Optimizing decisions in situations with unresolved ambiguity

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Decisions often need to be made in situations where one has incomplete knowledge about some of the parameters of the problem being addressed. This is for example the case in an inventory management problem where the future market demand for a product might be subject to change, or in a problem of portfolio selection where the future value of assets is uncertain. While there are many situations in which the nature of uncertainty can be fully characterized using distribution models, there is now a growing amount of evidence that indicates that such models are in most situation impossible to identify precisely and unequivocally. Indeed, in the era of “Big data”, it is now common practice for decision maker to extract distribution information from immense collection of historical data, yet such procedures necessarily leave one with an imprecise characterization of the distribution and of how much this distribution actually resembles the distribution of future outcomes. One might also evoke the debates and controversy that have emerged following the recent financial crisis regarding how to model the likelihood of joint realization of events (e.g. in the pricing of collateralized debt obligations) and even regarding how to quantify risk (e.g. the use of value at risk or expected shortfall in banking regulations as proposed by the Basel III accords). Both debates have serious implications for industrial engineering problems where risk needs to be mitigated.****The objective of this research program is to shed some light on how to properly and efficiently handle the unresolvable ambiguity that plagues a great number of important decision problems emerging from a wide range of engineering, management and governance contexts. In particular, this program will instigate theoretical and algorithmic discoveries that are expected to have serious impact for applications such as:*** Hydro-Québec's long-term planning of hydroelectric production in an environment where it is difficult to determine future water flows and yet where one cannot afford accidental flooding of neighbouring territories;*** Data routing over the Internet of packets by telecommunication companies like Videotron or Rogers, given the uncertainty of transmission times and pre-established agreements about quality of service;*** Development of efficient environmental policies to protect against global warming when sensitive variables of climate systems cannot be measured;*** Supply chain management for big retailers like Walmart or Sears, when some suppliers are located offshores and cannot yet be considered reliable;*** Design of recommendation systems for online commerce like Amazon in a market where clients are faced with a plethora of choices and where market manipulators thrive;*** Portfolio management and pricing of financial derivatives by Canadian banks in a context where one cannot rely on a distribution model for future asset values.***