Careful planning is essential to make efficient use of resources. For large-scale and complex systems, the use of mathematical optimisation can have a great impact on resource efficiency. Planning problems of this kind occur in many different sectors and the available resources can be anything from electronic components, vehicles, or machines to people that perform some tasks.
In situations when it is impossible for a human planner to fully grasp all the possibilities and choose a best possible plan, optimisation can be used to aid the decision process. This includes to formulate a mathematical model of the problem and to develop or select a solution method to compute a good, or preferably optimal, solution. Decision problems that are formulated to plan or schedule the use of resources often take the form of discrete optimisation problems.
Current research activities are described under the research domain Mathematics and algorithms for intelligent decision-making that introduces the work done in the group I’m leading.
My research area is discrete optimisation, with a special interest in decomposition methods and applications within scheduling and resource allocation. Our applied projects are often carried out in collaboration with industry or with other stakeholders. Examples of studied applications are the design of electronic systems in aircraft, staff scheduling in healthcare, underground mining, and railway crew planning. Some of these are highlighted in the list of research projects below.
Our research projects contribute to pushing the limits for when optimisation can be of practical use, both with respect to how a practically relevant problem is addressed and modelled, and through the development of efficient solution strategies.
On the method development side, areas of contribution include Dantzig-Wolfe decomposition, Lagrangian relaxation, column generation, branch-and-price, and logic-based Benders decomposition to hybridize MIP and CP. Other methodological contributions are within dynamic programming, decision diagrams for optimisation, metaheuristics, and mathheuristics.