This is a system I use for problem solving combined with a collection of notes I took from the Ventus Learning's Problem Solving course.

First of all: what is a problem?

For me, a problem is an unwanted situation or an open question that needs to be answered. It is something that disrupts the normal flow and requires a resolution. Answering hard situations becomes easier when you have a process—a specific, procedural methodology for dealing with them.

The method

The 2D-PEA method has 5 steps consisting of:

Definition

Do we know exactly what the problem is about? Defining the problem gives a clear vision about what the problem we are facing is about, align expectations about possible outcomes, and the means to achieve it. It is the most important step.
Decomposition

Break the bigger problem into small pieces. There are many ways to divide & conquer (or solve) them, but that depends on what sort of problem we are facing, its complexity and how we intend to solve it.
Prioritization

Prioritizing serves as a filter to select the fewer actions that will bring the most and biggest results, serving as a accelerator for solving the problem quicker.
Evaluation

Evaluation is essential for testing hypotheses. This step can be the most time-consuming and, therefore, needs to be carefully planned. The evaluation phase is where coordination and teamwork are most crucial, as it is necessary to frequently synthesize the findings from different analyses to ensure that the solution found is robust enough.
Action suggestion

After the evaluation step, tested hypothesis data will be either validated and discarded. Now, it's time to communicate the action suggestion. It needs to be clear and concise in a way that every involved party can understand what have to be done to solve the problem.

The method is good by itself, but communication is essential for getting it done.

Engage people

Throughout the whole iterative method, peers and stakeholders need to be on top of what is being dealt with. The problem-solving process has no impact if it is not carried out by engaging and aligning the different individuals involved along the way. Therefore, engaging people at every step of the method is key to the success and subsequent implementation of the solution.

Definition

Why invest time in defining what the problem is?

In the rush of everyday life, our natural tendency is to jump straight to the solution without stopping to clearly define the problem. But what impact does this tendency have?

The most serious mistakes are not being made as a result of wrong answers. The true dangerous thing is asking the wrong question.

Peter Drucker

Key ideas

A definition that is too narrow can lead to a short-sighted solution.
A definition that is too broad can leave the team lost.
Investing in problem definition is like investing in insurance that will protect you from pitfalls.
The key question should be phrased as a SMART question.
Thinking big with a clear purpose can motivate and mobilize people.
Ambition can shape the way you think and solve problems.
Problem definition should be challenging. If you already know how to solve it, you're not dreaming big enough.
Frame the problem positively.

Examples

Airbnb - Transforming houses into potential hotels

This innovative idea introduced a win-win model, in which homeowners with empty rooms can safely rent out their space, and travelers can find accommodation at fairer prices. This was made possible by a new definition of the problem of lodging supply:

Before, the question was: "How to increase the number of hotels in city X?"

The founders of Airbnb managed to redefine this question, framing it as follows:

"How to increase the supply of rooms available for accommodation, leveraging the idle capacity in residential apartments?"

In this way, they expanded the definition of the problem and created a very successful business.

iPhone - Creating a new mobile experience

Apple managed to innovate with the creation of the iPhone by redefining the question "How to create phones with more functionalities?" This question had been asked by all companies in the market (Nokia, Samsung, Motorola, among others).

The phones became smaller, had more functions, but remained very similar to each other (keys, menus, etc.). Apple proposed to see the problem in a completely different way, redefining the question to "How to amaze users with a handheld computer?"

With this, they created a phone that was at the same time a phone, an iPod/music player, and an internet browser, three things integrated with an experience more similar to a desktop (navigation icons). Making calls became a secondary experience in the new functionalities of the phone. With this new vision, Apple revolutionized the industry and created an innovative product.

Magazine Luiza—Fantastic Sale in January

January is historically known as the worst month of the year for retail. The common problem for this industry is that stores end up stocking many items for the Christmas season and need to quickly renew their inventory and get rid of older items that will soon become obsolete. Therefore, a definition for this problem could be: "How to accelerate sales in January and reduce the stock of items at risk of obsolescence?" Do you agree?

