# Mathematics and algorithms for intelligent decision-making

There are many benefits of using mathematics and algorithms to aid decision-making in complex settings. Our main focus is on discrete optimisation for decision problems that aim to schedule or allocate resources. In our research projects, we both find new ways to address decision problems by optimisation and develop new methods for solving them.

Thanks to digitalisation, the available amount of data to support decision-making has reached a high level of maturity, and so has the capability of processing this data. Alongside the data science disciplines, optimisation — used for decision support — plays a key role in the further development of tools to support advanced decision-making. The scale and complexity of the problems relevant to address continue to increase and this calls for research that address the mathematics and algorithms needed in optimisation methods.

## Intelligent decision-making

We believe that truly intelligent decision-making is achieved through an integration of model-based and data-driven approaches that are designed or used in interaction with a human decision-maker. To successfully apply mathematics and algorithms as part of real-world decision-making requires careful mathematical modelling and data collection. An inherent property of many decision problems of practical relevance is that they are computationally challenging. Solving such a problem within a reasonable amount of time often requires the development of specialised methods that exploit the mathematical structure of the problem.

On the journey towards sustainability, our contribution is to develop mathematical models and solution methods for practically relevant but computationally challenging problems in scheduling and resource allocation.

### Discrete optimisation

There are many types of decision problems that aim to schedule or allocate resources, and these lend themselves to be addressed as discrete optimisation problems. Most practically relevant discrete optimisation problems are NP-hard, which means that their worst-case solution times grow exponentially with the problem size. The practical consequence of this is that, for challenging instances, even the state-of-the-art optimisation solvers will frequently fail to deliver a solution within weeks or even thousands of years of computational time.

Over the last decades, there has been an impressive development of methods for solving discrete optimisation problems. Thanks to this, many important planning and scheduling problems can be solved with a reasonable computational effort—however, many practically relevant problems still pose great challenges.

### Organisation

This research direction, formerly called Operations Research Methods for Scheduling and Resource Allocation Problems has been established through funding from the Center for Industrial Information Technology (CENIIT) and is carried out at the Division of Applied Mathematics (TIMA) in the Department of Mathematics (MAI). Leader of the group is Elina Rönnberg.

Some of our applied projects and PhD thesis projects are highlighted in the list of research projects below.