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The Art of Problem Solving!

“Given an election with 2 candidates A and B, where A receives m votes and B receives n votes and A is the winner, what are the chances that A is always ahead of B throughout the counting process.”

The above problem is called the Ballot problem. We have all faced puzzles and problems such as the above during our high school and college days. Some of the problems are simple, such as above, with extremely complex solutions, while others have a difficult problem definition with fairly simple solutions. However in such cases, the common factor was that we knew what problem we were trying to solve. What will happen if we are not even sure of the problem? How do we know that we are solving the ‘right’ problem? This is typically the situation in most business contexts. This article will introduce you to tools to assist in problem solving!

Consider the following business situation: “Your organization has been facing a ‘higher-than-average’ spend on temporary labor for their administrative activities. As the rookie in the company, you have been asked to find out the reasons for this and recommend solutions.”

Simple question, right? One of the mistakes made by people is to take this situation at face value and then develop solution themes for the same. So, a typical approach will be to re-phrase the above situation into the problem below:

“What can be done to reduce spend on temporary labor for administrative activities at the organization?”

Solutions that address the above problems include one or all of the following – (a) Renegotiate terms with agencies that provide the temporary labor services, (b) Get existing permanent staff to take on more responsibilities and reduce the number of temporary labor workforce, (c) Identify extent of automation of the administrative activities possible and so on. We don’t know whether this will address the problem at all.

However, if you re-read the situation again, you will notice that the core problem is that the organization has a ‘higher-than-average spend’ on temporary labor in administration. SO, what will happen if you re-phrase the question as below:

“Why is there a higher-than-average-spend in temporary labor in administration?”

The immediate impact of this is that the focus changes from trying to find solutions to trying to identify the root-cause of the high spend. A root-cause of a problem is the most fundamental reason why the problem has manifested in the organization.

One of the tools that help in identifying the root-cause of a problem is called an issue tree. An issue tree is a collection of mutually exclusive and collectively exhaustive factors that can explain a possible situation. An illustrative issue tree for our example is given in Figure 1.

AOPS

As soon as we do this, we start observing that the possible reasons could include a lot of factors beyond the possibility of the agencies charging higher rates for temporary labor.

An issue tree can have multiple levels, with each level being a problem of its own with its own root-causes. As we drill down further, we are closer to identifying the core issues that affect the problem.

Once the root-cause or causes have been identified, the next step is developing the solution themes. Usually, unlike mathematics or any of the other academic courses, in a business situation, solutions are much more apparent once we know the root cause of a problem.

The approach used for developing solution themes is called ‘brainstorming’. As the name suggests, the approach is to get a group of people sit down and throw in all possible ideas that can help address the situation. In the initial stage of brainstorming, no ideas are evaluated. All ideas are equally valid and acceptable. Also, having people from multiple backgrounds and functions is good for generating ‘out-of-the-box solutions’. Once there are enough ideas collated, the next step is to determine the best solution that addresses the root problem.

In the above situation, brain storming can lead to potential ideas such as “Train the permanent staff to do these activities”, “Most of the activities being done by the temporary labor are unnecessary and can be eliminated!” or “Use computers and offshore resources to get the job done at lower cost”.

Coming back to the Ballot Problem, the answer is (m – n)/(m + n). This is not obtained through brainstorming! The approach to this kind of problems will be discussed in a separate article.

What approaches have you or your organization used to define problems and identify solutions? Do you think the approaches mentioned above will be useful to address your issues better?

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