Holding a sale is nothing new for retail—Black Friday, for example, considered the biggest promotion event on the planet, emerged in the 1950s in Philadelphia. However, Luiza Trajano, who had just taken over as CEO of Magazine Luiza, managed to innovate by asking a different question: "How can we leverage our store positioning with the best prices, increasing sales during a low-movement period and reducing the stock of items at risk of obsolescence?"

With this new question, we started to look at the problem with new eyes. As important as sales, is the message we want to convey to the consumer. This is where the Fantastic Sale comes in—a pioneering sale held by the Magazine Luiza network that has attracted hordes of customers since 1993 to get discounts of up to 80% on selected items.

Quarter-block-long lines are part of it and are even encouraged because they reinforce the perception of excessive, exaggerated discounts. Some choices of the network reinforce this point: opening stores at 5 a.m. and saying that you can take everything you can carry with your hands.

With this strategy, the network went far beyond boosting sales and reducing its idle stock to become the largest retailer in Brazil. The Fantastic Sale is still a symbol for Brazilian retail, and Luiza Trajano, its creator, is a symbol of entrepreneurship and innovation.

Be SMART

Being SMART when defining the problem means being:

Specific

Since we're dealing with problems and not ideal growth scenarios, we need to think the other way around. Think of a company losing market share. We are not gonna think and elaborate a question like “How can we improve the company profitably”? Instead, ask “How can we revert the market share loss in the next six months?”
Measurable

Here we want a measurable way to determine the problem. This number will serve as the guiding star of the solution. For example, “How can we double the company's revenue, or triple the number of customers, in one year?”
Action-oriented

We don't want the definition to be something like “Can we gain 10% of market share?” because the answer may be yes, but this answer does not help we move towards the action. So, instead, ask “What actions do we need to take to gain 10% of market share?”. The answer to this question will naturally contain concrete actions.
Relevant

It is very important to test if our problem is actually relevant to the company and the company's leadership. If we ask ourselves if this is a really relevant problem for the company, we may realize that, in fact, the problem is a symptom of an even more relevant problem.
Timely

In a defined time, every goal must have a deadline to be achieved. A very good friend of mine says that "a goal without a deadline is nothing but a dream." Defining the problem deadline can completely change its solution if the deadline is from 1 to 2 months or 10 years.

In the first case, the focus will probably be on quick actions to gain market share, while in the second we can consider a revision of the value proposition, expansion to other regions, categories, acquisitions, etc.

Example

Vacation

If you think about it, it involves decision-making with thousands of possibilities, And there has to be an alignment between the decision-makers involved, me and my girlfriend, in my case. Let's see together how we can make this definition SMART.

How about starting with the question of where we should go on vacation to have a lot of fun? It's very specific, isn't it? And it can have a very specific answer. Atrani, in Italy, for example. There are other factors that define the best vacation you've ever had.

So, it would include something like how to define the place and the experience, instead of just the place. And lastly, do we have a set time? Not yet. So, let's add this element. At the end "How to define a place to go on vacation at the end of the year and a set of experiences that will make these the best vacations we've ever had?"

Dream big

A spacial dream

But why, some say, the moon? Why choose this as our goal? And they may well ask why climb the highest mountain? Why, 35 years ago, fly the Atlantic? Why does Rice play Texas? We choose to go to the moon! We choose to go to the moon in this decade and do the other things, not because they are easy, but because they are hard. Because that goal will serve to organize and measure the best of our energies and skills. Because that challenge is one that we're willing to accept. One we are unwilling to postpone, and one we intend to win, and the others too.

John F. Kennedy

Reflections:

Which problem was JFK trying to solve?
Did he define the problem well?
Was he ambitious?

Kennedy's speech illustrates the power of an ambitious goal. Thinking big, in addition to generating inspiration, can shape the way we think and solve problems.

