Initially, integer programming has been a major area of research. In particular the development of cutting planes for mixed integer programming has had a significant influence in the development of the remarkably powerful mixed integer programming systems now available. In addition the area of production planning has benefitted both theoretically and practically from research in this area.
The importance of structure in convex optimization, with the growing awareness of its applicability in both engineering, discrete optimization and other branches of mathematics, is another area in which work at CORE has played a major role. Recent work has shown that structure affects even fundamental methods such as Newton’s method, and basic nonlinear optimization can benefit significantly both theoretically and computationally from this new viewpoint.
The study of large energy investments as well as of electricity transfers and markets has been a major activity for over twenty five years, while the design and regulation of markets in Europe has become of particular importance in the last 5-10 years. The importance of these ties has been concretized in the creation of the Tractebel Chair at CORE and the creation of a major research group at Electrabel employing numerous researchers who have obtained their UCL doctorates at CORE.
Current research areas
Research in Operations Research at CORE is concentrated in the areas of optimisation (mathematical programming) and the calculation of equilibria. The three major research areas are:
- Modelling and solution of industrial Economics Problems
- The theory of incomplete markets: the role of money and monetary policy when asset markets are incomplete; general equilibrium with asymmetric information; uncertainty and insurance in equilibrium models
- Analysis of problems of industrial economics with and without treatment of uncertainty. These problems derive from the current movement towards deregulation in network industries such as natural gas, electricity, telecommunications, railways. They in part deal with market simulation under imperfect competition and computation of access pricing rules
- Study of the economic foundations of the location of firms, including aspects such as pricing, organisation of production, externalities and competition
- Design of algorithmic procedures for the modelling and solution of the problems identified above. Use has mainly been made of existing software (optimisation and complementarity algorithms) in order to compute equilibria. Reusability is one important aspect of this activity. Problems involving several agents and/or several scenarios are natural candidates for parallel algorithms. For the solution of location problems, methods used also include the computation of equilibria, as well as global and discrete optimisation
- Discrete optimization: Theory, algorithms and software for modeling and solving mixed integer programming problems. Topics studied include
- Tight a priori formulations for various structures arising in applications in the areas of production planning, network design and telecommunications, scheduling, location and logistics
- “Strong” or effective cutting planes for problems of different structure and algorithms to use such cuts in a branch-and-cut framework
- Intelligent heuristic algorithms for intractable problems that provide reasonable practical performance guarantees
- Parallel and decomposition algorithms for large or intractable models (in particular models involving uncertainty)
- More effective integration of model knowledge into the optimization algorithm
- Linear and nonlinear optimisation. Major research topics are :
- Interior point algorithms from both a theoretical and computational point of view. The research in interior point methods is aimed at providing a full convergence and complexity theory for special symmetric nonlinear problems, such as linear problems, semi-definite problems, and problems based on Lorentz cones. Future work is planned to extend existing algorithms to handle applications ranging from Control Theory and Plasticity Theory to Discrete Optimisation and Equilibrium models. In many cases these algorithms can be used as auxiliary tools in general methods for treating nonconvex problems
- Interactive software development based on new computational paradigms.To tackle the challenging application domains such as material sciences and control, algorithms for large scale models with intertemporal structure will be developed and implemented. The software developed will depend both on parallel computation, and the adoption of object oriented paradigms for both modelling and software reusability
Case studies
The Centre of Excellence in Supply Chain Management (CESCM) gathers a critical mass of faculty, researchers and experts in the field "supply chain management" (SCM).
The definition of SCM is interpreted broadly to cover all aspects of production, logistics and the supplier relations. It combines operations management, management science and industrial organization in a systematic attempt to understand, model and support the multi-level organizational behavior.
CESCM research is in particular oriented towards :
empirical analysis, the economic and systemic modeling of inter-organizational relations
the study and development of methodologies and techniques for the decision support systems at all hierarchical levels of the chain
the study, modeling and optimization of systems of decentralized or distributed coordination.
CESCM members are closely affiliated with CORE: Center of Operations Research and Economics and further organizational cooperation is underway.
The CESCM organizes in collaboration with ABCAL two executive programs in Supply Chain Management.
The first program, the "Executive Master in Supply Chain Management" was first launched in 2005.
To get some more information : www.uclouvain.be/formation-continue-supply.html
The second program, the "Executive Master in International Procurement and Sourcing" will be launched in 2009.
It will be conducted in English.
Both aim is to be one amongst the highest level executive program in Europe in their field.
They combine lectures with top faculty from different European Universities, lectures with leading practitioners and in company case studies.
