Identify Goal
Define Problem
Define Problem
Gather Data
Define Causes
Identify Options
Clarify Problem
Generate Ideas
Evaluate Options
Generate Ideas
Choose the Best Solution
Implement Solution
Select Solution
Take Action
MacLeod offers her own problem solving procedure, which echoes the above steps:
“1. Recognize the Problem: State what you see. Sometimes the problem is covert. 2. Identify: Get the facts — What exactly happened? What is the issue? 3. and 4. Explore and Connect: Dig deeper and encourage group members to relate their similar experiences. Now you're getting more into the feelings and background [of the situation], not just the facts. 5. Possible Solutions: Consider and brainstorm ideas for resolution. 6. Implement: Choose a solution and try it out — this could be role play and/or a discussion of how the solution would be put in place. 7. Evaluate: Revisit to see if the solution was successful or not.”
Many of these problem solving techniques can be used in concert with one another, or multiple can be appropriate for any given problem. It’s less about facilitating a perfect CPS session, and more about encouraging team members to continually think outside the box and push beyond personal boundaries that inhibit their innovative thinking. So, try out several methods, find those that resonate best with your team, and continue adopting new techniques and adapting your processes along the way.
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In this episode of the McKinsey Podcast , Simon London speaks with Charles Conn, CEO of venture-capital firm Oxford Sciences Innovation, and McKinsey senior partner Hugo Sarrazin about the complexities of different problem-solving strategies.
Podcast transcript
Simon London: Hello, and welcome to this episode of the McKinsey Podcast , with me, Simon London. What’s the number-one skill you need to succeed professionally? Salesmanship, perhaps? Or a facility with statistics? Or maybe the ability to communicate crisply and clearly? Many would argue that at the very top of the list comes problem solving: that is, the ability to think through and come up with an optimal course of action to address any complex challenge—in business, in public policy, or indeed in life.
Looked at this way, it’s no surprise that McKinsey takes problem solving very seriously, testing for it during the recruiting process and then honing it, in McKinsey consultants, through immersion in a structured seven-step method. To discuss the art of problem solving, I sat down in California with McKinsey senior partner Hugo Sarrazin and also with Charles Conn. Charles is a former McKinsey partner, entrepreneur, executive, and coauthor of the book Bulletproof Problem Solving: The One Skill That Changes Everything [John Wiley & Sons, 2018].
Charles and Hugo, welcome to the podcast. Thank you for being here.
Hugo Sarrazin: Our pleasure.
Charles Conn: It’s terrific to be here.
Simon London: Problem solving is a really interesting piece of terminology. It could mean so many different things. I have a son who’s a teenage climber. They talk about solving problems. Climbing is problem solving. Charles, when you talk about problem solving, what are you talking about?
Charles Conn: For me, problem solving is the answer to the question “What should I do?” It’s interesting when there’s uncertainty and complexity, and when it’s meaningful because there are consequences. Your son’s climbing is a perfect example. There are consequences, and it’s complicated, and there’s uncertainty—can he make that grab? I think we can apply that same frame almost at any level. You can think about questions like “What town would I like to live in?” or “Should I put solar panels on my roof?”
You might think that’s a funny thing to apply problem solving to, but in my mind it’s not fundamentally different from business problem solving, which answers the question “What should my strategy be?” Or problem solving at the policy level: “How do we combat climate change?” “Should I support the local school bond?” I think these are all part and parcel of the same type of question, “What should I do?”
I’m a big fan of structured problem solving. By following steps, we can more clearly understand what problem it is we’re solving, what are the components of the problem that we’re solving, which components are the most important ones for us to pay attention to, which analytic techniques we should apply to those, and how we can synthesize what we’ve learned back into a compelling story. That’s all it is, at its heart.
I think sometimes when people think about seven steps, they assume that there’s a rigidity to this. That’s not it at all. It’s actually to give you the scope for creativity, which often doesn’t exist when your problem solving is muddled.
Simon London: You were just talking about the seven-step process. That’s what’s written down in the book, but it’s a very McKinsey process as well. Without getting too deep into the weeds, let’s go through the steps, one by one. You were just talking about problem definition as being a particularly important thing to get right first. That’s the first step. Hugo, tell us about that.
Hugo Sarrazin: It is surprising how often people jump past this step and make a bunch of assumptions. The most powerful thing is to step back and ask the basic questions—“What are we trying to solve? What are the constraints that exist? What are the dependencies?” Let’s make those explicit and really push the thinking and defining. At McKinsey, we spend an enormous amount of time in writing that little statement, and the statement, if you’re a logic purist, is great. You debate. “Is it an ‘or’? Is it an ‘and’? What’s the action verb?” Because all these specific words help you get to the heart of what matters.
Simon London: So this is a concise problem statement.
Hugo Sarrazin: Yeah. It’s not like “Can we grow in Japan?” That’s interesting, but it is “What, specifically, are we trying to uncover in the growth of a product in Japan? Or a segment in Japan? Or a channel in Japan?” When you spend an enormous amount of time, in the first meeting of the different stakeholders, debating this and having different people put forward what they think the problem definition is, you realize that people have completely different views of why they’re here. That, to me, is the most important step.
Charles Conn: I would agree with that. For me, the problem context is critical. When we understand “What are the forces acting upon your decision maker? How quickly is the answer needed? With what precision is the answer needed? Are there areas that are off limits or areas where we would particularly like to find our solution? Is the decision maker open to exploring other areas?” then you not only become more efficient, and move toward what we call the critical path in problem solving, but you also make it so much more likely that you’re not going to waste your time or your decision maker’s time.
How often do especially bright young people run off with half of the idea about what the problem is and start collecting data and start building models—only to discover that they’ve really gone off half-cocked.
Hugo Sarrazin: Yeah.
Charles Conn: And in the wrong direction.
Simon London: OK. So step one—and there is a real art and a structure to it—is define the problem. Step two, Charles?
Charles Conn: My favorite step is step two, which is to use logic trees to disaggregate the problem. Every problem we’re solving has some complexity and some uncertainty in it. The only way that we can really get our team working on the problem is to take the problem apart into logical pieces.
What we find, of course, is that the way to disaggregate the problem often gives you an insight into the answer to the problem quite quickly. I love to do two or three different cuts at it, each one giving a bit of a different insight into what might be going wrong. By doing sensible disaggregations, using logic trees, we can figure out which parts of the problem we should be looking at, and we can assign those different parts to team members.
Simon London: What’s a good example of a logic tree on a sort of ratable problem?
Charles Conn: Maybe the easiest one is the classic profit tree. Almost in every business that I would take a look at, I would start with a profit or return-on-assets tree. In its simplest form, you have the components of revenue, which are price and quantity, and the components of cost, which are cost and quantity. Each of those can be broken out. Cost can be broken into variable cost and fixed cost. The components of price can be broken into what your pricing scheme is. That simple tree often provides insight into what’s going on in a business or what the difference is between that business and the competitors.
If we add the leg, which is “What’s the asset base or investment element?”—so profit divided by assets—then we can ask the question “Is the business using its investments sensibly?” whether that’s in stores or in manufacturing or in transportation assets. I hope we can see just how simple this is, even though we’re describing it in words.
When I went to work with Gordon Moore at the Moore Foundation, the problem that he asked us to look at was “How can we save Pacific salmon?” Now, that sounds like an impossible question, but it was amenable to precisely the same type of disaggregation and allowed us to organize what became a 15-year effort to improve the likelihood of good outcomes for Pacific salmon.
Simon London: Now, is there a danger that your logic tree can be impossibly large? This, I think, brings us onto the third step in the process, which is that you have to prioritize.
Charles Conn: Absolutely. The third step, which we also emphasize, along with good problem definition, is rigorous prioritization—we ask the questions “How important is this lever or this branch of the tree in the overall outcome that we seek to achieve? How much can I move that lever?” Obviously, we try and focus our efforts on ones that have a big impact on the problem and the ones that we have the ability to change. With salmon, ocean conditions turned out to be a big lever, but not one that we could adjust. We focused our attention on fish habitats and fish-harvesting practices, which were big levers that we could affect.
People spend a lot of time arguing about branches that are either not important or that none of us can change. We see it in the public square. When we deal with questions at the policy level—“Should you support the death penalty?” “How do we affect climate change?” “How can we uncover the causes and address homelessness?”—it’s even more important that we’re focusing on levers that are big and movable.
Simon London: Let’s move swiftly on to step four. You’ve defined your problem, you disaggregate it, you prioritize where you want to analyze—what you want to really look at hard. Then you got to the work plan. Now, what does that mean in practice?
Hugo Sarrazin: Depending on what you’ve prioritized, there are many things you could do. It could be breaking the work among the team members so that people have a clear piece of the work to do. It could be defining the specific analyses that need to get done and executed, and being clear on time lines. There’s always a level-one answer, there’s a level-two answer, there’s a level-three answer. Without being too flippant, I can solve any problem during a good dinner with wine. It won’t have a whole lot of backing.
Simon London: Not going to have a lot of depth to it.
Hugo Sarrazin: No, but it may be useful as a starting point. If the stakes are not that high, that could be OK. If it’s really high stakes, you may need level three and have the whole model validated in three different ways. You need to find a work plan that reflects the level of precision, the time frame you have, and the stakeholders you need to bring along in the exercise.
Charles Conn: I love the way you’ve described that, because, again, some people think of problem solving as a linear thing, but of course what’s critical is that it’s iterative. As you say, you can solve the problem in one day or even one hour.
Charles Conn: We encourage our teams everywhere to do that. We call it the one-day answer or the one-hour answer. In work planning, we’re always iterating. Every time you see a 50-page work plan that stretches out to three months, you know it’s wrong. It will be outmoded very quickly by that learning process that you described. Iterative problem solving is a critical part of this. Sometimes, people think work planning sounds dull, but it isn’t. It’s how we know what’s expected of us and when we need to deliver it and how we’re progressing toward the answer. It’s also the place where we can deal with biases. Bias is a feature of every human decision-making process. If we design our team interactions intelligently, we can avoid the worst sort of biases.
Simon London: Here we’re talking about cognitive biases primarily, right? It’s not that I’m biased against you because of your accent or something. These are the cognitive biases that behavioral sciences have shown we all carry around, things like anchoring, overoptimism—these kinds of things.
Both: Yeah.
Charles Conn: Availability bias is the one that I’m always alert to. You think you’ve seen the problem before, and therefore what’s available is your previous conception of it—and we have to be most careful about that. In any human setting, we also have to be careful about biases that are based on hierarchies, sometimes called sunflower bias. I’m sure, Hugo, with your teams, you make sure that the youngest team members speak first. Not the oldest team members, because it’s easy for people to look at who’s senior and alter their own creative approaches.
Hugo Sarrazin: It’s helpful, at that moment—if someone is asserting a point of view—to ask the question “This was true in what context?” You’re trying to apply something that worked in one context to a different one. That can be deadly if the context has changed, and that’s why organizations struggle to change. You promote all these people because they did something that worked well in the past, and then there’s a disruption in the industry, and they keep doing what got them promoted even though the context has changed.
Simon London: Right. Right.
