The Department of Mathematics and Computer Science has openings for four PhD positions,
on various topics in stochastics and in algorithms. These positions are offered in the context of the NETWORKS project, a collaboration of world-leading researchers from four institutions in The Netherlands: TU Eindhoven, University of Amsterdam, Leiden University and the Centrum Wiskunde & Informatica (CWI). Research in NETWORKS focuses on stochastics and algorithmics for network problems. NETWORKS offers a highly stimulating research environment and an extensive training program for PhD students.

Possible topics for the four positions at TU Eindhoven are as follows:

• Fairness in Combinatorial Optimization (supervisor: Frits Spieksma)

Recently the issue of fairness in decision-making algorithms is getting more and more attention. The goal of this project is to study fairness in combinatorial-optimization problems. As an illustration, consider the following problem. Given a directed graph, we want to find a cycle packing (that is, a collection of disjoint cycles) covering as many nodes as possible. A node can stand for an individual, and when a node is selected to be in the cycle packing, the corresponding individual receives something valuable. In addition, each node is labelled with a property, say {red, blue}. Fairness of a solution dictates that this feature should be taken into account when producing a solution. For instance, if all nodes in the cycle packing are blue (or if they are all red), the solution is deemed unfair. Clearly, there are various ways of taking fairness into account, e.g.,  by adding a constraint, or by weighing this in the objective. In this project we want to develop efficient algorithms that lead to high-quality, fair solutions for various combinatorial-optimization problems, and we want to investigate trade-offs between fairness and quality of the solutions.

• Statistical mechanics of and on random graphs (supervisor: Remco van der Hofstad)

There are intimate ties between algorithmic problems, statistical mechanical models and random graphs. Here, we plan to explore these connections. What can be said about the solution space of the algorithmic assignments, and how do these correspond to phase transitions in the system? What are the right observables to describe such phase transitions, and how do such observables scale in the near-critical regimes? Examples are k-SAT assignment problems, as well as Ising and Potts models.

• Performance analysis of automated warehousing systems (supervisors: Jacques Resing and Ivo Adan)

Order picking is the process of finding and extracting products from a storage location in a distribution center to fulfill customer orders. Picking has been recognized as one of the most challenging activities in terms of time, labor, and cost for most warehouses. E-Commerce companies are automating their warehouses at an increased pace to achieve high speed and flexibility in their picking operations. Recent advances in robotics offer a rich variety of warehouse automation technologies that may help realize these objectives. Consequently, warehouse managers are confronted with complex decisions on identifying and tailoring the right mix of warehouse automation technologies. In this project we aim to develop and apply stochastic modeling, simulation, optimization and control techniques  to assess the performance of different types of warehouse automation concepts, including (but not limited to) (i) milkrun picking systems, where pickers travel on automated trolleys along the aisles to dynamically pick orders, (ii) collaborative picking which is a semi-automated picking concept where automated guided vehicles assist pickers, and (iii) mobile fulfillment systems where autonomous shuttles do the picking.  

• Optimal Routing of Autonomous Vehicles (supervisors: Sem Borst and Marko Boon)

This project focuses on optimal traffic flow of self-driving vehicles.  This emerging technology creates unique opportunities for managing traffic intersections in a fair and efficient manner, reducing traffic congestion.  Utilizing real-time information on the location of each vehicle and being able to communicate with each of them, we can consider new routing policies to steer vehicles through a road traffic network.  Specifically, under certain ideal circumstances, slot reservation schemes or platoon forming algorithms can drastically increase the capacity of traffic intersections compared to the current situation.  Still, this technology also raises significant mathematical challenges, and little is known about how these algorithms will perform in a network setting and how their performance is in terms of fairness and environment friendliness.  These challenges arise in particular from the stochastic nature of traffic flows and the quite complex interactions between autonomous and human operated vehicles.

Eligibility criteria

We are looking for enthusiastic and motivated applicants with a background in mathematics
(in particular stochastics) and an affinity for computer science, or with a background in computer science (in particular algorithms) with affinity for mathematics. At the starting date of your employment as a PhD student in the NETWORKS COFUND program, you should be in possession of a MSc degree.

In order to be eligible, make sure you send your complete application before the deadline of the call. Moreover, you meet the mobility requirement of the MSCA. This mobility requirement is: You may not have resided or carried out your main activity (work, studies, etc.) in the Netherlands for more than twelve months in the three years immediately before the starting date of your employment.

• Application deadline: March 31, 2021
• Contract: full time employment contract for 4 years
• Salary indication: from € 2.395,- to € 3.061,- in 4 years
• Location: the Netherlands (Amsterdam, Eindhoven, Leiden)

Before applying, first download and read the information package with more information on the NETWORKS research and the COFUND positions.