The objective of this project is to set up a joint collaboration between NTNU and Universite Paris Sud in the development of numerical methods for solving an important class of applied decision problems, which are stochastic bilevel optimization problems. This class of problems has emerged recently as the modelling vehicle of choice when the optimal decisions should be taken in the presence of several independent actors and, in addition, substantial uncertainty is present in the problem data.
Numerous ap plications of these problems include pricing of telecommunications infrastructure and services, collaborative service provision in service industries, supply chain management, transportation, energy markets. Despite high theoretical and practical value of such problems, the current state of solution techniques is inadequate for many realistic applications.
Both Norwegian and French counterparts of the proposed collaboration have obtained recently important breakthroughs in the development of numerical me thods for solution of bilevel stochastic problems, pursuing different approaches. Further progress very much depends on successful collaboration and exchange of results during short research visits by senior and junior research staff of both sides. We exp ect that such exchange will result in synergies between our respective approaches, which will allow the development of methodology, numerical tools and applications of qualitatively higher level compared to what we could have obtained independently. Impor tant component of our objectives is training of young researchers (post doctoral and PhD students) who will be capable to work on these topics further.
The project will focus on the following interrelated aspects
- Methodology (structural properties of bi level problems and modeling of risk in bilevel setting)
- Algorithms and software tools.
- Applications to industry and services (Analysis of optimal pricing of infrastructure and services in ICT environment)