Hugo Sarrazin: So it’s the same thing in problem solving.
Charles Conn: And it’s why diversity in our teams is so important. It’s one of the best things about the world that we’re in now. We’re likely to have people from different socioeconomic, ethnic, and national backgrounds, each of whom sees problems from a slightly different perspective. It is therefore much more likely that the team will uncover a truly creative and clever approach to problem solving.
Simon London: Let’s move on to step five. You’ve done your work plan. Now you’ve actually got to do the analysis. The thing that strikes me here is that the range of tools that we have at our disposal now, of course, is just huge, particularly with advances in computation, advanced analytics. There’s so many things that you can apply here. Just talk about the analysis stage. How do you pick the right tools?
Charles Conn: For me, the most important thing is that we start with simple heuristics and explanatory statistics before we go off and use the big-gun tools. We need to understand the shape and scope of our problem before we start applying these massive and complex analytical approaches.
Simon London: Would you agree with that?
Hugo Sarrazin: I agree. I think there are so many wonderful heuristics. You need to start there before you go deep into the modeling exercise. There’s an interesting dynamic that’s happening, though. In some cases, for some types of problems, it is even better to set yourself up to maximize your learning. Your problem-solving methodology is test and learn, test and learn, test and learn, and iterate. That is a heuristic in itself, the A/B testing that is used in many parts of the world. So that’s a problem-solving methodology. It’s nothing different. It just uses technology and feedback loops in a fast way. The other one is exploratory data analysis. When you’re dealing with a large-scale problem, and there’s so much data, I can get to the heuristics that Charles was talking about through very clever visualization of data.
You test with your data. You need to set up an environment to do so, but don’t get caught up in neural-network modeling immediately. You’re testing, you’re checking—“Is the data right? Is it sound? Does it make sense?”—before you launch too far.
Simon London: You do hear these ideas—that if you have a big enough data set and enough algorithms, they’re going to find things that you just wouldn’t have spotted, find solutions that maybe you wouldn’t have thought of. Does machine learning sort of revolutionize the problem-solving process? Or are these actually just other tools in the toolbox for structured problem solving?
Charles Conn: It can be revolutionary. There are some areas in which the pattern recognition of large data sets and good algorithms can help us see things that we otherwise couldn’t see. But I do think it’s terribly important we don’t think that this particular technique is a substitute for superb problem solving, starting with good problem definition. Many people use machine learning without understanding algorithms that themselves can have biases built into them. Just as 20 years ago, when we were doing statistical analysis, we knew that we needed good model definition, we still need a good understanding of our algorithms and really good problem definition before we launch off into big data sets and unknown algorithms.
Simon London: Step six. You’ve done your analysis.
Charles Conn: I take six and seven together, and this is the place where young problem solvers often make a mistake. They’ve got their analysis, and they assume that’s the answer, and of course it isn’t the answer. The ability to synthesize the pieces that came out of the analysis and begin to weave those into a story that helps people answer the question “What should I do?” This is back to where we started. If we can’t synthesize, and we can’t tell a story, then our decision maker can’t find the answer to “What should I do?”
Simon London: But, again, these final steps are about motivating people to action, right?
Charles Conn: Yeah.
Simon London: I am slightly torn about the nomenclature of problem solving because it’s on paper, right? Until you motivate people to action, you actually haven’t solved anything.
Charles Conn: I love this question because I think decision-making theory, without a bias to action, is a waste of time. Everything in how I approach this is to help people take action that makes the world better.
Simon London: Hence, these are absolutely critical steps. If you don’t do this well, you’ve just got a bunch of analysis.
Charles Conn: We end up in exactly the same place where we started, which is people speaking across each other, past each other in the public square, rather than actually working together, shoulder to shoulder, to crack these important problems.
Simon London: In the real world, we have a lot of uncertainty—arguably, increasing uncertainty. How do good problem solvers deal with that?
Hugo Sarrazin: At every step of the process. In the problem definition, when you’re defining the context, you need to understand those sources of uncertainty and whether they’re important or not important. It becomes important in the definition of the tree.
You need to think carefully about the branches of the tree that are more certain and less certain as you define them. They don’t have equal weight just because they’ve got equal space on the page. Then, when you’re prioritizing, your prioritization approach may put more emphasis on things that have low probability but huge impact—or, vice versa, may put a lot of priority on things that are very likely and, hopefully, have a reasonable impact. You can introduce that along the way. When you come back to the synthesis, you just need to be nuanced about what you’re understanding, the likelihood.
Often, people lack humility in the way they make their recommendations: “This is the answer.” They’re very precise, and I think we would all be well-served to say, “This is a likely answer under the following sets of conditions” and then make the level of uncertainty clearer, if that is appropriate. It doesn’t mean you’re always in the gray zone; it doesn’t mean you don’t have a point of view. It just means that you can be explicit about the certainty of your answer when you make that recommendation.
Simon London: So it sounds like there is an underlying principle: “Acknowledge and embrace the uncertainty. Don’t pretend that it isn’t there. Be very clear about what the uncertainties are up front, and then build that into every step of the process.”
Hugo Sarrazin: Every step of the process.
Simon London: Yeah. We have just walked through a particular structured methodology for problem solving. But, of course, this is not the only structured methodology for problem solving. One that is also very well-known is design thinking, which comes at things very differently. So, Hugo, I know you have worked with a lot of designers. Just give us a very quick summary. Design thinking—what is it, and how does it relate?
Hugo Sarrazin: It starts with an incredible amount of empathy for the user and uses that to define the problem. It does pause and go out in the wild and spend an enormous amount of time seeing how people interact with objects, seeing the experience they’re getting, seeing the pain points or joy—and uses that to infer and define the problem.
Simon London: Problem definition, but out in the world.
Hugo Sarrazin: With an enormous amount of empathy. There’s a huge emphasis on empathy. Traditional, more classic problem solving is you define the problem based on an understanding of the situation. This one almost presupposes that we don’t know the problem until we go see it. The second thing is you need to come up with multiple scenarios or answers or ideas or concepts, and there’s a lot of divergent thinking initially. That’s slightly different, versus the prioritization, but not for long. Eventually, you need to kind of say, “OK, I’m going to converge again.” Then you go and you bring things back to the customer and get feedback and iterate. Then you rinse and repeat, rinse and repeat. There’s a lot of tactile building, along the way, of prototypes and things like that. It’s very iterative.
Simon London: So, Charles, are these complements or are these alternatives?
Charles Conn: I think they’re entirely complementary, and I think Hugo’s description is perfect. When we do problem definition well in classic problem solving, we are demonstrating the kind of empathy, at the very beginning of our problem, that design thinking asks us to approach. When we ideate—and that’s very similar to the disaggregation, prioritization, and work-planning steps—we do precisely the same thing, and often we use contrasting teams, so that we do have divergent thinking. The best teams allow divergent thinking to bump them off whatever their initial biases in problem solving are. For me, design thinking gives us a constant reminder of creativity, empathy, and the tactile nature of problem solving, but it’s absolutely complementary, not alternative.
Simon London: I think, in a world of cross-functional teams, an interesting question is do people with design-thinking backgrounds really work well together with classical problem solvers? How do you make that chemistry happen?
Hugo Sarrazin: Yeah, it is not easy when people have spent an enormous amount of time seeped in design thinking or user-centric design, whichever word you want to use. If the person who’s applying classic problem-solving methodology is very rigid and mechanical in the way they’re doing it, there could be an enormous amount of tension. If there’s not clarity in the role and not clarity in the process, I think having the two together can be, sometimes, problematic.
The second thing that happens often is that the artifacts the two methodologies try to gravitate toward can be different. Classic problem solving often gravitates toward a model; design thinking migrates toward a prototype. Rather than writing a big deck with all my supporting evidence, they’ll bring an example, a thing, and that feels different. Then you spend your time differently to achieve those two end products, so that’s another source of friction.
Now, I still think it can be an incredibly powerful thing to have the two—if there are the right people with the right mind-set, if there is a team that is explicit about the roles, if we’re clear about the kind of outcomes we are attempting to bring forward. There’s an enormous amount of collaborativeness and respect.
Simon London: But they have to respect each other’s methodology and be prepared to flex, maybe, a little bit, in how this process is going to work.
Hugo Sarrazin: Absolutely.
Simon London: The other area where, it strikes me, there could be a little bit of a different sort of friction is this whole concept of the day-one answer, which is what we were just talking about in classical problem solving. Now, you know that this is probably not going to be your final answer, but that’s how you begin to structure the problem. Whereas I would imagine your design thinkers—no, they’re going off to do their ethnographic research and get out into the field, potentially for a long time, before they come back with at least an initial hypothesis.
Hugo Sarrazin: That is a great callout, and that’s another difference. Designers typically will like to soak into the situation and avoid converging too quickly. There’s optionality and exploring different options. There’s a strong belief that keeps the solution space wide enough that you can come up with more radical ideas. If there’s a large design team or many designers on the team, and you come on Friday and say, “What’s our week-one answer?” they’re going to struggle. They’re not going to be comfortable, naturally, to give that answer. It doesn’t mean they don’t have an answer; it’s just not where they are in their thinking process.
Simon London: I think we are, sadly, out of time for today. But Charles and Hugo, thank you so much.
Charles Conn: It was a pleasure to be here, Simon.
Hugo Sarrazin: It was a pleasure. Thank you.
Simon London: And thanks, as always, to you, our listeners, for tuning into this episode of the McKinsey Podcast . If you want to learn more about problem solving, you can find the book, Bulletproof Problem Solving: The One Skill That Changes Everything , online or order it through your local bookstore. To learn more about McKinsey, you can of course find us at McKinsey.com.
Charles Conn is CEO of Oxford Sciences Innovation and an alumnus of McKinsey’s Sydney office. Hugo Sarrazin is a senior partner in the Silicon Valley office, where Simon London, a member of McKinsey Publishing, is also based.
Related articles.
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From deciding what to eat for dinner to considering whether it's the right time to buy a house, problem-solving is a large part of our daily lives. Learn some of the problem-solving strategies that exist and how to use them in real life, along with ways to overcome obstacles that are making it harder to resolve the issues you face.
In cognitive psychology , the term 'problem-solving' refers to the mental process that people go through to discover, analyze, and solve problems.
A problem exists when there is a goal that we want to achieve but the process by which we will achieve it is not obvious to us. Put another way, there is something that we want to occur in our life, yet we are not immediately certain how to make it happen.
Maybe you want a better relationship with your spouse or another family member but you're not sure how to improve it. Or you want to start a business but are unsure what steps to take. Problem-solving helps you figure out how to achieve these desires.
The problem-solving process involves:
Before problem-solving can occur, it is important to first understand the exact nature of the problem itself. If your understanding of the issue is faulty, your attempts to resolve it will also be incorrect or flawed.
Several mental processes are at work during problem-solving. Among them are:
There are many ways to go about solving a problem. Some of these strategies might be used on their own, or you may decide to employ multiple approaches when working to figure out and fix a problem.
An algorithm is a step-by-step procedure that, by following certain "rules" produces a solution. Algorithms are commonly used in mathematics to solve division or multiplication problems. But they can be used in other fields as well.
