Step by step problem solving

Getting started with solving real life problems - an introduction

 

Welcome to Real Life Problem Solving. Hope you have gone through our previous post.

We made only one recommendation last time: "be aware about your own problem solving process."

As you would agree, real life problems can be of innumerable types. Can there be any single formula or method of solving any kind of real life problem? Obviously there can’t be. Just as no mathematical problem can be solved using a single formula or method, for different types of mathematical problems you need to apply different methods; similarly you need to adopt an appropriate and suitable approach for solving a real life problem.

But there is a big difference between a mathematical problem and a real life problem. A mathematical problem, if it is solvable (there are unsolvable mathematical problems), however hard it is, someone somewhere can solve it using known techniques and methods. In other words, mathematical problems:

a.    Are Well defined and well structured with no uncertainty

b.   Have clearly known methods for reaching the solution(s), and

c.   Even the solutions are precise and exact.

Though there are mathematical problems not yet declared to be unsolvable, those are perhaps of interest only to mathematicians.

In contrast, real life problems:

a.      Are generally ill defined and ill structured

b.     Have no prescribed method of reaching the solution

c.     Involves lots of uncertainty, and

d.      Have no precise or exact solution. We can say - solution of a real life problem is a solution only when it is acceptable to the people affected and involved in the problem.

Real life Problem Solving as a separate discipline

Till this point of time we have solved all kinds of problems in our personal and work lives, but we have solved them according to our problem solving abilities, without any formal teaching on the process and methods of problem solving. Did you ever think how you solved a particular problem? Did anyone systematically explain how a particular problem has been solved? Were you ever taught how to solve real world problems better?

Here we will deal with Problem Solving as a separate discipline and will mostly concentrate on the process of problem solving rather than the solutions we have reached.

Though we are only interested in solving real world problems, we will take recourse to solving a number of mathematical problems not so much as to learn mathematics but rather to learn the principles and techniques involved in solving the problems. The same principles and techniques used in solving well-prepared mathematical problems can be used effectively in solving real world problems also.

What is the central mental activity in solving a problem? Basically it is Decision Making. For each action we have to take a decision.

Can you cite some examples of decision making?

So while we discuss Problem Solving, we would automatically discuss decision making required to solve the problems. Decision Making will be an interwoven subject of discussion.

Innovation

All problem solving requires innovative capabilities, but the experts usually have qualities to see beyond the obvious, generate totally novel possibilities and arrive at very high value solutions. By using these qualities people innovate. And in today’s world, especially in the cutting edge competitive world, innovation is considered to be the most valuable human resource. Countries measure their trend of national innovative capability content and take steps to improve on this front. For organizations in a competitive environment, Innovation becomes the key capability that differentiates the players. Only routine efficient work won’t finally succeed. You need to innovate.

So at some point of time with due regard we will go into Innovation as a separate topic. 
 
In spite of this daunting nature of real life problem solving, it is possible

a.      To approach any such problem not in a random manner, but in a systematic, scientific and effective manner

b.      To select suitable powerful and abstract principles, techniques, tools, methods and strategies, and

c.·    Arrive at low-cost solutions that are acceptable to the people affected.

In fact all the renowned Business Consultants use their own business problem solving resources to advise their clients effectively. Some are very effective some are not so effective. There is no guarantee even in a business problem solving scene that the Consultant will produce a fully satisfactory solution to the client.

In real life, all physicians, lawyers, property consultants, tax consultants and so on are actually real life problem solvers, but working in their specific work areas.

Who can advise you in your general kind of problem? Suppose, you have had a serious difference with your boyfriend. Who can advise you how to go ahead and take decisions that will prove to be good for you? Or take the case of the dilemma of deciding where to go for a 5 day trip during your holidays with highly satisfying experience of all concerned. You will consult with concerned people and choose a trip plan in your own way. Can this trip planning process be improved?

We recognize two objectives at this point of time:

1.        To improve quality of solution for any real life problem, and

2.         To improve learner’s own real life problem solving ability.

Decision problem

When there is more than one choice, a decision is to be taken

Two important persons in a decision problem world are the Decision Analyst or DA and the Decision Maker or the DM. The DA is responsible for expert analysis of the problem and advising the DM. Only DM can actually take the decisions, either as advised by the DA or according to his own judgments. Many times both roles are combined into one person.

A decision is to be made when there is more than one choice. By evaluating the available feasible choices, according to a set of relevant criteria, a proper decision is to be made which will hopefully fulfill some stated objective, that is, in other words, will solve an identified problem.

So a decision problem consists of

    problem definition that includes goals or objectives of solution,

    criteria of evaluation of choices, and

    the set of choices available.

It also consists of the

    set of actors or the entities comprising of affected parties, stakeholders, decision makers (we will call them DM), the drivers of problem solution process and the Decision Analysts (we will call them DA) (Who are all the stakeholders in a business?)

    equipments and processes,

    resource constrains, and

    the domain principles, truths, and concept relationships.

 
In other words, in a problem scenario, we have specifically three important active agents:

a.      Problem owner: One or more than one person affected by the problem, interested in solving the problem and having minimum resources to solve the problem. In many cases real life problems do exist but it becomes difficult to find a clearly identifiable problem owner. All big problems of this world are of such types.

b.      Decision maker or DM: One or more than one person authorized and capable of making decisions in implementing the solution to a problem. Many times but not always the DM and the problem owner are the same entity.

c.       Decision Analyst or the DA: One or more than one person whom we can call the Problem Solver. It is the responsibility of the DA to analyze the problem and come up with recommendations to the DM for reaching the solution.

