Business problems do not have a straightforward solution. It is not like giving candy to a crying child. As there are multiple stakeholders and complex issues, there are many potential solutions to a single problem. Such complex problems that cannot be solved in one go are called unstructured problems. Such problems have to be structured so that a solution can be thought of, using decision theory.

With this introduction in mind, let us go into details of each of the terms we have used above.

All the problems in this world can be categorized into 3 types –

• Structured problem
• Unstructured problem
• Semi-structured problem

Introduction to structured and unstructured problems

In an ideal world, people always face structured problems where there is one known solution for the problem. The problem is clear – for example, you hurt your ankle, there is no denying that you should do first-aid. If there are 3 people in the room, all of them will have the same opinion and there will be no other perspective.

But we don’t live in an ideal world.

And real-world scenarios are not easy – there are complex problems faced, and more than often there are ambiguities, differences of opinions and perspectives and lack of complete knowledge about the problem. As we have already seen, such problems are called unstructured problems.

Some examples of unstructured problems are – an airplane crash, stock market behavior, the covid19 pandemic, etc…

The need for problem structuring

An unstructured problem cannot be solved efficiently, because the knowledge and definition of the problem are uncertain, the individual decisions are uncertain, leading to ambiguity. The ambiguity can be eliminated or reduced only when all the stakeholders jointly define the problem clearly and find the best possible solution using the decision theory. This process of integration of all the different (divergent) views of a problem to define the problem is called problem structuring.

With problem structuring, decision making becomes easy and organized.

Below diagram summarises the need for problem structuring –

1. Soft systems methodology (SSM) – This method uses the concept of a neutral ‘system’ as a device to interrogate and act upon the divergent views from various involved parties.
2. Cognitive mapping – In this method, the perceptions and behavior of individual decision-makers are analyzed using cognitive maps. Mapping allows us to build a comprehensive vision of the problem and the many decisions by the decision-makers.

Decision Theory

Decision theory is a study of choices from various contributors to the solution of a problem. There could be many ways to solve a problem and each person can have a different perspective on it. Decision theory helps decide the best solution to a problem by collecting facts and applying statistical methods on the data. There are three branches of decision theory –

• Normative decision theory – the decision is based only on facts and rationality
• Prescriptive decision theory – the decision is based on a set of guidelines, under an uncertain environment
• Descriptive decision theory – the decision is based on human behavior along with facts and data

While normative theory tries to find the most ideal solution (or what should happen), descriptive theory finds the most practical solution – what is going to happen. For example, investing in stocks is a decision that depends not only on market value, but also depends on an individual’s assessment of risk, uncertainty, and definition of profit. The decision made by one person may not seem logical to others and vice versa because the expected utility of that decision for each person might be different.

The decision-maker thus knows his preferences and accordingly expands the alternatives he has.

There are three different types of decisions that can be made –

• Decisions under certainty – when there is a lot of information available about the problem, a decision can be made easily.
• Decisions when there is uncertainty – uncertainty can be due to lack of information, knowledge or other unknown variables that can impact the decision. In this case, the best probabilistic decision can be taken.
• Decisions under conflict – conflicts can arise when two or more people have different opinions on the same problem. The outcome is based on each other’s decision, and the optimal decision includes facts, data as well as human behavior.
  

  Decision making vs Problem-solving

Note that decision making is not the same as problem-solving. There can be many solutions to a problem, however, the decision for the final solution is only one. Decision making has to be done at each step of the problem-solving process to arrive at the next step. For example,

Problem statement – Should I stock up food for the next 21 days because there might be a country lockdown for that period?

Probabilities –

• The government will not stop essential services
• Fruits, vegetables, and milk may or may not be available every day
• Police might retain people who go out more than once per day
• The lockdown period might be extended in future

The solution depends on finding answers to the probabilities. This involves taking the decision based on whether the probabilities are true or not.

• The government will not stop essential services like medicine, ATM, groceries – if this is true, then I need not stock food.
• Fruits, vegetables, and milk will be available every day – if this is true, then I need not stock food.
• Police might retain people who go out more than once per day – If this is true, I will have to stock food.
• The lockdown period might be extended in future – if this is true, I will have to stock food, provided 1 and 2 conditions are false.

So, at each step, we decide to solve the problem. The outcome here could be YES because that is the majority (solution for 2 of the possibilities).

From the above, we can also infer that decision making is critical to solving any complex problem (a problem that has more than one outcome or perspective).

Making decisions with problem structuring

We have understood that problem structuring is essential to define a comprehensive problem statement. We also learnt before that unstructured problem is tough to deal with. This means that traditional decision making and analysis tools are not sufficient to solve unstructured problems because along with statistical, fact-based analysis, a lot of intuitive and emotional aspects need to be considered. The basic steps to solve an unstructured problem are –

We have already discussed defining the problem. The next steps are to select the criteria and find alternatives for each criterion, and then make decisions through statistical analysis methods.

Criteria include the elements that help us differentiate between alternatives and choose one. For example, I have land that I can sell for Rs 5 lakhs, however, I get to know that there is a hidden treasure deep down that needs digging. The treasure is worth 25 lakhs and the cost of digging is about 10 lakhs. Now, I have the following alternatives –

• Sell the land for 5 lakhs.
• Spend 10 lakhs to dig and find the treasure.
• Find the treasure worth 25 lakhs.
• Find nothing and sell – 3 lakhs.

The criteria (row) -alternative (column) table can be made as –

How do we make a decision?

There are many analysis methods to do that –

• MaxMax method – a risk-seeking choice. We decide the best (max) outcome for each decision and then find the maximum out of those. In our case, the max of each row is 5 and 15 lakhs, and the max of 5 & 15 is 15. This means the outcome of this approach will be to dig.
• MaxMin – For every decision, we find the worst (minimum) outcome first. Then, we choose the maximum of the minimums. From the above table, the minimum values of sell and dig are 5 and -7lakhs. The max of these is 5 lakhs. So, the outcome would be to sell.
• MinMax regret – In this approach, we calculate the regret value. For example, if we sell the property and it is found that there is no treasure, the regret will be 0. However, if we dig and then find no treasure, the regret will be 12 lakhs (numeric value of -7-5 lakhs). Same way, if we sell and find that there is a treasure, 15 lakhs, whereas if we dig and find the treasure, the regret will be 0. The max regret will be the max values of both alternatives, 12 and 15. The min value of both is 12, which means the outcome is to dig.

Note that there are no probabilities in the above problem.

If we introduce probabilities, we have to use the Bayesian decision theory, instead of the statistical decision theory we used above. In the Bayesian approach, the available observations are combined with prior beliefs (events that are believed to be true) to derive an optimal decision.

Conclusion

In this article, we have discussed the basics of decision theory with problem structuring. Data scientists use decision theory quite often to make strategic decisions that are data-driven and more effective. Through better decision making, data science and machine learning algorithms can solve complex unstructured problems accurately and in less time.