In psychology, algorithms can be used to help identify individuals with a greater risk of mental health issues. For instance, research suggests that certain algorithms might help us recognize children with an elevated risk of suicide or self-harm.
One benefit of algorithms is that they guarantee an accurate answer. However, they aren't always the best approach to problem-solving, in part because detecting patterns can be incredibly time-consuming.
There are also concerns when machine learning is involved—also known as artificial intelligence (AI)—such as whether they can accurately predict human behaviors.
Heuristics are shortcut strategies that people can use to solve a problem at hand. These "rule of thumb" approaches allow you to simplify complex problems, reducing the total number of possible solutions to a more manageable set.
If you find yourself sitting in a traffic jam, for example, you may quickly consider other routes, taking one to get moving once again. When shopping for a new car, you might think back to a prior experience when negotiating got you a lower price, then employ the same tactics.
While heuristics may be helpful when facing smaller issues, major decisions shouldn't necessarily be made using a shortcut approach. Heuristics also don't guarantee an effective solution, such as when trying to drive around a traffic jam only to find yourself on an equally crowded route.
A trial-and-error approach to problem-solving involves trying a number of potential solutions to a particular issue, then ruling out those that do not work. If you're not sure whether to buy a shirt in blue or green, for instance, you may try on each before deciding which one to purchase.
This can be a good strategy to use if you have a limited number of solutions available. But if there are many different choices available, narrowing down the possible options using another problem-solving technique can be helpful before attempting trial and error.
In some cases, the solution to a problem can appear as a sudden insight. You are facing an issue in a relationship or your career when, out of nowhere, the solution appears in your mind and you know exactly what to do.
Insight can occur when the problem in front of you is similar to an issue that you've dealt with in the past. Although, you may not recognize what is occurring since the underlying mental processes that lead to insight often happen outside of conscious awareness .
Research indicates that insight is most likely to occur during times when you are alone—such as when going on a walk by yourself, when you're in the shower, or when lying in bed after waking up.
If you're facing a problem, you can implement one or more of these strategies to find a potential solution. Here's how to use them in real life:
Problem-solving is not a flawless process as there are a number of obstacles that can interfere with our ability to solve a problem quickly and efficiently. These obstacles include:
In the end, if your goal is to become a better problem-solver, it's helpful to remember that this is a process. Thus, if you want to improve your problem-solving skills, following these steps can help lead you to your solution:
You can find a way to solve your problems as long as you keep working toward this goal—even if the best solution is simply to let go because no other good solution exists.
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By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."
Lucid Content
Reading time: about 6 min
Let’s face it: Things don’t always go according to plan. Systems fail, wires get crossed, projects fall apart.
Problems are an inevitable part of life and work. They’re also an opportunity to think critically and find solutions. But knowing how to get to the root of unexpected situations or challenges can mean the difference between moving forward and spinning your wheels.
Here, we’ll break down the key elements of problem solving, some effective problem solving approaches, and a few effective tools to help you arrive at solutions more quickly.
Broadly defined, problem solving is the process of finding solutions to difficult or complex issues. But you already knew that. Understanding problem solving frameworks, however, requires a deeper dive.
Think about a recent problem you faced. Maybe it was an interpersonal issue. Or it could have been a major creative challenge you needed to solve for a client at work. How did you feel as you approached the issue? Stressed? Confused? Optimistic? Most importantly, which problem solving techniques did you use to tackle the situation head-on? How did you organize thoughts to arrive at the best possible solution?
Here’s the good news: Good problem solving skills can be learned. By its nature, problem solving doesn’t adhere to a clear set of do’s and don’ts—it requires flexibility, communication, and adaptation. However, most problems you face, at work or in life, can be tackled using four basic steps.
First, you must define the problem . This step sounds obvious, but often, you can notice that something is amiss in a project or process without really knowing where the core problem lies. The most challenging part of the problem solving process is uncovering where the problem originated.
Second, you work to generate alternatives to address the problem directly. This should be a collaborative process to ensure you’re considering every angle of the issue.
Third, you evaluate and test potential solutions to your problem. This step helps you fully understand the complexity of the issue and arrive at the best possible solution.
Finally, fourth, you select and implement the solution that best addresses the problem.
Following this basic four-step process will help you approach every problem you encounter with the same rigorous critical and strategic thinking process, recognize commonalities in new problems, and avoid repeating past mistakes.
In addition to these basic problem solving skills, there are several best practices that you should incorporate. These problem solving approaches can help you think more critically and creatively about any problem:
You may not feel like you have the right expertise to resolve a specific problem. Don’t let that stop you from tackling it. The best problem solvers become students of the problem at hand. Even if you don’t have particular expertise on a topic, your unique experience and perspective can lend itself to creative solutions.
Standard problem solving methodologies and problem solving frameworks are a good starting point. But don’t be afraid to challenge assumptions and push boundaries. Good problem solvers find ways to apply existing best practices into innovative problem solving approaches.
Sometimes it’s hard to see a problem, even if it’s right in front of you. Clear answers could be buried in rows of spreadsheet data or lost in miscommunication. Use visualization as a problem solving tool to break down problems to their core elements. Visuals can help you see bottlenecks in the context of the whole process and more clearly organize your thoughts as you define the problem.
It might be cliche, but there’s truth in the old adage that 99% of inspiration is perspiration. The best problem solvers ask why, test, fail, and ask why again. Whether it takes one or 1,000 iterations to solve a problem, the important part—and the part that everyone remembers—is the solution.
Today’s problems are more complex, more difficult to solve, and they often involve multiple disciplines. They require group expertise and knowledge. Being open to others’ expertise increases your ability to be a great problem solver. Great solutions come from integrating your ideas with those of others to find a better solution. Excellent problem solvers build networks and know how to collaborate with other people and teams. They are skilled in bringing people together and sharing knowledge and information.
As you work through the problem solving steps, try these tools to better define the issue and find the appropriate solution.
Similar to pulling weeds from your garden, if you don’t get to the root of the problem, it’s bound to come back. A root cause analysis helps you figure out the root cause behind any disruption or problem, so you can take steps to correct the problem from recurring. The root cause analysis process involves defining the problem, collecting data, and identifying causal factors to pinpoint root causes and arrive at a solution.
Less structured than other more traditional problem solving methods, the 5 Whys is simply what it sounds like: asking why over and over to get to the root of an obstacle or setback. This technique encourages an open dialogue that can trigger new ideas about a problem, whether done individually or with a group. Each why piggybacks off the answer to the previous why. Get started with the template below—both flowcharts and fishbone diagrams can also help you track your answers to the 5 Whys.
A meeting of the minds, a brain dump, a mind meld, a jam session. Whatever you call it, collaborative brainstorming can help surface previously unseen issues, root causes, and alternative solutions. Create and share a mind map with your team members to fuel your brainstorming session.
Sometimes you don’t know where the problem is until you determine where it isn’t. Gap filling helps you analyze inadequacies that are preventing you from reaching an optimized state or end goal. For example, a content gap analysis can help a content marketer determine where holes exist in messaging or the customer experience. Gap analysis is especially helpful when it comes to problem solving because it requires you to find workable solutions. A SWOT analysis chart that looks at a problem through the lens of strengths, opportunities, opportunities, and threats can be a helpful problem solving framework as you start your analysis.
Beyond these practical tips and tools, there are myriad methodical and creative approaches to move a project forward or resolve a conflict. The right approach will depend on the scope of the issue and your desired outcome.
Depending on the problem, Lucidchart offers several templates and diagrams that could help you identify the cause of the issue and map out a plan to resolve it. Learn more about how Lucidchart can help you take control of your problem solving process .
Lucidchart, a cloud-based intelligent diagramming application, is a core component of Lucid Software's Visual Collaboration Suite. This intuitive, cloud-based solution empowers teams to collaborate in real-time to build flowcharts, mockups, UML diagrams, customer journey maps, and more. Lucidchart propels teams forward to build the future faster. Lucid is proud to serve top businesses around the world, including customers such as Google, GE, and NBC Universal, and 99% of the Fortune 500. Lucid partners with industry leaders, including Google, Atlassian, and Microsoft. Since its founding, Lucid has received numerous awards for its products, business, and workplace culture. For more information, visit lucidchart.com.
How you can use creative problem solving at work.
Sometimes you're faced with challenges that traditional problem solving can't fix. Creative problem solving encourages you to find new, creative ways of thinking that can help you overcome the issue at hand more quickly.
Root cause analysis refers to any problem-solving method used to trace an issue back to its origin. Learn how to complete a root cause analysis—we've even included templates to get you started.
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Posted on May 29, 2019
Constant disruption has become a hallmark of the modern workforce and organisations want problem solving skills to combat this. Employers need people who can respond to change – be that evolving technology, new competitors, different models for doing business, or any of the other transformations that have taken place in recent years.
In addition, problem solving techniques encompass many of the other top skills employers seek . For example, LinkedIn’s list of the most in-demand soft skills of 2019 includes creativity, collaboration and adaptability, all of which fall under the problem-solving umbrella.
Despite its importance, many employees misunderstand what the problem solving method really involves.
Effective problem solving doesn’t mean going away and coming up with an answer immediately. In fact, this isn’t good problem solving at all, because you’ll be running with the first solution that comes into your mind, which often isn’t the best.
Instead, you should look at problem solving more as a process with several steps involved that will help you reach the best outcome. Those steps are:
Let’s look at each step in a little more detail.
The first step to solving a problem is defining what the problem actually is – sounds simple, right? Well no. An effective problem solver will take the thoughts of everyone involved into account, but different people might have different ideas on what the root cause of the issue really is. It’s up to you to actively listen to everyone without bringing any of your own preconceived notions to the conversation. Learning to differentiate facts from opinion is an essential part of this process.
An effective problem solver will take the opinions of everyone involved into account
The same can be said of data. Depending on what the problem is, there will be varying amounts of information available that will help you work out what’s gone wrong. There should be at least some data involved in any problem, and it’s up to you to gather as much as possible and analyse it objectively.
Once you’ve identified what the real issue is, it’s time to think of solutions. Brainstorming as many solutions as possible will help you arrive at the best answer because you’ll be considering all potential options and scenarios. You should take everyone’s thoughts into account when you’re brainstorming these ideas, as well as all the insights you’ve gleaned from your data analysis. It also helps to seek input from others at this stage, as they may come up with solutions you haven’t thought of.
Depending on the type of problem, it can be useful to think of both short-term and long-term solutions, as some of your options may take a while to implement.
Each option will have pros and cons, and it’s important you list all of these, as well as how each solution could impact key stakeholders. Once you’ve narrowed down your options to three or four, it’s often a good idea to go to other employees for feedback just in case you’ve missed something. You should also work out how each option ties in with the broader goals of the business.
There may be a way to merge two options together in order to satisfy more people.
Only now should you choose which solution you’re going to go with. What you decide should be whatever solves the problem most effectively while also taking the interests of everyone involved into account. There may be a way to merge two options together in order to satisfy more people.
