**Problem-solving and Heuristics**

Can you decompose a management problem and “recombine its elements in some new manner”?

Strategies are used to make the problem easier to understand and solve.

In economics, sociology, and political science, a decision or situation is often called rational if it is in some sense optimal, and individuals or organizations are often called rational if they tend to act somehow optimally in pursuit of their goals. Thus one speaks, for example, of a rational allocation of resources, or of a rational corporate strategy. In this concept of “rationality”, the individual’s goals or motives are taken for granted and not made subject to criticism, ethical or otherwise. Thus rationality simply refers to the success of goal attainment, whatever those goals may be. Sometimes, in this context, rationality is equated with behavior that is self-interested to the point of being selfish. Sometimes rationality implies having complete knowledge about all the details of a given situation.

Debates arise in these three fields about whether or not people or organizations are “really” rational, as well as whether it make sense to model them as such in formal models. Some have argued that a kind of bounded rationality makes more sense for such models.

Problem solving forms part of thinking. Considered the most complex of all intellectual functions, problem solving has been defined as higher-order cognitive process that requires the modulation and control of more routine or fundamental skills (Goldstein and Levin, 1987). It occurs if an organism or an artificial intelligence system does not know how to proceed from a given state to a desired goal state. It is part of the larger problem process that includes problem finding and problem shaping.

Perhaps the most fundamental heuristic is “trial and error”, which can be used in everything from matching bolts to bicycles to finding the values of variables in algebra problems.

Goldstein F. C., & Levin H. S. (1987). Disorders of reasoning and problem-solving ability. In M. Meier, A. Benton, & L. Diller (Eds.), *Neuropsychological rehabilitation. *London: Taylor & Francis Group.

**Characteristics of difficult problems**

As elucidated by Dietrich Dörner and later expanded upon by Joachim Funke, difficult problems have some typical characteristics that can be summarized as follows:

**Intransparency**(lack of clarity of the situation)- commencement opacity
- continuation opacity
**Polytely (multiple goals)**- inexpressiveness
- opposition
- transience
**Complexity (large numbers of items, interrelations, and decisions)**- enumerability
- connectivity (hierarchy relation, communication relation, allocation relation)
- heterogeneity
**Dynamics (time considerations)**- temporal constraints
- temporal sensitivity
- phase effects
- dynamic unpredictability

The resolution of difficult problems requires a direct attack on each of these characteristics that are encountered.

Here are a few other commonly used heuristics, from Polya’s classic How to Solve It.

* Look to the unknown.

* If you are having difficulty understanding a problem, try drawing a picture.

* If you can’t find a solution, try assuming that you have a solution and seeing what you can derive from that (“working backward”).

* If the problem is abstract, try examining a concrete example.

* Try solving a more general problem first (the “inventor’s paradox”: the more ambitious plan may have more chances of success).

Other heuristics.

Heuristic |
Informal Description |
Formal analogue |

Analogy | Can you find a problem analogous to your problem and solve that? | Map |

Generalization | Can you find a problem more general than your problem? | Generalization |

Induction | Can you solve your problem by deriving a generalization from some examples? | Induction |

Variation of the Problem | Can you vary or change your problem to create a new problem (or set of problems) whose solution(s) will help you solve your original problem? | Search |

Auxiliary Problem | Can you find a subproblem or side problem whose solution will help you solve your problem? | Subgoal |

Here is a problem related to yours and solved before | Can you find a problem related to yours that has already been solved and use that to solve your problem? | Pattern recognition Pattern matching Reduction |

Specialization | Can you find a problem more specialized? | Specialization |

Decomposing and Recombining | Can you decompose the problem and “recombine its elements in some new manner”? | Divide and conquer |

Working backward | Can you start with the goal and work backwards to something you already know? | Backward chaining |

Draw a Figure | Can you draw a picture of the problem? | Diagrammatic Reasoning ^{[3]} |

Auxiliary Elements | Can you add some new element to your problem to get closer to a solution? | Extension |

Day 4 – The Foundations of decision-Making

You can go directly to slideshare HERE to download the PowerPoint slides and print the notes pages.

## Leave a Reply