Grant: Discovery Grants Program - Individual

Decisions often need to be made in situations where one has incomplete knowledge about some of the parameters of the problem that he is addressing. This is for example the case in a problem of portfolio selection where the future value of an asset is uncertain, or in an inventory management problem where the future market demand for a product might be subject to changing. Distributionally robust optimization is a generalization of stochastic programming that can provide essential guidance in managing such decision problems since it can account for ambiguity in the choice of a distribution model. Such ambiguity is often present in practice and can make the solution of a stochastic program misleading. The mission of my research program is two-fold. 1) I plan to develop theory that will help answer important open questions that are preventing the distributionally robust model to be applicable at a large scale. 2) I also plan to take a leading role in the integration of the methodology to important industrial problems. These will include: - Resource allocation problems such as the selection and valuation of a portfolio of investment for long term retirement plans. - Inventory management problems such as the problem faced by airline companies when composing a fleet of aircraft prior to knowing the actual demand for flights. - Development of mines and production of renewable energy where uncertainty is omnipresent due to the little knowledge of the available resources. - Marketing problems such as how to propose items more likely to be purchased by an online customer or present him the most effective ad. My hope is that distributionally robust optimization and its derivatives soon become common practice in the field of decision making under uncertainty.