At this point you might be thinking it’s time to sit back and relax – problem solved, right? There are actually two more steps involved if you want your problem solving method to be truly effective. The first is to create an implementation plan. After all, if you don’t carry out your solution effectively, you’re not really solving the problem at all.
Create an implementation plan on how you will put your solution into practice. One problem solving technique that many use here is to introduce a testing and feedback phase just to make sure the option you’ve selected really is the most viable. You’ll also want to include any changes to your solution that may occur in your implementation plan, as well as how you’ll monitor compliance and success.
There’s one last step to consider as part of the problem solving methodology, and that’s communicating your solution . Without this crucial part of the process, how is anyone going to know what you’ve decided? Make sure you communicate your decision to all the people who might be impacted by it. Not everyone is going to be 100 per cent happy with it, so when you communicate you must give them context. Explain exactly why you’ve made that decision and how the pros mean it’s better than any of the other options you came up with.
Employers are increasingly seeking soft skills, but unfortunately, while you can show that you’ve got a degree in a subject, it’s much harder to prove you’ve got proficiency in things like problem solving skills. But this is changing thanks to Deakin’s micro-credentials. These are university-level micro-credentials that provide an authoritative and third-party assessment of your capabilities in a range of areas, including problem solving. Reach out today for more information .
Struggling to overcome challenges in your life? We all face problems, big and small, on a regular basis.
So how do you tackle them effectively? What are some key problem-solving strategies and skills that can guide you?
Effective problem-solving requires breaking issues down logically, generating solutions creatively, weighing choices critically, and adapting plans flexibly based on outcomes. Useful strategies range from leveraging past solutions that have worked to visualizing problems through diagrams. Core skills include analytical abilities, innovative thinking, and collaboration.
Want to improve your problem-solving skills? Keep reading to find out 17 effective problem-solving strategies, key skills, common obstacles to watch for, and tips on improving your overall problem-solving skills.
Problem-solving is the process of understanding an issue, situation, or challenge that needs to be addressed and then systematically working through possible solutions to arrive at the best outcome.
It involves critical thinking, analysis, logic, creativity, research, planning, reflection, and patience in order to overcome obstacles and find effective answers to complex questions or problems.
The ultimate goal is to implement the chosen solution successfully.
Problem-solving strategies are like frameworks or methodologies that help us solve tricky puzzles or problems we face in the workplace, at home, or with friends.
Imagine you have a big jigsaw puzzle. One strategy might be to start with the corner pieces. Another could be looking for pieces with the same colors.
Just like in puzzles, in real life, we use different plans or steps to find solutions to problems. These strategies help us think clearly, make good choices, and find the best answers without getting too stressed or giving up.
Knowing different problem-solving strategies is important because different types of problems often require different approaches to solve them effectively. Having a variety of strategies to choose from allows you to select the best method for the specific problem you are trying to solve.
This improves your ability to analyze issues thoroughly, develop solutions creatively, and tackle problems from multiple angles. Knowing multiple strategies also aids in overcoming roadblocks if your initial approach is not working.
Here are some reasons why you need to know different problem-solving strategies:
Knowing different ways to solve problems helps you tackle anything that comes your way, making life a bit easier and more fun!
Effective problem-solving strategies include breaking the problem into smaller parts, brainstorming multiple solutions, evaluating the pros and cons of each, and choosing the most viable option.
Critical thinking and creativity are essential in developing innovative solutions. Collaboration with others can also provide diverse perspectives and ideas.
By applying these strategies, you can tackle complex issues more effectively.
Now, consider a challenge you’re dealing with. Which strategy could help you find a solution? Here we will discuss key problem strategies in detail.
This strategy involves looking back at previous similar problems you have faced and the solutions that were effective in solving them.
It is useful when you are facing a problem that is very similar to something you have already solved. The main benefit is that you don’t have to come up with a brand new solution – you already know the method that worked before will likely work again.
However, the limitation is that the current problem may have some unique aspects or differences that mean your old solution is not fully applicable.
The ideal process is to thoroughly analyze the new challenge, identify the key similarities and differences versus the past case, adapt the old solution as needed to align with the current context, and then pilot it carefully before full implementation.
An example is using the same negotiation tactics from purchasing your previous home when putting in an offer on a new house. Key terms would be adjusted but overall it can save significant time versus developing a brand new strategy.
This involves gathering a group of people together to generate as many potential solutions to a problem as possible.
It is effective when you need creative ideas to solve a complex or challenging issue. By getting input from multiple people with diverse perspectives, you increase the likelihood of finding an innovative solution.
The main limitation is that brainstorming sessions can sometimes turn into unproductive gripe sessions or discussions rather than focusing on productive ideation —so they need to be properly facilitated.
The key to an effective brainstorming session is setting some basic ground rules upfront and having an experienced facilitator guide the discussion. Rules often include encouraging wild ideas, avoiding criticism of ideas during the ideation phase, and building on others’ ideas.
For instance, a struggling startup might hold a session where ideas for turnaround plans are generated and then formalized with financials and metrics.
This technique involves envisioning that the problem has already been solved and then working step-by-step backward toward the current state.
This strategy is particularly helpful for long-term, multi-step problems. By starting from the imagined solution and identifying all the steps required to reach it, you can systematically determine the actions needed. It lets you tackle a big hairy problem through smaller, reversible steps.
A limitation is that this approach may not be possible if you cannot accurately envision the solution state to start with.
The approach helps drive logical systematic thinking for complex problem-solving, but should still be combined with creative brainstorming of alternative scenarios and solutions.
An example is planning for an event – you would imagine the successful event occurring, then determine the tasks needed the week before, two weeks before, etc. all the way back to the present.
This method, named after author Rudyard Kipling, provides a framework for thoroughly analyzing a problem before jumping into solutions.
It consists of answering six fundamental questions: What, Where, When, How, Who, and Why about the challenge. Clearly defining these core elements of the problem sets the stage for generating targeted solutions.
The Kipling method enables a deep understanding of problem parameters and root causes before solution identification. By jumping to brainstorm solutions too early, critical information can be missed or the problem is loosely defined, reducing solution quality.
Answering the six fundamental questions illuminates all angles of the issue. This takes time but pays dividends in generating optimal solutions later tuned precisely to the true underlying problem.
The limitation is that meticulously working through numerous questions before addressing solutions can slow progress.
The best approach blends structured problem decomposition techniques like the Kipling method with spurring innovative solution ideation from a diverse team.
An example is using this technique after a technical process failure – the team would systematically detail What failed, Where/When did it fail, How it failed (sequence of events), Who was involved, and Why it likely failed before exploring preventative solutions.
This technique involves attempting various potential solutions sequentially until finding one that successfully solves the problem.
Trial and error works best when facing a concrete, bounded challenge with clear solution criteria and a small number of discrete options to try. By methodically testing solutions, you can determine the faulty component.
A limitation is that it can be time-intensive if the working solution set is large.
The key is limiting the variable set first. For technical problems, this boundary is inherent and each element can be iteratively tested. But for business issues, artificial constraints may be required – setting decision rules upfront to reduce options before testing.
Furthermore, hypothesis-driven experimentation is far superior to blind trial and error – have logic for why Option A may outperform Option B.
Examples include fixing printer jams by testing different paper tray and cable configurations or resolving website errors by tweaking CSS/HTML line-by-line until the code functions properly.
Heuristics refers to applying existing problem-solving formulas or frameworks rather than addressing issues completely from scratch.
This allows leveraging established best practices rather than reinventing the wheel each time.
It is effective when facing recurrent, common challenges where proven structured approaches exist.
However, heuristics may force-fit solutions to non-standard problems.
For example, a cost-benefit analysis can be used instead of custom weighting schemes to analyze potential process improvements.
Onethread allows teams to define, save, and replicate configurable project templates so proven workflows can be reliably applied across problems with some consistency rather than fully custom one-off approaches each time.
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Insight is a problem-solving technique that involves waiting patiently for an unexpected “aha moment” when the solution pops into your mind.
It works well for personal challenges that require intuitive realizations over calculated logic. The unconscious mind makes connections leading to flashes of insight when relaxing or doing mundane tasks unrelated to the actual problem.
Benefits include out-of-the-box creative solutions. However, the limitations are that insights can’t be forced and may never come at all if too complex. Critical analysis is still required after initial insights.
A real-life example would be a writer struggling with how to end a novel. Despite extensive brainstorming, they feel stuck. Eventually while gardening one day, a perfect unexpected plot twist sparks an ideal conclusion. However, once written they still carefully review if the ending flows logically from the rest of the story.
This approach involves deconstructing a problem in reverse sequential order from the current undesirable outcome back to the initial root causes.
By mapping the chain of events backward, you can identify the origin of where things went wrong and establish the critical junctures for solving it moving ahead. Reverse engineering provides diagnostic clarity on multi-step problems.
However, the limitation is that it focuses heavily on autopsying the past versus innovating improved future solutions.
An example is tracing back from a server outage, through the cascade of infrastructure failures that led to it finally terminating at the initial script error that triggered the crisis. This root cause would then inform the preventative measure.
This technique defines the current problem state and the desired end goal state, then systematically identifies obstacles in the way of getting from one to the other.
By mapping the barriers or gaps, you can then develop solutions to address each one. This methodically connects the problem to solutions.
A limitation is that some obstacles may be unknown upfront and only emerge later.
For example, you can list down all the steps required for a new product launch – current state through production, marketing, sales, distribution, etc. to full launch (goal state) – to highlight where resource constraints or other blocks exist so they can be addressed.
Onethread allows dividing big-picture projects into discrete, manageable phases, milestones, and tasks to simplify execution just as problems can be decomposed into more achievable components. Features like dependency mapping further reinforce interconnections.
Using Onethread’s issues and subtasks feature, messy problems can be decomposed into manageable chunks.
This technique involves asking “Why did this problem occur?” and then responding with an answer that is again met with asking “Why?” This process repeats five times until the root cause is revealed.
Continually asking why digs deeper from surface symptoms to underlying systemic issues.
It is effective for getting to the source of problems originating from human error or process breakdowns.
However, some complex issues may have multiple tangled root causes not solvable through this approach alone.
An example is a retail store experiencing a sudden decline in customers. Successively asking why five times may trace an initial drop to parking challenges, stemming from a city construction project – the true starting point to address.
This involves analyzing a problem or proposed solution by categorizing internal and external factors into a 2×2 matrix: Strengths, Weaknesses as the internal rows; Opportunities and Threats as the external columns.
Systematically identifying these elements provides balanced insight to evaluate options and risks. It is impactful when evaluating alternative solutions or developing strategy amid complexity or uncertainty.
The key benefit of SWOT analysis is enabling multi-dimensional thinking when rationally evaluating options. Rather than getting anchored on just the upsides or the existing way of operating, it urges a systematic assessment through four different lenses:
Multiperspective analysis provides the needed holistic view of the balanced risk vs. reward equation for strategic decision making amid uncertainty.
However, SWOT can feel restrictive if not tailored and evolved for different issue types.
Teams should view SWOT analysis as a starting point, augmenting it further for distinct scenarios.
An example is performing a SWOT analysis on whether a small business should expand into a new market – evaluating internal capabilities to execute vs. risks in the external competitive and demand environment to inform the growth decision with eyes wide open.
