Description

Information-gap decision theory was initiated and developed by Ben-Haim (1996) and has its origins in the early 1980s in convex Modelling of materials, mechanical and dynamical problems. A system model is parameterised so that system response to loading is represented by nested sets containing excursions of system behaviour. Of particular interest is the level at which system behaviour exceeds some failure criterion. In work with Elishakoff (Ben-Haim and Elishakoff, 1990), Ben-Haim demonstrated how diligently applied probabilistic methods can result in disturbingly inaccurate estimates of the probability of failure of safety-critical systems, whilst convex analysis identified more reliable bounds on system behaviour (Ben-Haim and Elishakoff, 1990). This work was cultivated into a theory of non-probabilistic robust reliability (Ben-Haim, 1996) and subsequently into a complete theory of decision-making under severe uncertainty (Ben-Haim, 2006).

An info-gap analysis has three components: a system model, an info-gap uncertainty model and performance requirements. The system model describes the structure and behaviour of the system in question, using as much information as is reasonably available. The system model may, for example, be in the form of a set of partial differential equations, a network model, or indeed a probabilistic model such as a Poisson process. The uncertainty in the system model is parameterised with an uncertainty parameter alpha (a positive real number), which defines a family of nested sets that bound regions or clusters of system behaviour. When alpha = 0 the prediction from the system model converges to a point, which is the anticipated system behaviour, given current available information. However, it is recognised that the system model is incomplete so there will be a range of variation around the nominal behaviour. Uncertainty, as defined by the parameter, is therefore a range of variation of the actual around the nominal. No further commitment is made to the structure of uncertainty. Alpha is not normalised and has no betting interpretation, so is clearly distinct from a probability.

Next, two contrasting consequences of uncertainty are introduced: ‘catastrophic failure’ and ‘windfall success’. Two immunity functions, a robustness function and an opportunity function, describe the variation of alpha with the magnitude of the unfavourable and favourable consequences. Info gap theory therefore seeks to gain from favourable excursions in uncertain system behaviour as well as developing robust strategies that guard against the effects of unfavourable excursions. Excessive emphasis on failure can result in a loss of opportunity, but the two are not always mutually exclusive.

Software

none

Advantages

• Provides a quantitative measure of the robustness of decision options to severe uncertainty.

Disadvantages

• Computing robustness and opportuneness curves involves solving optimisation (minimisation and maximisation) problems that can be computationally expensive.

• Comparison of robustness curves from different settings can be challenging, though Ben-Haim (2006) devotes Chapter 4 of his book to addressing this problem.

Critique

Sniedovich (2007) has severely criticized Info-Gap decision theory, claiming that it is unsuitable for decision making under severe uncertainty. This criticism is presented on the Wikipedia Info-Gap page, with responses from Ben-Haim. Some of the history of the discussion can also be found on the related Wikipedia discussion page. We do not want to duplicate this discussion, and recommend that the interested reader follow its development at Wikipedia.

References and Further Reading

Ben-Haim, Y., 1996. Robust Reliability in the Mechanical Sciences. Springer, Berlin.

Ben-Haim, Y., 2001. Information-Gap Decision Theory: Decisions Under Severe Uncertainty. Academic Press, San Diego.

Ben-Haim, Y., 2006. Info-Gap Decision Theory: Decisions Under Severe Uncertainty. Academic Press, San Diego. p.384

Ben-Haim, Y. and Elishakoff, I., 1990. Convex Methods of Uncertainty in Applied Mechanics. Elsevier, Amsterdam.

Ben-Tal A., El Ghaoui L., Nemirovski, A., 2006. Mathematical Programming, Special issue on Robust Optimization, Volume 107(1-2).

Hall, Jim and Ben-Haim, Yakov, 2007, Making Responsible Decisions (When it Seems that You Can't). Engineering Design and Strategic Planning Under Severe Uncertainty.

Kouvelis, P. and Yu G., 1997. Robust Discrete Optimization and Its Applications. Kluwer.

Rosenblatt, M.J. and Lee H.L., 1987. A robustness approach to facilities design, International Journal of Production Research, 25(4), 479-486.

Rosenhead, M.J., Elton M., Gupta S.K., 1972. Robustness and Optimality as Criteria for Strategic Decisions, Operational Research Quarterly, 23(4), 413-430.

Rustem, B. and Howe M., 2002. Algorithms for Worst-Case Design and Applications to Risk Management. Princeton University Press.

Sniedovich, M., 2007. The art and science of modeling decision-making under severe uncertainty, Decision-Making in Manufacturing and Services, 1(1-2), 109-134.