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Tutorial on Solving a Complex Problem – Returning Life to Normal with Safety and Economy after the Pandemic

Lately in the US, and I suppose in the rest of the world also, leaders face the problem of “re-opening the market” after the abatement of the coronavirus pandemic. On the one end, you want to prevent an economic recession/depression as much as possible; on the other hand there is the safety of the population to be concerned. You wish to find an optimal course of action(s).

It is clear the possible courses of actions in such a real world problem are endless and with all kinds of uncertainty; and to consider and evaluate carefully each course of action will be an impossible calculation burden (note 1). Yet as a leader choosing a course of action he must, including “do nothing and let nature take its course” as a plan of action. In practice, we consult widely and decide on a plan based on our experience, knowledge, gut feeling and hope for the best. 

In this article, I wish to use this real life example to illustrate how one approach such a problem as a consulting engineer/adviser who can

·       rationally attack such a problem in a systematic manner,

·       quantify our approach,

·       handle the uncertainties,

·       make clear the distinction between theory and real world problems.

Hopefully such a discussion will help the general public in understanding the role and limit of science in policy making. Actually the US National Academy of Medicine has a series of webnairs discussion on the the details of the pandemic https://www.covid19conversations.org/. They should be taken as authoritative. My use of this pandemic example is for illustrative purpose of a complex problem only.   So here goes my article.

Consider the following steps you take as a leader

1.           Assembly a panel of economists, medical experts, government officials, merchant association representatives.

2.           Start with a re-opening date and a schedule of phased return to normal (people will have different ideas about such a schedule. Don’t worry. Consider any reasonable schedule to start). Now ask the panel to give their best GUESS (no need for accuracy just estimate) as to the economic/environmental/safety consequences of such a “re-opening” schedule

3.           Now using the same schedule but postpone the starting date by one week and re-estimate the consequences.

4.           Repeat step 3 for the next nine weeks. This will give you a total of ten scenarios each with different consequences.

5.           Now repeat steps 2 thru 4  with a different schedule (again based on the suggestions of this panel of experts) and starting date to get another ten scenarios

6.           Repeat step 5 until you get a total of 200 different scenarios.

7.           Note this requires the panel to come up with only 20 not 200 different possible schedules – a very doable task.

8.           You can order these 200 guessed solutions according to their estimated goodness. Again, you are asking the panel to make guesses and to do rough tradeoff and NOT to guarantee their assessments.

9.           Now you have a list of 200 ordered (in terms of estimated goodness) solutions.

10.     Take the top12 of these estimated and ordered solutions, the theory of Ordinal Optimization then guarantees that among these 12 solution approaches, there are some 3 or 4 actual top 12 solutions if you really had the time to investigate all 200 of the approaches.

11.     Now you can take your time to examine these estimated top 12 schedules in greater detail and get at least 3 or 4 truly good schedules to pick from.

Now let us discuss and make clear what we have done. First, it should be clear that the numbers “200, top 12, starting date of one week apart . . .” used above are clearly arbitrary and used for illustrating purposes only. We can use other numbers as we see fit and desire. We used them for illustration and for coordinate the discussion with demonstration purposes http://people.seas.harvard.edu/~ho/DEDS/OO/Demo/Simple.html.  The theory and its conclusion covers other choices. Second, the theory only avoids the impossible task of evaluating accurately all “200” possible solutions and replaced it with the more reasonable task of investigating in detail “12” of these solutions – a computational saving of approximately twenty to one. This is the contribution of the theory. Third, human judgement/experience are still needed from the panel of experts to come up with possible initial schedules.  But we have utilized these expert where their expertise (gut feeling and experience but not accuracy) can be put to greatest use. Fourth, we have glossed over the problem of ordering the consequences of the 200 estimated solutions. Note the problem of trade off economics with safety so that the alternatives can be ordered is a non-trivial problem in itself  - the so called pareto optimality problem. The theory/practice on that is worth a separate article or book http://blog.sciencenet.cn/home.php?mod=space&uid=468147&do=blog&id=723662 review: Introduction to Multi-objective Optimization.

Of course, the above is only an overly simplified description of policy making, decision choice, theory vs. practice and the role of each. Reader with more question are welcomed to comment and/or write to me directly with questions. 

Note 1 Because of uncertainties, to calculate the expected cost/benefit of a complex problem via detail simulation one must average over a large number of repeated calculations. Even with fastest computer, this can often be extremely time consuming.

Additional References http://blog.sciencenet.cn/home.php?mod=space&uid=1565&do=blog&id=1117595 Optimization Theory vs. Practice

http://blog.sciencenet.cn/home.php?mod=space&uid=1565&do=blog&id=759185 On Optimization

Ordinal optimization: Soft Optimization of Hard Problems, Y.C.Ho, Q.C. Zhao, Q.S. Jia, Springer 2007