This technique involves comparing the current state of performance, output, or results to the desired or expected levels to highlight shortfalls.
By quantifying the gaps, you can identify problem areas and prioritize address solutions.
Gap analysis is based on the simple principle – “you can’t improve what you don’t measure.” It enables facts-driven problem diagnosis by highlighting delta to goals, not just vague dissatisfaction that something seems wrong. And measurement immediately suggests improvement opportunities – address the biggest gaps first.
This data orientation also supports ROI analysis on fixing issues – the return from closing larger gaps outweighs narrowly targeting smaller performance deficiencies.
However, the approach is only effective if robust standards and metrics exist as the benchmark to evaluate against. Organizations should invest upfront in establishing performance frameworks.
Furthermore, while numbers are invaluable, the human context behind problems should not be ignored – quantitative versus qualitative gap assessment is optimally blended.
For example, if usage declines are noted during software gap analysis, this could be used as a signal to improve user experience through design.
A Gemba walk involves going to the actual place where work is done, directly observing the process, engaging with employees, and finding areas for improvement.
By experiencing firsthand rather than solely reviewing abstract reports, practical problems and ideas emerge.
The limitation is Gemba walks provide anecdotes not statistically significant data. It complements but does not replace comprehensive performance measurement.
An example is a factory manager inspecting the production line to spot jam areas based on direct reality rather than relying on throughput dashboards alone back in her office. Frontline insights prove invaluable.
This involves assessing the marketplace around a problem or business situation via five key factors: competitors, new entrants, substitute offerings, suppliers, and customer power.
Evaluating these forces illuminates risks and opportunities for strategy development and issue resolution. It is effective for understanding dynamic external threats and opportunities when operating in a contested space.
However, over-indexing on only external factors can overlook the internal capabilities needed to execute solutions.
A startup CEO, for example, may analyze market entry barriers, whitespace opportunities, and disruption risks across these five forces to shape new product rollout strategies and marketing approaches.
The Six Thinking Hats is a technique developed by Edward de Bono that encourages people to think about a problem from six different perspectives, each represented by a colored “thinking hat.”
The key benefit of this strategy is that it pushes team members to move outside their usual thinking style and consider new angles. This brings more diverse ideas and solutions to the table.
It works best for complex problems that require innovative solutions and when a team is stuck in an unproductive debate. The structured framework keeps the conversation flowing in a positive direction.
Limitations are that it requires training on the method itself and may feel unnatural at first. Team dynamics can also influence success – some members may dominate certain “hats” while others remain quiet.
A real-life example is a software company debating whether to build a new feature. The white hat focuses on facts, red on gut feelings, black on potential risks, yellow on benefits, green on new ideas, and blue on process. This exposes more balanced perspectives before deciding.
Onethread centralizes diverse stakeholder communication onto one platform, ensuring all voices are incorporated when evaluating project tradeoffs, just as problem-solving should consider multifaceted solutions.
Drawing out a problem involves creating visual representations like diagrams, flowcharts, and maps to work through challenging issues.
This strategy is helpful when dealing with complex situations with lots of interconnected components. The visuals simplify the complexity so you can thoroughly understand the problem and all its nuances.
Key benefits are that it allows more stakeholders to get on the same page regarding root causes and it sparks new creative solutions as connections are made visually.
However, simple problems with few variables don’t require extensive diagrams. Additionally, some challenges are so multidimensional that fully capturing every aspect is difficult.
A real-life example would be mapping out all the possible causes leading to decreased client satisfaction at a law firm. An intricate fishbone diagram with branches for issues like service delivery, technology, facilities, culture, and vendor partnerships allows the team to trace problems back to their origins and brainstorm targeted fixes.
An algorithm is a predefined step-by-step process that is guaranteed to produce the correct solution if implemented properly.
Using algorithms is effective when facing problems that have clear, binary right and wrong answers. Algorithms work for mathematical calculations, computer code, manufacturing assembly lines, and scientific experiments.
Key benefits are consistency, accuracy, and efficiency. However, they require extensive upfront development and only apply to scenarios with strict parameters. Additionally, human error can lead to mistakes.
For example, crew members of fast food chains like McDonald’s follow specific algorithms for food prep – from grill times to ingredient amounts in sandwiches, to order fulfillment procedures. This ensures uniform quality and service across all locations. However, if a step is missed, errors occur.
The problem-solving process typically includes defining the issue, analyzing details, creating solutions, weighing choices, acting, and reviewing results.
In the above, we have discussed several problem-solving strategies. For every problem-solving strategy, you have to follow these processes. Here’s a detailed step-by-step process of effective problem-solving:
The problem-solving process starts with identifying the problem. This step involves understanding the issue’s nature, its scope, and its impact. Once the problem is clearly defined, it sets the foundation for finding effective solutions.
Identifying the problem is crucial. It means figuring out exactly what needs fixing. This involves looking at the situation closely, understanding what’s wrong, and knowing how it affects things. It’s about asking the right questions to get a clear picture of the issue.
This step is important because it guides the rest of the problem-solving process. Without a clear understanding of the problem, finding a solution is much harder. It’s like diagnosing an illness before treating it. Once the problem is identified accurately, you can move on to exploring possible solutions and deciding on the best course of action.
Breaking down the problem is a key step in the problem-solving process. It involves dividing the main issue into smaller, more manageable parts. This makes it easier to understand and tackle each component one by one.
After identifying the problem, the next step is to break it down. This means splitting the big issue into smaller pieces. It’s like solving a puzzle by handling one piece at a time.
By doing this, you can focus on each part without feeling overwhelmed. It also helps in identifying the root causes of the problem. Breaking down the problem allows for a clearer analysis and makes finding solutions more straightforward.
Each smaller problem can be addressed individually, leading to an effective resolution of the overall issue. This approach not only simplifies complex problems but also aids in developing a systematic plan to solve them.
Coming up with potential solutions is the third step in the problem-solving process. It involves brainstorming various options to address the problem, considering creativity and feasibility to find the best approach.
After breaking down the problem, it’s time to think of ways to solve it. This stage is about brainstorming different solutions. You look at the smaller issues you’ve identified and start thinking of ways to fix them. This is where creativity comes in.
You want to come up with as many ideas as possible, no matter how out-of-the-box they seem. It’s important to consider all options and evaluate their pros and cons. This process allows you to gather a range of possible solutions.
Later, you can narrow these down to the most practical and effective ones. This step is crucial because it sets the stage for deciding on the best solution to implement. It’s about being open-minded and innovative to tackle the problem effectively.
Analyzing the possible solutions is the fourth step in the problem-solving process. It involves evaluating each proposed solution’s advantages and disadvantages to determine the most effective and feasible option.
After coming up with potential solutions, the next step is to analyze them. This means looking closely at each idea to see how well it solves the problem. You weigh the pros and cons of every solution.
Consider factors like cost, time, resources, and potential outcomes. This analysis helps in understanding the implications of each option. It’s about being critical and objective, ensuring that the chosen solution is not only effective but also practical.
This step is vital because it guides you towards making an informed decision. It involves comparing the solutions against each other and selecting the one that best addresses the problem.
By thoroughly analyzing the options, you can move forward with confidence, knowing you’ve chosen the best path to solve the issue.
Implementing and monitoring the solutions is the final step in the problem-solving process. It involves putting the chosen solution into action and observing its effectiveness, making adjustments as necessary.
Once you’ve selected the best solution, it’s time to put it into practice. This step is about action. You implement the chosen solution and then keep an eye on how it works. Monitoring is crucial because it tells you if the solution is solving the problem as expected.
If things don’t go as planned, you may need to make some changes. This could mean tweaking the current solution or trying a different one. The goal is to ensure the problem is fully resolved.
This step is critical because it involves real-world application. It’s not just about planning; it’s about doing and adjusting based on results. By effectively implementing and monitoring the solutions, you can achieve the desired outcome and solve the problem successfully.
Following a defined process to solve problems is important because it provides a systematic, structured approach instead of a haphazard one. Having clear steps guides logical thinking, analysis, and decision-making to increase effectiveness. Key reasons it helps are:
The problem-solving process is a powerful tool that can help us tackle any challenge we face. By following these steps, we can find solutions that work and learn important skills along the way.
Efficient problem-solving requires breaking down issues logically, evaluating options, and implementing practical solutions.
Key skills include critical thinking to understand root causes, creativity to brainstorm innovative ideas, communication abilities to collaborate with others, and decision-making to select the best way forward. Staying adaptable, reflecting on outcomes, and applying lessons learned are also essential.
With practice, these capacities will lead to increased personal and team effectiveness in systematically addressing any problem.
Let’s explore the powers you need to become a problem-solving hero!
Critical thinking and analytical skills are vital for efficient problem-solving as they enable individuals to objectively evaluate information, identify key issues, and generate effective solutions.
These skills facilitate a deeper understanding of problems, leading to logical, well-reasoned decisions. By systematically breaking down complex issues and considering various perspectives, individuals can develop more innovative and practical solutions, enhancing their problem-solving effectiveness.
Effective communication skills are essential for efficient problem-solving as they facilitate clear sharing of information, ensuring all team members understand the problem and proposed solutions.
These skills enable individuals to articulate issues, listen actively, and collaborate effectively, fostering a productive environment where diverse ideas can be exchanged and refined. By enhancing mutual understanding, communication skills contribute significantly to identifying and implementing the most viable solutions.
Strong decision-making skills are crucial for efficient problem-solving, as they enable individuals to choose the best course of action from multiple alternatives.
These skills involve evaluating the potential outcomes of different solutions, considering the risks and benefits, and making informed choices. Effective decision-making leads to the implementation of solutions that are likely to resolve problems effectively, ensuring resources are used efficiently and goals are achieved.
Planning and prioritization are key for efficient problem-solving, ensuring resources are allocated effectively to address the most critical issues first. This approach helps in organizing tasks according to their urgency and impact, streamlining efforts towards achieving the desired outcome efficiently.
Emotional intelligence enhances problem-solving by allowing individuals to manage emotions, understand others, and navigate social complexities. It fosters a positive, collaborative environment, essential for generating creative solutions and making informed, empathetic decisions.
Leadership skills drive efficient problem-solving by inspiring and guiding teams toward common goals. Effective leaders motivate their teams, foster innovation, and navigate challenges, ensuring collective efforts are focused and productive in addressing problems.
Time management is crucial in problem-solving, enabling individuals to allocate appropriate time to each task. By efficiently managing time, one can ensure that critical problems are addressed promptly without neglecting other responsibilities.
Data analysis skills are essential for problem-solving, as they enable individuals to sift through data, identify trends, and extract actionable insights. This analytical approach supports evidence-based decision-making, leading to more accurate and effective solutions.
Research skills are vital for efficient problem-solving, allowing individuals to gather relevant information, explore various solutions, and understand the problem’s context. This thorough exploration aids in developing well-informed, innovative solutions.
Becoming a great problem solver takes practice, but with these skills, you’re on your way to becoming a problem-solving hero.
Improving your problem-solving skills can make you a master at overcoming challenges. Learn from experts, practice regularly, welcome feedback, try new methods, experiment, and study others’ success to become better.
