Topic B.3: Robust multi-criteria optimization

The consideration of uncertainties in multi-criteria optimization problems for the assessment of resource efficiency presents a challenge from an economic, as well as a mathematical perspective. Robust optimization is currently an active research field. Various draft concepts on how single-criterion problems with data uncertainties should be handled to find robust solutions have been published in the past few years (Scholl, 2001; Bertsimas, Sim, 2004; Ben-Tal et al., 2010). This topic links up with these studies and expands on them in two respects. On the one hand, the robustness concepts under consideration are applied to multi-criteria optimization problems. This raises many exciting theoretical questions regarding properties and computability. On the other hand, the applicability of the models is tested on the basis of the practical questions in the mentioned forestry and agricultural applications. The models are therefore redesigned according to these demands and specific uncertainties (such as weather conditions, insect infestations, etc.), and the algorithms adapted to these problem formulations. MCDM models are specifically enhanced for a comprehensive assessment of action options in supply chains regarding the new robust planning tools and new mathematical approaches developed for “robust sensitivity analysis” in multi-criteria problems. The methodology is based on case studies from topic A.1 and then tested on the analyzed uncertainties in that topic. In conjunction with topics A.1 and B.1, assumptions are formulated for future development paths and potential uncertainties.

Methodologically, discrete optimization approaches - specifically from network optimization - are applied and, with the latter’s help, efficient method are developed according to the uncertainty structure (Cicerone et al., 2008; Schöbel, Kratz, 2009; Cicerone et al., 2009; Goerigk, Schöbel, 2010). Our preliminary work in this field refers to, among other things, a comparison of various robustness concepts within the context of the scheduling of time tables (Goerigk, Schöbel, 2010), as well as to the development of a bi-criteria approach to robust optimization (Schöbel, Kratz, 2009).