Info-Gap Decision Theory | Voodoo Decision-Making | Robust Decisions | Severe Uncertainty | Satisficing vs Optimizing | Maximin

## Towers of Hanoi

A very interesting and educationally rich puzzle. I regard it as a very good framework for describing how DP works. In fact, in my DP book I publicly declared that this is, in my mind, the Mother of all DP examples.

It is a pity that this treasure is not as popular in the official OR/MS literature as it is in the computer science literature where it is often used as a prime example to illustrate recursions.

In any case, in a an old paper, I discussed this games from an OR/MS point of view and explained how it can be solved by DP. The paper also describes a simple non-recursive solution to the problem, and there is an online interactive module for experimentation with the game.

Interestingly, in the framework of the traditional version of the problem the objective is to minimize the number of moves required to move the pieces from one platform to another (there are 2n-1 such moves). This is not very consistent with the original formulation of the problem according to which the End of the Universe will come when the task is completed.

In my paper I develop a new version of the problem involving the maximization of the number of moves. In this case the optimal solution requires 3n-1 moves.

The module animating the solutions to these two versions of the problem is an excellent tool for illustrating the difference between a 2n and a 3n complexity!

In any case, I highly recommend this paper to lectures teaching OR/MS and/or CS subjects dealing with algorithms.

An online implementation of the game is available on the front page of my site.

## Recent Articles, Working Papers, Notes

Also, see my complete list of articles
 Moshe's new book!
• Sniedovich, M. (2012) Fooled by local robustness, Risk Analysis, in press.

• Sniedovich, M. (2012) Black swans, new Nostradamuses, voodoo decision theories and the science of decision-making in the face of severe uncertainty, International Transactions in Operational Research, in press.

• Sniedovich, M. (2011) A classic decision theoretic perspective on worst-case analysis, Applications of Mathematics, 56(5), 499-509.

• Sniedovich, M. (2011) Dynamic programming: introductory concepts, in Wiley Encyclopedia of Operations Research and Management Science (EORMS), Wiley.

• Caserta, M., Voss, S., Sniedovich, M. (2011) Applying the corridor method to a blocks relocation problem, OR Spectrum, 33(4), 815-929, 2011.

• Sniedovich, M. (2011) Dynamic Programming: Foundations and Principles, Second Edition, Taylor & Francis.

• Sniedovich, M. (2010) A bird's view of Info-Gap decision theory, Journal of Risk Finance, 11(3), 268-283.

• Sniedovich M. (2009) Modeling of robustness against severe uncertainty, pp. 33- 42, Proceedings of the 10th International Symposium on Operational Research, SOR'09, Nova Gorica, Slovenia, September 23-25, 2009.

• Sniedovich M. (2009) A Critique of Info-Gap Robustness Model. In: Martorell et al. (eds), Safety, Reliability and Risk Analysis: Theory, Methods and Applications, pp. 2071-2079, Taylor and Francis Group, London.
• .
• Sniedovich M. (2009) A Classical Decision Theoretic Perspective on Worst-Case Analysis, Working Paper No. MS-03-09, Department of Mathematics and Statistics, The University of Melbourne.(PDF File)

• Caserta, M., Voss, S., Sniedovich, M. (2008) The corridor method - A general solution concept with application to the blocks relocation problem. In: A. Bruzzone, F. Longo, Y. Merkuriev, G. Mirabelli and M.A. Piera (eds.), 11th International Workshop on Harbour, Maritime and Multimodal Logistics Modeling and Simulation, DIPTEM, Genova, 89-94.

• Sniedovich, M. (2008) FAQS about Info-Gap Decision Theory, Working Paper No. MS-12-08, Department of Mathematics and Statistics, The University of Melbourne, (PDF File)

• Sniedovich, M. (2008) A Call for the Reassessment of the Use and Promotion of Info-Gap Decision Theory in Australia (PDF File)

• Sniedovich, M. (2008) Info-Gap decision theory and the small applied world of environmental decision-making, Working Paper No. MS-11-08
This is a response to comments made by Mark Burgman on my criticism of Info-Gap (PDF file )

• Sniedovich, M. (2008) A call for the reassessment of Info-Gap decision theory, Decision Point, 24, 10.