Improving problem-solving skills by learning from experts involves seeking mentorship, attending workshops, and studying case studies. Experts provide insights and techniques that refine your approach, enhancing your ability to tackle complex problems effectively.
To enhance your problem-solving skills, learning from experts can be incredibly beneficial. Engaging with mentors, participating in specialized workshops, and analyzing case studies from seasoned professionals can offer valuable perspectives and strategies.
Experts share their experiences, mistakes, and successes, providing practical knowledge that can be applied to your own problem-solving process. This exposure not only broadens your understanding but also introduces you to diverse methods and approaches, enabling you to tackle challenges more efficiently and creatively.
Improving problem-solving skills through practice involves tackling a variety of challenges regularly. This hands-on approach helps in refining techniques and strategies, making you more adept at identifying and solving problems efficiently.
One of the most effective ways to enhance your problem-solving skills is through consistent practice. By engaging with different types of problems on a regular basis, you develop a deeper understanding of various strategies and how they can be applied.
This hands-on experience allows you to experiment with different approaches, learn from mistakes, and build confidence in your ability to tackle challenges.
Regular practice not only sharpens your analytical and critical thinking skills but also encourages adaptability and innovation, key components of effective problem-solving.
Being open to feedback is like unlocking a secret level in a game. It helps you boost your problem-solving skills. Improving problem-solving skills through openness to feedback involves actively seeking and constructively responding to critiques.
This receptivity enables you to refine your strategies and approaches based on insights from others, leading to more effective solutions.
Learning new approaches and methodologies is like adding new tools to your toolbox. It makes you a smarter problem-solver. Enhancing problem-solving skills by learning new approaches and methodologies involves staying updated with the latest trends and techniques in your field.
This continuous learning expands your toolkit, enabling innovative solutions and a fresh perspective on challenges.
Experimentation is like being a scientist of your own problems. It’s a powerful way to improve your problem-solving skills. Boosting problem-solving skills through experimentation means trying out different solutions to see what works best. This trial-and-error approach fosters creativity and can lead to unique solutions that wouldn’t have been considered otherwise.
Analyzing competitors’ success is like being a detective. It’s a smart way to boost your problem-solving skills. Improving problem-solving skills by analyzing competitors’ success involves studying their strategies and outcomes. Understanding what worked for them can provide valuable insights and inspire effective solutions for your own challenges.
Facing obstacles when solving problems is common. Recognizing these barriers, like fear of failure or lack of information, helps us find ways around them for better solutions.
Fear of failure is like a big, scary monster that stops us from solving problems. It’s a challenge many face. Because being afraid of making mistakes can make us too scared to try new solutions.
How can we overcome this? First, understand that it’s okay to fail. Failure is not the opposite of success; it’s part of learning. Every time we fail, we discover one more way not to solve a problem, getting us closer to the right solution. Treat each attempt like an experiment. It’s not about failing; it’s about testing and learning.
Lack of information is like trying to solve a puzzle with missing pieces. It’s a big challenge in problem-solving. Because without all the necessary details, finding a solution is much harder.
How can we fix this? Start by gathering as much information as you can. Ask questions, do research, or talk to experts. Think of yourself as a detective looking for clues. The more information you collect, the clearer the picture becomes. Then, use what you’ve learned to think of solutions.
A fixed mindset is like being stuck in quicksand; it makes solving problems harder. It means thinking you can’t improve or learn new ways to solve issues.
How can we change this? First, believe that you can grow and learn from challenges. Think of your brain as a muscle that gets stronger every time you use it. When you face a problem, instead of saying “I can’t do this,” try thinking, “I can’t do this yet.” Look for lessons in every challenge and celebrate small wins.
Everyone starts somewhere, and mistakes are just steps on the path to getting better. By shifting to a growth mindset, you’ll see problems as opportunities to grow. Keep trying, keep learning, and your problem-solving skills will soar!
Jumping to conclusions is like trying to finish a race before it starts. It’s a challenge in problem-solving. That means making a decision too quickly without looking at all the facts.
How can we avoid this? First, take a deep breath and slow down. Think about the problem like a puzzle. You need to see all the pieces before you know where they go. Ask questions, gather information, and consider different possibilities. Don’t choose the first solution that comes to mind. Instead, compare a few options.
Feeling overwhelmed is like being buried under a mountain of puzzles. It’s a big challenge in problem-solving. When we’re overwhelmed, everything seems too hard to handle.
How can we deal with this? Start by taking a step back. Breathe deeply and focus on one thing at a time. Break the big problem into smaller pieces, like sorting puzzle pieces by color. Tackle each small piece one by one. It’s also okay to ask for help. Sometimes, talking to someone else can give you a new perspective.
Confirmation bias is like wearing glasses that only let you see what you want to see. It’s a challenge in problem-solving. Because it makes us focus only on information that agrees with what we already believe, ignoring anything that doesn’t.
How can we overcome this? First, be aware that you might be doing it. It’s like checking if your glasses are on right. Then, purposely look for information that challenges your views. It’s like trying on a different pair of glasses to see a new perspective. Ask questions and listen to answers, even if they don’t fit what you thought before.
Groupthink is like everyone in a group deciding to wear the same outfit without asking why. It’s a challenge in problem-solving. It means making decisions just because everyone else agrees, without really thinking it through.
How can we avoid this? First, encourage everyone in the group to share their ideas, even if they’re different. It’s like inviting everyone to show their unique style of clothes.
Listen to all opinions and discuss them. It’s okay to disagree; it helps us think of better solutions. Also, sometimes, ask someone outside the group for their thoughts. They might see something everyone in the group missed.
Overcoming obstacles in problem-solving requires patience, openness, and a willingness to learn from mistakes. By recognizing these barriers, we can develop strategies to navigate around them, leading to more effective and creative solutions.
The most common techniques include brainstorming, the 5 Whys, mind mapping, SWOT analysis, and using algorithms or heuristics. Each approach has its strengths, suitable for different types of problems.
There’s no one-size-fits-all strategy. The best approach depends on the problem’s complexity, available resources, and time constraints. Combining multiple techniques often yields the best results.
Improve your problem-solving skills by practicing regularly, learning from experts, staying open to feedback, and continuously updating your knowledge on new approaches and methodologies.
Yes, tools like mind mapping software, online courses on critical thinking, and books on problem-solving techniques can be very helpful. Joining forums or groups focused on problem-solving can also provide support and insights.
Common mistakes include jumping to conclusions without fully understanding the problem, ignoring valuable feedback, sticking to familiar solutions without considering alternatives, and not breaking down complex problems into manageable parts.
Mastering problem-solving strategies equips us with the tools to tackle challenges across all areas of life. By understanding and applying these techniques, embracing a growth mindset, and learning from both successes and obstacles, we can transform problems into opportunities for growth. Continuously improving these skills ensures we’re prepared to face and solve future challenges more effectively.
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June 14, 2022 - 10 min read
Solving complex problems may be difficult but it doesn't have to be excruciating. You just need the right frame of mind and a process for untangling the problem at hand.
Luckily for you, there are plenty of techniques available to solve whatever problems come at you in the workplace.
When faced with a doozy of a problem, where do you start? And what problem-solving techniques can you use right now that can help you make good decisions?
Today's post will give you tips and techniques for solving complex problems so you can untangle any complication like an expert.
At its core, problem-solving is a methodical four-step process. You may even recall these steps from when you were first introduced to the Scientific Method.
When applying problem-solving techniques, you will be using a variation of these steps as your foundation.
Takeaway: Before you can solve a problem, seek to understand it fully.
Time to get creative! You might think this will just be a list of out-of-the-box ways to brainstorm ideas. Not exactly.
Creative problem solving (CPS) is actually a formal process formulated by Sidney Parnes and Alex Faickney Osborn , who is thought of as the father of traditional brainstorming (and the "O" in famous advertising agency BBDO).
Their creative problem solving process emphasizes several things, namely:
Takeaway: When brainstorming solutions, generate ideas first by using questions and building off of existing ideas. Do all evaluating and judging later.
If you take a look at the history of problem-solving techniques in psychology, you'll come across a wide spectrum of interesting ideas that could be helpful.
In 1911, the American psychologist Edward Thorndike observed cats figuring out how to escape from the cage he placed them in. From this, Thorndike developed his law of effect , which states: If you succeed via trial-and-error, you're more likely to use those same actions and ideas that led to your previous success when you face the problem again.
Takeaway: Your past experience can inform and shed light on the problem you face now. Recall. Explore.
The Gestalt psychologists built on Thorndike's ideas when they proposed that problem-solving can happen via reproductive thinking — which is not about sex, but rather solving a problem by using past experience and reproducing that experience to solve the current problem.
What's interesting about Gestalt psychology is how they view barriers to problem-solving. Here are two such barriers:
Takeaway: Think outside of the box! And by box, we mean outside of the past experience you're holding on to, or outside any preconceived ideas on how a tool is conventionally used.
Hurson's productive thinking model.
In his book "Think Better," author and creativity guru Tim Hurson proposed a six-step model for solving problems creatively. The steps in his Productive Thinking Model are:
The most important part of defining the problem is looking at the possible root cause. You'll need to ask yourself questions like: Where and when is it happening? How is it occurring? With whom is it happening? Why is it happening?
You can get to the root cause with a fishbone diagram (also known as an Ishikawa diagram or a cause and effect diagram).
Basically, you put the effect on the right side as the problem statement. Then you list all possible causes on the left, grouped into larger cause categories. The resulting shape resembles a fish skeleton. Which is a perfect way to say, "This problem smells fishy."
Analogical thinking uses information from one area to help with a problem in a different area. In short, solving a different problem can lead you to find a solution to the actual problem. Watch out though! Analogies are difficult for beginners and take some getting used to.
An example: In the "radiation problem," a doctor has a patient with a tumor that cannot be operated on. The doctor can use rays to destroy the tumor but it also destroys healthy tissue.
Two researchers, Gick and Holyoak , noted that people solved the radiation problem much more easily after being asked to read a story about an invading general who must capture the fortress of a king but be careful to avoid landmines that will detonate if large forces traverse the streets. The general then sends small forces of men down different streets so the army can converge at the fortress at the same time and can capture it at full force.
In her book " The Architecture of All Abundance ," author Lenedra J. Carroll (aka the mother of pop star Jewel) talks about a question-and-answer technique for getting out of a problem.
When faced with a problem, ask yourself a question about it and brainstorm 12 answers ("12 what elses") to that problem. Then you can go further by taking one answer, turning it into a question and generating 12 more "what elses." Repeat until the solution is golden brown, fully baked, and ready to take out of the oven.
Hopefully you find these different techniques useful and they get your imagination rolling with ideas on how to solve different problems.
And if that's the case, then you have four different takeaways to use the next time a problem gets you tangled up:
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Lionel is a former Content Marketing Manager of Wrike. He is also a blogger since 1997, a productivity enthusiast, a project management newbie, a musician and producer of electronic downtempo music, a father of three, and a husband of one.
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Discover what problem-solving is, and why it's important for managers. Understand the steps of the process and learn about seven problem-solving skills.
