The Art and Science of Modeling Decision-Making Under Severe Uncertainty

Authors

DOI:

https://doi.org/10.7494/dmms.2007.1.2.111

Keywords:

mathematical modeling, severe uncertainty, maximin, worst-case analysis, robust optimization, info-gap

Abstract

For obvious reasons, models for decision-making under severe uncertainty are austere. Simply put, there is precious little to work with under these conditions. This fact highlights the great importance of utilizing in such cases the ingredients of the mathematical model to the fullest extent, which in turn brings under the spotlight the art of mathematical modeling. In this discussion we examine some of the subtle considerations that are called for in the mathematical modeling of decision-making under severe uncertainty in general, and worst-case analysis in particular. As a case study we discuss the lessons learnt on this front from the Info-Gap experience.

References

Avriel M. (1976). Nonlinear Programming: Analysis and Methods. Englewood Cliffs, NJ: Prentice-Hall.

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

Ben-Haim Y. (2006). Info-Gap Decision Theory: Decisions Under Severe Uncertainty. 2nd Edition. Amsterdam: Academic Press/Elsevier. DOI: https://doi.org/10.1016/B978-0-12-373552-2.X5000-0.

Ben-Haim Y. (2005). Value-at-risk with info-gap uncertainty. The Journal of Risk Finance, 6(5), pp. 388–403. DOI: https://doi.org/10.1108/15265940510633460.

Ben-Tal A., El Ghaoui L. & Nemirovski A. (2006). Foreword: Special issue on robust optimization. Mathematical Programming, 107(1–2), pp. 1–3. DOI: https://doi.org/10.1007/s10107-005-0676-2.

French S. (1988). Decision Theory: An Introduction to the Mathematics of Rationality. Chichester: Ellis Horwood.

Grünig R. & Kühn R. (2005). Successful Decision-Making: A Systematic Approach to Complex Problems. Berlin–Heidelberg: Springer. DOI: https://doi.org/10.1007/3-540-27503-7.

Hillier F.S. & Lieberman G.J. (2005). Introduction to Operations Research. 8th Edition. New York: McGraw-Hill.

Markland R.E. & Sweigart J.R. (1987). Quantitative Methods: Applications to Managerial Decision Making. New York: John Wiley & Sons.

Kouvelis P. & Yu G. (1997). Robust Discrete Optimization and Its Applications. Nonconvex Optimization and Its Applications, 14. Dordrecht: Kluwer Academic Publishers. DOI: https://doi.org/10.1007/978-1-4757-2620-6.

Ragsdale C.T. (2004). Spreadsheet Modeling and Decision Analysis: A Practical Introduction to Management Science. 4th Edition. Mason, OH: Thomson South-Western.

Rustem B. & Howe M. (2002). Algorithms for Worst-Case Design and Applications to Risk Management. Princeton, NJ: Princeton University Press. DOI: https://doi.org/10.1515/9781400825110.

Sniedovich M. (2003). OR/MS Games: 3. The counterfeit coin problem. INFORMS Transactions on Education, 3(2), pp. 32–41. DOI: https://doi.org/10.1287/ited.3.2.32.

Sniedovich M. (2006). What’s Wrong with Info-Gap? An Operations Research Perspective. Working Paper MS-1-06, presented at the ASOR Mini-Conference, Melbourne, Australia, December 1, 2006. URL: https://info-gap.moshe-online.com/info-gap.pdf [20.08.2026].

Steuer R.E. (1986). Multiple Criteria Optimization: Theory, Computation, and Application. New York: John Wiley & Sons.

Vladimirou H. & Zenios S.A. (1997). Stochastic programming and robust optimization. In: Gal T. & Greenberg H.J. (Eds.), Advances in Sensitivity Analysis and Parametric Programming. International Series in Operations Research & Management Science, 6, pp. 395–447. Boston, MA: Kluwer Academic Publishers. DOI: https://doi.org/10.1007/978-1-4615-6103-3_12.

Wald A. (1945). Statistical decision functions which minimize the maximum risk. Annals of Mathematics, 46(2), pp. 265–280. DOI: https://doi.org/10.2307/1969022.

Wald A. (1950). Statistical Decision Functions. New York: John Wiley & Sons.

Winston W.L. (1994). Operations Research: Applications and Algorithms. 3rd Edition. Belmont, CA: Duxbury Press.

Downloads

Published

2007-10-11

Issue

Section

Articles

How to Cite

Sniedovich, M. (2007). The Art and Science of Modeling Decision-Making Under Severe Uncertainty. Decision Making in Manufacturing and Services, 1(2), 111-136. https://doi.org/10.7494/dmms.2007.1.2.111