Wanted: Mathematical Programming for Human-Centric, Robust Decision Support

1. Wanted: Mathematical Programming for Human-Centric, Robust Decision Support Dipti Deodhare AINN Group, CAIR

2. The Unk-Unk (Unknown Unknown) • Uncertainties that are unanticipated. • United States Secretary of Defense Donald Rumsfield said at a press conference in 2003: “Reports that say that something hasn't happened are always interesting to me, because as we know, there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns — the ones we don't know we don't know.”

3. The Foot in Mouth award is awarded each year by the British Plain English Campaign for "a baffling comment by a public figure". (Source: Wikipedia)

4. Sources of Uncertainty • Ignorance • Noise such as measurement errors, or incomplete data • Events that have not yet occurred • The decision should avoid a catastrophic effect if any – problem should be modeled in such a way that the space of feasible solutions should exclude solutions that might have a catastrophic effect!

5. Classical Models – Mean-Risk • Markowitz’s Investment Portfolio Selection theory - analysis of asset selection which maximizes the return and minimizes risk for an investor. • Asset diversification: spreads risk over a mixture of equities, bonds, commodities, precious metals, property and currencies.

6. Classical Methods Contd. • Motivating application: planning production levels in the face of uncertain sales. • Recourse model – 2 stage with two vectors of decision • x specified before uncertain parameters get known (stage 1) – specify production and process operation levels • The second stage variables, y, take recourse in deciding what to do about any excess or shortage. • Chance-constrained model

7. Limitations • Mean-risk model: needs the variances, covariances • Recourse model: estimated cost structure needs to be defined • Chance-constrained model: probability distributions need to be known

8. Robust Optimization • Allow for flexibility in the solution after the uncertain values become known. • Solutions are designed to be insensitive to the underlying assumptions such as data values, functional relations between variables etc.

9. Decision-maker VS Stakeholder • Officers who contribute to the design of the decision support tool, the “decision-makers” are not usually the people who might use the tool, the “stakeholder”. • “Collective wisdom" has been demonstrated in both theoretical and empirical analyses to tend strongly toward risk averse options or poorly thought out "group-think" alternatives – the "brilliant" alternative or innovative approach foreseen by one individual is most likely to be the winning strategy!

10. VUCA! • Today’s unconventional combat environment, described as “naturalistic” in military literature, has Volatility, Uncertainty, Complexity, and Ambiguity (abbreviated to VUCA) - difficult to pre-program rational solutions. • Decision tools should be “human-centric” and facilitate what-if analysis and allow the user to set variables based on experience and personality.

11. Proposed Models • Worst-case Hedge: a policy that does as well as possible under worst possible outcomes • Interval Uncertainty Model • Minimax Regret • Uncertainty Sets • Train-by-example paradigms – neural networks? • Build a toolbox that helps you pick the right tool and includes suitable validation methods!

12. Acknowledgement http://www-math.cudenver.edu/~hgreenbe/booksEtc/GreenbergMorrison07chapter.pdf

13. Thank You