Much research in multi-objective optimization has focused on developing what is known as “criterion-space search algorithms”. These methods make clever use of the extraordinary power of modern day single-objective branch-and-cut algorithms such as Cplex, Gurobi, and Express. Some examples of these methods are the classical ε-constrained method, variations of the box algorithm and the triangle splitting method(s).

This project, however, will focus on “decision-space search algorithms” (see Stidsen et al. (2014), Gadegaard et al. (2016), and Stidsen and Andersen (2018)) . That is, generalization of branch-and-cut algorithms to multiple objective optimization. Hence, methods for branching and bounding based on bound sets will be developed. In addition, cut-generation that cuts off dominated solutions and/or strengthens the bound sets will be studied. Peripheral subjects could be:

• The place of constraint programming in multi-objective optimization
• The impact of different variable and node selection rules to the overall performance
• Generation of minimal vs. maximal complete sets of efficient solutions

Methodology: Quantitative methods (optimization, linear and integer programming, heuristics, programming).

Prerequisite: strong background in mathematical optimization. Experience with programming is preferred.

Potential supervisors: Professor Lars Relund Nielsen and Assistant Professor Sune Lauth Gadegaard

Operations and Marketing related activities often require the most important business decisions, such as inventory, production/service planning, and pricing, delivery schedules, and service quality etc.

Within the area, there are plenty of interesting research topics, e.g.:

• The joint optimization of inventory and pricing decisions for single companies or supply chains;
• The optimization of multiple marketing efforts for single companies or supply chains;
• The cooperation and competition problems in service companies;
• Joint operations and marketing decisions in E-commerce environment.

However, the research should not be limited to these topics. It is always nice to discuss and spot new research topics with the aim to develop good research results.

Methodology: Mainly quantitative methods, e.g., optimization methods, heuristics, and simulation methods to deterministic or stochastic business systems.

Prerequisite: You are expected to have fundamental knowledge about optimization, operations management (operations research), and game theory.

Potential supervisor: Associate Professor Hongyan Jenny Li

Within the area of waste transportation, several different routing problems occur. Among these are

• Capacitated arc routing problems, often of very large scale (up to 10,000 edges) in a single or multi-compartment setup with or without additional constraints. This occur in curbside collection. See Kiilerich and Wøhlk (2018) for more information on these problems.

• Pick-up and delivery problems with availability for few items at the truck, and planning over one or several days. This occurs in container transportation.

• Inventory-routing problems. This occur in collection of recyclables from public locations. See Elbek and Wøhlk (2016) for more information on this. Additionally, periodic collection would result in a periodic VRP.

• Various location problems, location-routing problems, pick-up and delivery problems also occur within this overall frame.

Methodology: Real life data is available or can be obtained for many of these problems. As the problems are of large scale, the most natural research approach would be the use of (meta-)heuristics to obtain solutions. However, alternative approaches are more than welcome.

Prerequisite: You are expected to have experience with optimization and meta-heuristics and have strong programming skills.

Potential supervisor: Professor Sanne Wøhlk

Vehicle routing is generally concerned with the planning of routes for a fleet of vehicles in order to serve a given set of customers. Vehicle routing plays a significant role in several application areas and has been studied by several types of techniques, including both exact and heuristic algorithms. Please see the book Vehicle Routing: Problems, Methods, and Applications for an overview of vehicle routing.

For a PhD project, the point of origin may be a particular application area (e.g., routing in home care, routing of school buses), a particular type of technique (e.g., exact algorithms, branch-and-bound, branch-and-cut), a particular variation of a vehicle routing problem (e.g., vehicle routing with time-dependent travel speeds), or a combination of problem domains (e.g., location-routing). Other possibilities may also be considered. The promising PhD candidate is expected to play a major role in defining a promising project.

Methodology: Quantitative methods (optimization, heuristics, programming).

Prerequisite: Background in logistics, optimization, heuristics, programming.

Potential supervisor: Professor Jens Lysgaard

The warehouse represents an important component in many supply chains, and improvements in processes are of high value. Research within the area of warehousing includes several components, such as

• Warehouse design, layout
• Storage location assignment
• Order picking
• Coordination of inbound and outbound logistics.

See e.g. de Koster et al. (2007) and Gu et al. (2007) for an overview.

Research within warehousing offers a broad range of opportunities of using methods within the field of mathematical programming (exact methods or heuristics), stochastic models, or simulation.

As the topic is quite broad, there is plenty of opportunity for the potential student to identify a focus area of interest. It is recommended that the prospective student should develop a short statement of the specific problem he/she would like to work on.

Methodology: Quantitative methods, mathematical programming, stochastic optimization models, or simulation, depending on choice of focus.

Prerequisite: Excellent skills in computer programming and simulation. Knowledge of operations research and logistics.

Potential supervisors: Professor Christian Larsen and Professor Sanne Wøhlk