• Sniedovich, M. (2008) From Shakespeare to Wald: modeling wors-case analysis in the face of severe uncertainty, Decision Point, 22, 8-9.

• Sniedovich, M. (2008) Wald's Maximin model: a treasure in disguise!, Journal of Risk Finance, 9(3), 287-291.

• Sniedovich, M. (2008) Anatomy of a Misguided Maximin formulation of Info-Gap's Robustness Model (PDF File)
In this paper I explain, again, the misconceptions that Info-Gap proponents seem to have regarding the relationship between Info-Gap's robustness model and Wald's Maximin model.

• Sniedovich. M. (2008) The Mighty Maximin! (PDF File)
This paper is dedicated to the modeling aspects of Maximin and robust optimization.

• Sniedovich, M. (2007) The art and science of modeling decision-making under severe uncertainty, Decision Making in Manufacturing and Services, 1-2, 111-136. (PDF File) .

• Sniedovich, M. (2007) Crystal-Clear Answers to Two FAQs about Info-Gap (PDF File)
In this paper I examine the two fundamental flaws in Info-Gap decision theory, and the flawed attempts to shrug off my criticism of Info-Gap decision theory.

• My reply (PDF File) to Ben-Haim's response to one of my papers. (April 22, 2007)

This is an exciting development!

• Ben-Haim's response confirms my assessment of Info-Gap. It is clear that Info-Gap is fundamentally flawed and therefore unsuitable for decision-making under severe uncertainty.

• Ben-Haim is not familiar with the fundamental concept point estimate. He does not realize that a function can be a point estimate of another function.

So when you read my papers make sure that you do not misinterpret the notion point estimate. The phrase "A is a point estimate of B" simply means that A is an element of the same topological space that B belongs to. Thus, if B is say a probability density function and A is a point estimate of B, then A is a probability density function belonging to the same (assumed) set (family) of probability density functions.

Ben-Haim mistakenly assumes that a point estimate is a point in a Euclidean space and therefore a point estimate cannot be say a function. This is incredible!

• A formal proof that Info-Gap is Wald's Maximin Principle in disguise. (December 31, 2006)
This is a very short article entitled Eureka! Info-Gap is Worst Case (maximin) in Disguise! (PDF File)
It shows that Info-Gap is not a new theory but rather a simple instance of Wald's famous Maximin Principle dating back to 1945, which in turn goes back to von Neumann's work on Maximin problems in the context of Game Theory (1928).

• A proof that Info-Gap's uncertainty model is fundamentally flawed. (December 31, 2006)
This is a very short article entitled The Fundamental Flaw in Info-Gap's Uncertainty Model (PDF File) .
It shows that because Info-Gap deploys a single point estimate under severe uncertainty, there is no reason to believe that the solutions it generates are likely to be robust.

• A math-free explanation of the flaw in Info-Gap. ( December 31, 2006)
This is a very short article entitled The GAP in Info-Gap (PDF File) .
It is a math-free version of the paper above. Read it if you are allergic to math.

• A long essay entitled What's Wrong with Info-Gap? An Operations Research Perspective (PDF File) (December 31, 2006).
This is a paper that I presented at the ASOR Recent Advances in Operations Research (PDF File) mini-conference (December 1, 2006, Melbourne, Australia).

## Recent Lectures, Seminars, Presentations

If your organization is promoting Info-Gap, I suggest that you invite me for a seminar at your place. I promise to deliver a lively, informative, entertaining and convincing presentation explaining why it is not a good idea to use — let alone promote — Info-Gap as a decision-making tool.

Here is a list of relevant lectures/seminars on this topic that I gave in the last two years.

Disclaimer: This page, its contents and style, are the responsibility of the author (Moshe Sniedovich) and do not represent the views, policies or opinions of The University of Melbourne.

Disclaimer: This page, its contents and style, are the responsibility of the author (Moshe Sniedovich) and do not represent the views, policies or opinions of the organizations he is associated/affiliated with.