Planning for the unknown. Towards optimal decisions under uncertainty.


Many practical decisions have to be made before key information is known. For example, network operators have to make investments in the electricity grid while future costs of capital and future supply in renewable energy are uncertain. Decision support is required for such problems, also in healthcare, logistics and engineering. However, this support is only available to a limited degree because of the high complexity of the underlying mathematical optimization problems.

Such so-called stochastic mixed-integer optimization problems are extremely difficult to solve since they combine the difficulties of having integer decision variables (i.e., discrete or yes/no decisions) and uncertainty in the parameters of the problem. Traditional solution methods combine solution approaches from deterministic mixed-integer and stochastic continuous optimization, but are generally unable to solve practical problems of realistic sizes. Even simplified, deterministic versions of these problems are challenging since they are not convex, and thus efficient solution methods from the well-developed field of convex optimization cannot be used to solve them.

Interestingly, however, my recent work has shown that stochastic mixed-integer optimization problems are (approximately) convex. Thus, from a “convex” perspective, these stochastic problems are easier to solve than their deterministic counterparts. In this sense, the introduction of uncertainty to mixed-integer optimization problems overcomes the difficulty of having integer decision variables.

The aim of this project is to design fast solution methods for stochastic mixed-integer optimization problems, exploiting this new and exciting perspective and building on my previous work. The newly developed solution methodology will be validated by applying the developed methods to optimal investments in the electricity grid for a network operator.

In conclusion, this research project will yield a new and efficient type of solution methodology for stochastic mixed-integer optimization problems and enable better decision support for many practical decisions under uncertainty.





Dr. W. Romeijnders MSc

Verbonden aan

Rijksuniversiteit Groningen, Faculteit Economie en Bedrijfskunde, Operations


Dr. W. Romeijnders MSc


01/09/2017 tot 31/08/2020