The notion of fairness has a long history within mathematical optimization. Clearly, in problems where entities or agents face the task of distributing a certain amount of resources among them, fairness questions are imminent. In many discrete optimization problems, agents can be modeled as nodes (or arcs) in a graph, and a solution has not only a global aspect, but also immediate consequences for the individual agents.

To find fair solutions for individual agents, there exist several techniques to incorporate aspects of fairness into discrete optimization problems. In recent years, however, novel fairness questions have surfaced that require new tools and concepts for finding fair solutions, among others in:

• Tournament design. Fairness is deeply ingrained in for instance sports, and there is an abundant literature on the very concrete problem of designing a fair knockout tournament. More generally, the challenge of devising fair rules is one of increasing importance given the massive interests.
• Kidney exchange. To maximize the number of kidney exchanges within a pool of patients and donors, a classical model is to find a collection of disjoint cycles in a suitably defined graph that covers as many nodes as possible. Any such set of cycles maximizes the number of kidney exchanges. But in the presence of multiple optimal solutions, the question arises which solution is fairest.
• Matching. Weighted matching problems arise very frequently, e.g., in assigning passengers to a taxi pool, where edge weights model for instance the waiting time for passengers or travel cost. Any minimum cost maximum cardinality matching will then minimize the total waiting time/cost. But from an individual perspective, specific matchings will give a (dis-) advantage to some passengers, and the challenge is to find a matching that distributes cost also from an individual perspective in a fair way.

The goal of this research project is to increase our understanding of fairness in combinatorial optimization problems by identifying situations where fairness plays a role, by proposing criteria for what it means for a solution to be fair, and by designing (and implementing) methods that yield fair solutions.

The successful candidate for this PhD position will work in the group Combinatorial Optimization of the department of Mathematics and Computer Science of TU/e under supervision of Prof. dr. Frits Spieksma and dr. Christopher Hojny. The successful candidate is expected to:

• Perform scientific research on topics of the above-mentioned research project.
• Publish results at (international) conferences and/or in (international) journals.
• Collaborate with other group members.
• Assist with educational tasks (e.g., supervision of (under-) graduate students in instructions accompanying a course).

• You have a master degree in (Applied) Mathematics or a related field.
• You have a strong background in Combinatorial Optimization, Discrete Optimization, and/or Integer Programming.
• You have good communcation skills.
• You are creative, and ambitious, as well as self-motivated, proactive, and goal-oriented.
• You have a good command of the English language (knowledge of Dutch is not required).
• Experience in programming will be considered an advantage.

• A meaningful job in a dynamic and ambitious university with the possibility to present your work at international conferences.
• A full-time employment for four years, with an intermediate evaluation (go/no-go) after nine months.
• To develop your teaching skills, you will spend 10% of your employment on teaching tasks.
• To support you during your PhD and to prepare you for the rest of your career, you will make a Training and Supervision plan and you will have free access to a personal development program for PhD students (PROOF program).
• A gross monthly salary and benefits (such as a pension scheme, pregnancy and maternity leave, partially paid parental leave) in accordance with the Collective Labor Agreement for Dutch Universities.
• Additionally, an annual holiday allowance of 8% of the yearly salary, plus a year-end allowance of 8.3% of the annual salary.
• Should you come from abroad and comply with certain conditions, you can make use of the so-called '30% facility', which permits you not to pay tax on 30% of your salary.
• A broad package of fringe benefits, including an excellent technical infrastructure, moving expenses, and savings schemes.
• Family-friendly initiatives are in place, such as an international spouse program, and excellent on-campus children day care and sports facilities.