1Managers oversee the day-to-day operations of a particular department, and sometimes a whole company, using their problem-solving skills regularly. Managers with good problem-solving skills can help ensure companies run smoothly and prosper.
If you're a current manager or are striving to become one, read this guide to discover what problem-solving skills are and why it's important for managers to have them. Learn the steps of the problem-solving process, and explore seven skills that can help make problem-solving easier and more effective.
Problem-solving is both an ability and a process. As an ability, problem-solving can aid in resolving issues faced in different environments like home, school, abroad, and social situations, among others. As a process, problem-solving involves a series of steps for finding solutions to questions or concerns that arise throughout life.
Managers deal with problems regularly, whether supervising a staff of two or 100. When people solve problems quickly and effectively, workplaces can benefit in a number of ways. These include:
Greater creativity
Higher productivity
Increased job fulfillment
Satisfied clients or customers
Better cooperation and cohesion
Improved environments for employees and customers
Companies depend on managers who can solve problems adeptly. Although problem-solving is a skill in its own right, a subset of seven skills can help make the process of problem-solving easier. These include analysis, communication, emotional intelligence, resilience, creativity, adaptability, and teamwork.
As a manager , you'll solve each problem by assessing the situation first. Then, you’ll use analytical skills to distinguish between ineffective and effective solutions.
Effective communication plays a significant role in problem-solving, particularly when others are involved. Some skills that can help enhance communication at work include active listening, speaking with an even tone and volume, and supporting verbal information with written communication.
Emotional intelligence is the ability to recognize and manage emotions in any situation. People with emotional intelligence usually solve problems calmly and systematically, which often yields better results.
Emotional intelligence and resilience are closely related traits. Resiliency is the ability to cope with and bounce back quickly from difficult situations. Those who possess resilience are often capable of accurately interpreting people and situations, which can be incredibly advantageous when difficulties arise.
When brainstorming solutions to problems, creativity can help you to think outside the box. Problem-solving strategies can be enhanced with the application of creative techniques. You can use creativity to:
Approach problems from different angles
Improve your problem-solving process
Spark creativity in your employees and peers
Adaptability is the capacity to adjust to change. When a particular solution to an issue doesn't work, an adaptable person can revisit the concern to think up another one without getting frustrated.
Finding a solution to a problem regularly involves working in a team. Good teamwork requires being comfortable working with others and collaborating with them, which can result in better problem-solving overall.
Effective problem-solving involves five essential steps. One way to remember them is through the IDEAL model created in 1984 by psychology professors John D. Bransford and Barry S. Stein [ 1 ]. The steps to solving problems in this model include: identifying that there is a problem, defining the goals you hope to achieve, exploring potential solutions, choosing a solution and acting on it, and looking at (or evaluating) the outcome.
To solve a problem, you must first admit that one exists to then find its root cause. Finding the cause of the problem may involve asking questions like:
Can the problem be solved?
How big of a problem is it?
Why do I think the problem is occurring?
What are some things I know about the situation?
What are some things I don't know about the situation?
Are there any people who contributed to the problem?
Are there materials or processes that contributed to the problem?
Are there any patterns I can identify?
Every problem is different. The goals you hope to achieve when problem-solving depend on the scope of the problem. Some examples of goals you might set include:
Gather as much factual information as possible.
Brainstorm many different strategies to come up with the best one.
Be flexible when considering other viewpoints.
Articulate clearly and encourage questions, so everyone involved is on the same page.
Be open to other strategies if the chosen strategy doesn't work.
Stay positive throughout the process.
Once you've defined the goals you hope to achieve when problem-solving , it's time to start the process. This involves steps that often include fact-finding, brainstorming, prioritizing solutions, and assessing the cost of top solutions in terms of time, labor, and money.
Evaluate the pros and cons of each potential solution, and choose the one most likely to solve the problem within your given budget, abilities, and resources. Once you choose a solution, it's important to make a commitment and see it through. Draw up a plan of action for implementation, and share it with all involved parties clearly and effectively, both verbally and in writing. Make sure everyone understands their role for a successful conclusion.
Evaluation offers insights into your current situation and future problem-solving. When evaluating the outcome, ask yourself questions like:
Did the solution work?
Will this solution work for other problems?
Were there any changes you would have made?
Would another solution have worked better?
As a current or future manager looking to build your problem-solving skills, it is often helpful to take a professional course. Consider Improving Communication Skills offered by the University of Pennsylvania on Coursera. You'll learn how to boost your ability to persuade, ask questions, negotiate, apologize, and more.
You might also consider taking Emotional Intelligence: Cultivating Immensely Human Interactions , offered by the University of Michigan on Coursera. You'll explore the interpersonal and intrapersonal skills common to people with emotional intelligence, and you'll learn how emotional intelligence is connected to team success and leadership.
Tennessee Tech. “ The Ideal Problem Solver (2nd ed.) , https://www.tntech.edu/cat/pdf/useful_links/idealproblemsolver.pdf.” Accessed December 6, 2022.
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Phy 325 - numerical problem solving methods in physics.
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This course is designed for students who are interested in learning numerical and computational methods that can be utilized for solving physics problems. Students will learn Python to explore selected numerical methods needed for solving a variety of problems applicable to all physics courses. Offered fall semester. Prerequisites: PHY 230 and PHY 231. PHY 302 is recommended.
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Teachers can resolve challenges that come up over and over by using data to keep testing strategies until they find what works.
The start of a new school year is always filled with anticipation. Teachers hope for engaged students who want to attain success. Students set personal goals and often hope that this year will be better than last year. Parents want their children to try hard, do well, and they want their children’s teachers to be supportive and offer a safe learning space. The new school year is often filled with hope.
However, despite all the best intentions, at some point, the teacher will encounter a problem. Many problems can be resolved with the knowledge acquired through a teacher’s experience. Students may forget to bring a pencil to class, so you just keep a jar of sharpened pencils on your desk. Students who are English language learners struggle to read Shakespeare, so you provide them and all the other students with a link to the audio version of the play that they can listen to. These impromptu decisions have the potential to swiftly address the problem, thereby eliminating the need for further investigation.
But what is a teacher supposed to do if a problem persists over time? Some students are always late to class right after lunch. Some students never raise their hand to participate in a class discussion. Some students don’t effectively edit their work prior to handing it in. How can a teacher work to identify strategies that can solve these persistent classroom problems? This is where teacher inquiry becomes a valuable tool.
As Marilyn Cochran-Smith and Susan L. Lytle discuss in their book Inquiry as Stance: Practitioner Research for the Next Generation , teacher inquiry is a process of questioning, exploring, and implementing strategies to address persistent classroom challenges. It mirrors the active learning process we encourage in students and can transform recurring problems into opportunities for growth. Most important, it also creates space for students to share their voices and perspectives—allowing them to play a role in guiding the changes that are implemented in the classroom.
Identify the problem. Begin by clearly defining the issue. For example, if students are frequently late after lunch, consider this as your inquiry focus.
Gather action information. Before rushing to solutions, gather insights from blogs, research, books, or colleagues. For instance, if the problem is tardiness, you might explore strategies like greeting students at the door or starting the class with a high-energy, collaborative activity that is engaging for students .
Frame your inquiry question. Craft a focused question using the format: What impact does X have on Y? Here X is the planned intervention, and Y is the behavior.
This approach shifts the perspective from seeing students as the problem to exploring solutions to unwanted behaviors. Rather than saying, “Students are always late to class right after lunch,” we can ask, “What impact does an engaging collaborative activity at the start of class have on students’ punctuality?”
Plan data collection. Before implementing your strategy, decide how you’ll measure its effectiveness. This could involve the following:
Quantitative data: Use attendance records, test scores, or quick surveys—whether digital or paper-based—to track student engagement. For example, monitor the number of students arriving on time before and after you start greeting them. Choose the survey method that best fits your classroom’s needs, whether it’s a digital link or QR code for students with technology, or a paper survey for those without.
Qualitative data: Collect student feedback through informal interviews or reflective journals to understand their experiences.
Mixed methods: You can collect a combination of quantitative and qualitative data to allow for quick, easy-to-read facts (quantitative) with an understanding of the why (qualitative) for the data.
Tip: To avoid overwhelming yourself, use data that you’re already collecting and analyze it with your inquiry question in mind.
Implement the strategy. Start with a small, manageable change. If you’re trying to improve punctuality, greet students at the door for a week and note any changes.
Analyze the data . Review your collected data to see if there’s a noticeable effect. Did more students arrive on time? If you used a survey, what do the results indicate about students’ attitudes?
Reflect on the outcome. If the strategy worked, consider how it can be sustained or adapted for other challenges. If it didn’t, reflect on why. Did the strategy need more time, or should a different approach be tried?
Example: If greeting students didn’t improve punctuality, consider if greeting needs to be combined with another intervention, like a change in seating arrangements or communicating with students’ families to remind them about the importance of punctuality.
Not all inquiries lead to success, and that’s OK. If your initial strategy doesn’t yield the desired results, reflect on the process.
Adopt the same growth mindset you encourage in your students in order to view setbacks as learning opportunities . Inquiry is a cycle of continuous improvement, not a onetime fix.
Inquiry empowers teachers to approach challenges with curiosity and adaptability. By framing problems as opportunities to learn, gathering and analyzing data, and reflecting on outcomes, teachers model the persistence and growth mindset we aim to instill in our students. Even when results aren’t immediate, the process fosters a culture of continuous learning and improvement, benefiting teachers and students alike.
When ChatGPT and other large language models began entering the mainstream two years ago, it quickly became apparent the technology could excel at certain business functions, yet it was less clear how well artificial intelligence could handle more creative tasks.
Sure, generative AI can summarize the content of an article, identify patterns in data, and produce derivative work—say, a song in the style of Taylor Swift or a poem in the mood of Langston Hughes—but can the technology develop truly innovative ideas?
Specifically, Harvard Business School Assistant Professor Jacqueline Ng Lane was determined to find out “how AI handled open-ended problems that haven’t been solved yet—the kind where you need diverse expertise and perspectives to make progress.”
In a working paper published in the journal Organization Science , Lane and colleagues compare ChatGPT’s creative potential to crowdsourced innovations produced by people. Ultimately, the researchers found that both humans and AI have their strengths—people contribute more novel suggestions while AI creates more practical solutions—yet some of the most promising ideas are the ones people and machines develop together.
Lane cowrote the paper with Léonard Bouissioux, assistant professor at the University of Washington’s Foster School of Business; Miaomiao Zhang, an HBS doctoral student, Karim Lakhani, the Dorothy & Michael Hintze Professor of Business Administration at HBS; and Vladimir Jacimovic, CEO and founder of ContinuumLab.ai and executive fellow at HBS.
Any innovation process usually starts with brainstorming, says Lane, whose research has long looked at how creative ideas are produced.
“You start with defining the problem, then you generate ideas, then you evaluate them and choose which ones to implement.”
“It’s like a funnel,” she says. “You start with defining the problem, then you generate ideas, then you evaluate them and choose which ones to implement.”
