend the Benders’ decomposition framework in SCIP to handle a wider range of problem classes. This will involve the development of novel solution algorithms that can be applied to general problems instances.

This project requires a high competency in mathematics and software design and development. You will become part of the SCIP Development Team ( and contribute to the growth of this highly regarded general purpose solver. Knowledge of discrete optimisation, operations research and linear programming is a bonus.

This award provides annual funding to cover UK/EU/International tuition fees and a tax-free stipend. The studentship will be awarded on the basis of merit for 3.5 years of full-time study to commence in February 2020.

Funding Notes

The University of Exeter’s College of Engineering, Mathematics and Physical Sciences is inviting applications for a fully-funded PhD studentship to commence in February 2020 or as soon as possible thereafter. For eligible students the studentship will cover UK/EU/International tuition fees plus an annual tax-free stipend of at least £15,009 for 3.5 years full-time, or pro rata for part-time study. The student would be based in the College of Engineering, Mathematics and Physical Sciences at the Streatham Campus in Exeter.

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