A broad spectrum of very diverse resource allocation and decision problems arising in public infrastructure investment planning, power systems operation, supply chain management, production planning, fleet management, traffic planning, network design, economics, risk management, health care, project management, telecommunications, cloud computing, process control, etc. are naturally formulated as mathematical optimization problems. Most if not all of these optimization problems share the following key attributes.
- High dimensionality.
Decision makers typically need to orchestrate thousands of degrees of freedom that are subject to complex interdependencies and restrictions.
- Data uncertainty.
Many problem parameters are subject to substantial measurement errors or are simply unknown at the time when the optimization problem is formulated.
- Dynamic nature.
The information available to decision makers changes over time – often in unpredictable ways – which necessitates a chain of recourse actions and rebalancing decisions that are difficult to plan in advance.
Decision problems with these complicating features are often far beyond the reach of analytical methods or classical numerical techniques plagued by the notorious curse of dimensionality. The aim of our research is to develop rigorous new modeling paradigms for large-scale dynamic decision problems under uncertainty, to design efficient and reliable algorithms for their solution and to distil managerial insights and policy implications for innovative applications in energy systems engineering and management.