Art of Problem Solving

【Topic 1: Problem Solving; Subtopic 1.5: Art of Problem Solving】

HOW to solve a problem (thoughts of 80’s)?

You may be overwhelmed by Ackoff’s more than 288 theoretical functional concepts listed in his book “On Purposeful System” (“purpose” book) and wonder if they are practical to use?  Here is another Ackoff book “The Art of Problem Solving” (“art” book), published 1978 (close to the 80’s).  The book uses only a small portion of his functional concepts, but it provides you with a glance of how the concepts work in real world.  Because the book is written some 40 years ago, it is a good opportunity to see how things change since and, more importantly, how modern AI can help.  For instance, around 1978, decision analysis and decision support system are hot topics.  So, it is natural systems thinking authors include those technologies in their design examples.  Plus, around that time when PC and workstation are not there yet, most businesses are still looking for powerful minicomputer if they cannot afford mainframe.  Databases do not exist either.  Today, decision products are pretty much merged into enterprise ERP, CRM, etc. and are dominated by large enterprises like US Oracle and German SAP.  There is a trend towards business intelligence, but not yet intelligence that can replace human.  However, most of the decisions can be done by AI, human only needs to make policies about decisions, rather than decision itself.

In this “art” book, Ackoff uses two writing styles: (A) story-like fables and (B) business cases, both using no formalized math formulas.  As examples, let’s see how a small portion of the functional concepts are used in (A) and (B):

(A) Fables

If you see the table of contents of the “art” book, it seems Ackoff applies only 6 functional concepts: objective, controllable variables, uncontrollable variables, creativity, constraint, and relation between variables.  The first 3 appear in the “purpose” book and last 3 are invented in the “art” book. However, when a problem is solved, it often involves concepts beyond the 6, either newly introduced or the 288 in “purpose” book.  Also, these 6 functional concepts together can basically form a linear or non-linear programming problem.  However, separately, you can learn how wide each functional concept (out of more than 288!) can be applied to real world.  Each functional concept has several fables.  I pick only one fable each for you to get some flavor:

• Creativity & Constraint: Creativity often is curtailed by constraint.  The example of drawing at most 4 lines to connect all dots in a 3x3 dot-matrix demonstrates the self-constraint imposed by common people.  Creative problem solving also needs extended experience, demonstrated by examples or fables of “art” book, beyond analysis of the nature of problem.  Fables are also fun and recreative (as a continual pursuit to Aristotle’s producer of stability and contentment), in addition to creative (as a continual progress towards building Plato’s utopia Republic out of dissatisfaction).

• Objective: For your own objective, (1) you pursue fun and recreation; (2) the end of problem solving is the beginning of another problem; (3) an ideal design often stimulates minds, collects intelligence and forms consensus. Ideal is also helpful to find out your real objective. However, people often erroneously thought others have the same objective as theirs.  One fable is to plan birth control of married couples in India.  Distributing contraceptives and usage instructions to them has no effects.  The real objective of the couples is to get more children so that more insurance is collected due to a policy of India government.  Thus, it is important to encourage participation during an ideal design.  Moreover, if different objectives of two or more parties are related, there are often conflicts to be solved.  One way of conflict resolution is to change their objectives.

• Controllable variable: there are 13 fables demonstrating various principles for controllable variables. One principle says “Customers are seldom irrational but manufacturer can be irrational” which has a fable about a kitchen appliance manufacturer.  Managers of the manufacturer blame the failure of dish-washer sales on customer’s irrationality, because survey says customers need such a machine, plus other appliances in the same show room sell well.  It turns out customers dislike the design of dish-washer which requires customers to bend or squat to load or pickup dishes in the machine.  In general, systems thinking often reveals available but overlooked solutions.  First, an interdisciplinary team may cover those relevant controllable variables overlooked due to discipline or profession.  Next, solutions to convert the “culprit” into a constructive force are possible by adding them to the environment, not subtracting them from it.  Although not easy, incentives can be uncovered, examined and corrected. Thirdly, reference projection can help to predict what cannot happen. Finally, a solution may lie in other places from problem’s symptom.  Hence, we often are restricted by the dimensionality of our mental pictures.  Increase of dimension may reveal solutions.

• Un-controllable Variable: There are three categories of uncontrollable variables. (1) self-evident fact data collected for the uncontrollable variable.  (2) Problems of vertical or horizontal integration for business organization may come from uncontrollable variable.  When you enlarge the system taken to be relevant, you may find opportunity to solve it by converting uncontrollable to controllable. (3) Uncontrollable variable caused by extrinsic behavior can be brought under control if you can produce relevant knowledge.  One example is a university parking lot entrance control mechanism beaten by students to park illegally in the lot.  The suggestion is to use a countermeasure group to beat various simulated “enemy” behaviors.

• Relation: usually it is wrong just to find the association relation between group when trying to solve problems.  You have to find the cause of problem, hence to resolve the problematic effect.  Sometimes the causality variables are in the association variables and can be selected to study further.  An example is about an oil company failing to design gas stations correctly.  A regression study of many associated variables cannot find out why sales of gas station cannot go up.  This is resolved by actually watching how cars entering the gas station to pump gas and make a few experiments to test causal hypothesis regarding “lost time” (a causal variable) of customers.  The explanation of the lost time enables the company to improve the performance of gas station.

(B) Business Cases

The following business cases are solutions to a problem that deserves a study of bigger scale, longer time and more creativity.  Most of them eventually lead to a “design” with certain creativity, hence there is no other stated rule (the only common rule is a creative design).

• The National Scientific Communication and Technology Transfer System (SCATT). SCATT is a typical information system whose technology is pretty old from today’s standards like internet-based arXiv or Research Gate services or even Google search.  The lesson learned here is how consensus is reached via discourse of large number of stakeholders, especially SCATT users, to collaborate and avoid conflicts, such as ideal designs of meetings, relevance, redundancy check, participation allowance for young professionals with discounted fee, etc.

• Out of his purposeful thinking, Ackoff creates his version of multidimensional organizational structure.  This is usually called “M-Form” for corporation and is well accepted by today’s large conglomerate worldwide. I remember in the 80’s many companies use matrix management, where an employee may report to two supervisors.  Ackoff explains the drawbacks of matrix management and how M-Form can avoid the problem caused by matrix management.  He is hundred-percent correct judged by  M-form acceptance by various companies today and very few companies are using matrix management.

• Problem Solving System: in the “purpose” book, Ackoff does not emphasize “structure” of the functional variables because his aim is to define hundreds of function variables.  Now in the “Art” book when we face real-world problems, we need to know the structure.  Ackoff draws a diagrammatic representation for problem solving system, a structure where he considers 5 subsystems: the objective + environment subsystem, the decision subsystem, the information subsystem, the memory subsystem, and the diagnostic subsystem.  I think current AI technology can upgrade these subsystems, especially the diagnostic one.  In addition, AI can add the subsystems of prediction, design and configuration.

Ackoff’s approach towards real-world problems involves free-style, creative structure design work (with no stated methodology rules).  He explains his creative approach well with fables and business cases.  There are also many other practical techniques using systems thinking. The following 2 subtopics introduce Jay Forrester’s “System Dynamics” and Soft Systems Methodology from Peter Checkland of UK, both are fairly workbook-style (with stated methodology rules).