Usually, all three roles are combined into YOU, unless you are able to find a capable DA or become a DA yourself.

Multi-Criteria Decision Making (MCDM) problems

In a large class of real life problems we need to evaluate more than one choices or alternatives for fulfilling a desired goal. Examples are: choice of a house, buying a car, recruiting a new employe and so on. In all these cases, the alternatives are evaluated on the basis of a set of important criteria or characteristics that are important for making the final choice.
Before the sixties we did not have any reliable and relatively scientific method for carrying out this kind of evaluation. The difficulty arises because of the qualitative nature of the criteria that need to be evaluated for each of the possible alternatives.
From nineteen sixties onwards a few powerful methods were introduced for dealing with such problems. These qualitative multiple criteria based (MCDM) problems have been aptly classified under the group of MCDM problem solving methods. 
This class of problems are so prevalent that we will again show due regards to this special branch of problems and treat the topic of MCDM problems in a separate thread or blog.
Multi-attribute utility theory (MAUT) was the first such significant method followed by the most popular method of Analytic Hierarchic Process or AHP.

Problem life-cycle stages

Stage 1: Problem awareness or Problem identification: The awareness that a problem that needs solution has been created at this stage.

Stage 2: The decision that the problem needs to be solved taken: In many situations, even though it is known by all concerned that a serious problem exists, the overpowering sure confirmed decision to solve the problem is not taken.

Stage 3: Requisite ownerships in the problem domain have been established: In complex problem solving situations, responsibility or ownership of the problem, of the feasible solution and actions thereof are necessary prerequisites for proper problem definition, solution decision recommendations and the implementation of the recommendations. Ownership is needed at various levels.

Stage 4: Objectives analysis, Problem definition, Classification and specification:  At this stage, detailed analysis is carried out by the DA by study of domain information, structured discussions with domain owners (DO in short), the DMs and domain experts (DE in short) to form the Primary Objective Set for the problem solution. This set may be a single member set or multi-member or multi-objective set. Most complex problems we will deal are single objective multi-criteria decision making type.  Examples of single objective MCDM problems are,

    To find a suitable location for a new factory

    To rate or evaluate an organization against a benchmark of performance

    To resolve a conflicting situation and so on.

But more complex multi-objective real-life problems do exist that are amenable to scientific decision solution approach. The term MODM is a frequently encountered terminology for such problems. Examples are,

    Creating a balanced budget that satisfies multiple objectives

    Forming a National Telecom Policy that is expected to satisfy multiple goals

    Creating an integrated marketing and production plan for a product portfolio of an organization so that within a stipulated time, profits are maximized up to a minimum expected level, market penetration is achieved up to a minimum expected level and also Customer goodwill is increased to a minimum expected level.

Apart from MCDM problems there are other problem types. At this stage of problem life-cycle, the nature of the problem is first understood clearly.

Stage 5: Formation of the problem solving model:  At this stage, the problem solving model is created from the problem specification. A good model includes plan of problem solving as well.

Stage 6: Problem solving decision recommendations and actions:  At this stage, the DA applies suitable scientific and pragmatic methods on the Problem solving model and solution recommendations are submitted to the Decision Maker or DM for taking appropriate decisions and actions. If it is a Dynamic Decision Making class of problem, repeated recommendations and actions will take place.

Stage 7: Status Review and solution effectiveness measurement:  At every stage of decision making and action, there needs to be a good mechanism to review the status in terms of measurable effectiveness to see whether the desired goal is reached at that stage.

Stage 8: Recommendation and implementation of Problem Prevention and Problem identification mechanisms:  A good DA will include in his recommendations a set of recommendations for prevention of recurrence of the problem as also detection of the problem if it recurs in future. If it so happens, then the life-cycle starts again from Stage 1, but with increased knowledge and experience, of course if such knowledge is captured by the problem owner organization in usable form.

Before we end this session we would like to leave two short problems and one question-linked innovative anecdote for you to dwell upon.

Short problem 1:

What can you hold in your right hand, but not in your left?

What is your reasoning?

Short problem 2:

How can you throw a ball as hard as you can, and make it stop and return to you, without hitting anything and with nothing attached to it?

What are crucial parts of the problem description that are responsible in making the solution more difficult?

Anecdote 1:

After a difficult waiting period of three months (as I was traveling) I could finally undergo my cataract operation successfully. I had got my new specs and with a new vision was enjoying in a friends' meet. 

My friend on my left asked me, “I saw you two months ago but I couldn’t perceive that you had cataract. After the cataract operation, how do you feel?” I was not prepared for the question and answered noncommittally.  To compensate, my other friend on my right answered the first friend, “You could have understood if you had looked from the back of his eyes, not from the front.”

What are the principles used here?

To become a problem solver, you must solve problems and also recognize how you had solved the problem. Continuous building upon this problem solving experience will take you a long way towards becoming a problem solver 

 

Read my other blogs on Innovative idea generation and its basic principles and Get smart, get innovative usingTRIZ