A good goal

But you may be asking yourself, how do we know if the definition is ambitious enough? A good goal is a goal that you don't know how to achieve yet. If you already have a more or less clear idea of how to get there, you certainly aren't dreaming big enough.

Being ambitious, we have to get out of our comfort zone, innovate, develop new skills. So a little cold in the belly is part of the process. And don't forget that a big dream needs inspiration. And for that, it needs to be formulated in a positive way.

A practical example is, would you rather solve the problem “How can we reverse customer losses?” Or “How can we become a reference in the industry in customer retention?” Think about how to write the problem in a way to motivate people around you. Providing an element of transformation.

The purpose of what we are doing is to get to a very different and better place than where we are today. In short, whenever you have a smart definition that reflects your problem well, remember to take the big dream test. Are you ambitious enough? Is the dream big enough? Is it inspiring?

Dreaming big and dreaming small takes the same amount of work.

Jorge Paulo Lemann

Problem definition guide

Aspects

Key question

Concisely articulate in a question what needs to be solved. This focuses our work and ensures that our action suggestions are attainable.

Our question should be SMART: specific, measurable, action-oriented, relevant and time-bound.

Check that the question isn't too broad or narrow and try to make the question inspiring - a big dream.

Context

Think about the context of the problem we are facing. The main questions we should answer are: "Why is this a problem after all? How did it become a problem? Why is it a priority now? What are its implications and consequences?"

With this basic understanding, we can also include industry trends, limitations or barriers (e.g. financial availability, skills gaps in the organization) and we can also include solutions that have already been tested.

Success criteria

Start by asking what needs to happen for the solution to be successful. Also, think from the perspective of the involved parties: what does success mean for each one?

Consider that to achieve success, it will be necessary to build competencies, engage parts of the organization, change mindsets, ensure the sustainability of the action suggestions, etc.

For each success criterion, we should seek to apply the SMART concept, defining measurable goals, even if qualitatively.

Scope and restrictions

In this section, we define the boundaries within which our team can work to solve this problem. Specify what can and cannot be considered in the solution or if there is anything that cannot be a solution. The scope should be broad enough to ensure that we consider all relevant solutions, but specific enough to ensure that the team's work is manageable.

Usually defining a list of elements that are part of the scope is relatively easy, but the most relevant question for achieving alignment is what is NOT part of the scope. Often, different team members will give different answers to this question and it is very important to have this alignment.

For example, if our problem is to expand a business unit, does our scope include mergers and acquisitions? Is it possible to think about partnerships and joint ventures?

Also think about whether there are any elements that restrict our solution space. For example, are there budget constraints, regulatory limitations or skills gaps in the organization that limit our solution?

Stakeholders and third parties

Start with a list of the main stakeholders in our solution.

We need to think critically about the decision-makers and stakeholders who can support or block our solution. Also include stakeholders who can affect how our solution will be implemented.

Sources of insight

Think about the main sources of information that will help us find or refine the solution. What resources can we leverage? Departments, companies, experts, universities, specific reports, benchmarks? Identify the resources that will give you a new lens on the problem.

Be creative and expand our view of the problem. This will ensure that we don't repeat work that has already been done. The best sources of inspiration are often not the most obvious. Think about industries other than our own that may have some relevant parallel, some similarity that can bring value to our problem.

Define the sources specifically - define who, what, when, how and why, so that they are quickly accessible when needed.

Actions

Expand the way you think about the problem
Question the foundations of the problem
Align with the involved parties

Key ideas

The problem definition guide helps to orient the problem definition.
Following the guide will give you and your team a deeper understanding of the problem.
Thinking through each element and aligning them with the involved parties typically generates relevant and sometimes surprising insights.

On urgent problems

Key ideas

Think about the elements of the problem definition guide, especially the involved parties and scope.
Use the problem definition as an ally.
Don't make decisions based on your first impression or idea.