Research has shown that crowdsourcing can be an effective way to generate initial ideas. However, the approach can be time-consuming and expensive. Creative teams typically offer incentives to respondents for their ideas. Then teams often must wait for input and then comb through ideas to come up with the most promising leads.
An off-the-shelf large language model such as ChatGPT, however, is free or low cost for end users, and can generate an infinite number of ideas quickly, Lane says. But are the ideas any good?
To find out, Lane and her fellow researchers asked people to come up with business ideas for the sustainable circular economy, in which products are reused or recycled to make new products. They disseminated a request on an online platform, offering $10 for participating and $1,000 for the best idea. Here’s part of their request:
We would like you to submit your circular economy idea, which can be a unique new idea or an existent idea that is used in the industry.
Here is an example: Car sharing in order to reduce the carbon footprint associated with driving. …
Submit your real-life use cases on how companies can implement the circular economy in their businesses. New ideas are also welcome, even if they are “moonshots.”
The researchers asked for ideas that would involve “sharing, leasing, reusing, repairing, refurbishing [or] recycling existing materials and products as long as possible.” Suggestions would be scored for uniqueness, environmental benefits, profit potential, and feasibility.
Some 125 people replied with contributions, offering insights from a variety of industries and professional backgrounds. One, for example, proposed a dynamic pricing algorithm for supermarkets to cut down on food waste, while another suggested a mobile app that could store receipts to reduce paper waste.
At the same time, the research team employed prompt engineering techniques to craft a variety of AI prompts. Using these carefully designed prompts, they generated several hundred additional solutions through ChatGPT. The team strategically modified their prompts to:
The team then recruited some 300 evaluators well-versed in the circular economy to evaluate a randomized selection of the ideas based on the scoring criteria.
The evaluators judged the human solutions as more novel, employing more unique “out of the box” thinking. However, they found the AI-generated ideas to be more valuable and feasible.
For example, one participant from Africa proposed creating interlocking bricks using foundry dust and waste plastic, creating a new construction material and cutting down on air pollution at the same time. “The evaluators said, ‘Wow, this is really innovative, but it would never work,’” Lane says.
“We were surprised at how powerful these technologies were.”
One ChatGPT response, meanwhile, created an idea to convert food waste into biogas, a renewable energy source that could be used for electricity and fertilizer. Not the most novel idea, the researchers noted, but one that could be implemented and might show a clear financial return.
“We were surprised at how powerful these technologies were,” Lane says, “especially in these early stages in the creative process.”
The “best” ideas, Lane says, may come from those in which humans and AI collaborate, with people engineering prompts and continually working with AI to develop more original ideas.
“We consistently achieved higher quality results when AI would come up with an idea and then we had an instruction that said: Make sure before you create your next idea, it’s different from all the ones before it,” Lane explains.
Additional prompts increased the novelty of the ideas, generating everything from waste-eating African flies to beverage containers tracked by smart chips that instantly pay consumers for recycling them.
Based on the findings, the researchers suggest business leaders keep a few points in mind when implementing AI to develop creative solutions:
The most productive way to use generative AI, the research suggests, is to combine the novelty that people excel at with the practicality of the machine. Says Lane, “We still need to put our minds toward being forward-looking and envisioning new things as we are guiding the outputs of AI to create the best solutions.”
How transparency sped innovation in a $13 billion wireless sector.
Facility location-related decision problems pose a significant challenge for managers due to the multiple and conflicting factors involved. Moreover, incorrect decisions can lead to substantial impacts on companies' long-term strategic planning, resulting in losses for the business. This paper deals with a facility location problem in the educational sector in the northeast region of Brazil, which concerns the definition of the best location to place a private sector technical school, considering multiple objectives throughout a multicriteria approach. The decision-making process is structured based on a 9-step multicriteria model, and the preference elicitation phase is aided by the Flexible and Interactive Tradeoff (FITradeoff) method, using partial information provided by the decision-maker (DM). In the application presented in this paper, preference modeling is conducted considering the combination of two preference elicitation paradigms in the FITradeoff decision process: elicitation by decomposition and holistic evaluations, throughout a flexible approach. The DM’s preferences are elicited interactively, by means of a Decision Support System (DSS). At each interaction, the information given by the DM acts as constraints for a linear programming problem (LPP) model, which is computed in order to verify the potential optimality of each alternative. At the end of the elicitation process, a sensitivity analysis is performed so as to verify the robustness of the results obtained. Insights on the preference modeling paradigms combination with potential advantages for the decision process are also discussed in this paper.
Keywords: facility location; technical school location problem; multicriteria decision-making; preference modeling; FITradeoff method
Over the last decade, the demand for technical courses in Brazil has grown greatly, especially from the private sector. This is explained by the economic difficulties that the country has been facing in recent last years: in times of economic crisis, when the unemployment rate grows, people look for complementary courses that add to their qualifications, and thus technical and professional courses are seen as good targets. According to UNESCO (2018 UNESCO. 2018. Educação e formação técnica e profissional no Brasil. Available at: Available at: http://www.unesco.org/new/pt/brasilia/education/educational-quality/technical-and-vocational-education/ . accessed on August 27, 2018. http://www.unesco.org/new/pt/brasilia/ed... ), technical and professional education in Brazil needs to be expanded in order to prepare young people for entry into the labor market. In this context, the problem addressed here concerns the location of a branch of a technical school franchise, in a city in the northeast region of Brazil.
Decision-making concerning the location of facilities is not an easy task because wrong decisions can have severe impacts on the long-term strategic planning of the company and consequently may lead to incurring losses ( Pizzolato et al., 2004 PIZZOLATO ND, BARCELOS FB & NOGUEIRA LORENA LA. 2004. School location methodology in urban areas of developing countries. International Transactions in Operational Research , 11(6): 667-681. ). Besides that, decisions about the location of facilities have a high impact on the efficiency of the system in which the facility is involved ( Pludow et al., 2022 PLUDOW BA, MURRAY AT & CHURCH RL. 2022. Service quality modeling to support optimizing facility location in a microscale environment. Socio-Economic Planning Sciences , 82: 101273. ).
Studies applying Multicriteria Decision Making-Aiding techniques to solve facility location problems are commonly found in the literature, due to the inherent multifactorial nature of such problems. Farahani et al (2010 FARAHANI RZ, STEADIESEIFI M & ASGARI N. 2010. Multiple criteria facility location problems: A survey. Applied mathematical modelling, 34(7): 1689-1709. ) present a literature review on multicriteria facility location problems, highlighting those criteria that are most commonly used. The authors also draw attention to the main MCDM methods applied for solving facility location problems, including AHP, ELECTRE, MAUT, TOPSIS, and SMAA. Erkut et al (2008 ERKUT E, KARAGIANNIDIS A, PERKOULIDIS G & TJANDRA SA. 2008. A multicriteria facility location model for municipal solid waste management in North Greece. European Journal of Operational Research , 187(3): 1402-1421. ) present a multicriteria decision approach for addressing a solid waste management decision problem, using multiobjective linear programming (MOLP) and the Lexicographical minimax approach. Niyazi & Tavakkoli Mogghadam (2014 NIYAZI M & TAVAKKOLI-MOGHADDAM R. 2014. Solving a facility location problem by three multi-criteria decision making methods. International journal of research in industrial engineering, 3(4): 41-56. ) present three MCDM methods to solve a facility location problem: ARAS method, COPRAS method, and TOPSIS method; since the three methods recommend different rankings, the authors propose the REGIME method to find a final compromise solution. The FITradeoff multicriteria method has also been applied for solving facility location problems; Dell’Ovo et al (2017 DELL’OVO M, FREJ EA, OPPIO A, CAPOLONGO S, MORAIS DC & DE ALMEIDA AT. 2017. Multicriteria Decision Making for Healthcare Facilities Location with Visualization Based on FITradeoff Method. In: International Conference on Decision Support System Technology. p. 32-44. Cham: Springer . ) present an application of this method in the healthcare sector, and Sousa Ribeiro et al (2021 SOUSA RIBEIRO ML, PEIXOTO ROSELLI LR, ASFORA FREJ E, DE ALMEIDA A & COSTA MORAIS D. 2021. Using the FITradeoff method to solve a shopping mall location problem in the northeastern countryside of Brazil. Control & Cybernetics, 50(1). ) address the location of a shopping mall in Brazil.
The use of multicriteria methods and their Decision Support Systems (DSS) to address facility location problems is extensively explored in the chapters of Oppio et al (2020 OPPIO A, DELL’OVO M & CAPOLONGO S. 2020. Decision Support System for the Location of Healthcare Facilities: SitHealth Evaluation Tool. Springer Nature. ), but specifically to healthcare facility location problems. In the education section specifically, the work of Mayerle et al (2022 MAYERLE SF, RODRIGUES HF, FIGUEIREDO JN & CHIROLI DMDG. 2022. Optimal student/school/class/teacher/classroom matching to support efficient public school system resource allocation. Socio-Economic Planning Sciences, 83: 101341. ) presents a decision support methodology in the context of the public education sector, intending to improve the efficiency of the use of resources (including both human and infrastructure resources). This work, however, focuses on a specific real-life decision-making problem within the public sector. When it comes to education in the private sector, schools should be sited so that they attract the highest possible number of students. On the other hand, implementation costs should be as low as possible in order to maximize the profit margin of the unit. Therefore, this decision-making situation embraces several conflicting objectives that should be taken into consideration. Thus a multicriteria approach is developed here so as to structure and guide the decision-making process.
To the best of our knowledge, no previous work in the literature has addressed a private-sector technical school location problem through a multicriteria decision approach. The main contribution of this paper relies, therefore, on the construction of a structured multicriteria decision model to address a technical school location problem, considering a specific practical real-life case in the state of Piauí, in the Northeast region of Brazil.
A 9-step decision model is put forward to aid the process of making decisions on the location of a private-sector technical school, considering multiple and conflicting criteria. A crucial step in decision models involving multiple criteria is the preference modeling phase of the Decision Maker (DM), to obtain a measurement of prioritization on the multiple criteria involved in the process. To address such a challenge, the FITradeoff method ( De Almeida et al., 2016 DE ALMEIDA AT, ALMEIDA JA, COSTA APCS & ALMEIDA-FILHO AT. 2016. A New Method for Elicitation of Criteria Weights in Additive Models: Flexible and Interactive Tradeoff. European Journal of Operational Research, 250(1): 179-191. ; Frej et al., 2019 FREJ EA, DE ALMEIDA AT & COSTA APCS. 2019. Using data visualization for ranking alternatives with partial information and interactive tradeoff elicitation. Operational Research, 19, 5: 909-931. ; De Almeida et al., 2021 DE ALMEIDA AT, FREJ EA & ROSELLI LRP. 2021. Combining holistic and decomposition paradigms in preference modeling with the flexibility of FITradeoff. Central European Journal of Operations Research, 29(1): 7-47. ) is applied in the preference modeling phase, in order to achieve the best solution for the problem with not much effort spent from the DM, since it works based on partial information about the DMs’ preferences. This method has an innovative perspective, combining, in its structure, two paradigms of preference modeling: the classical elicitation by decomposition and holistic evaluations ( De Almeida et al., 2021 DE ALMEIDA AT, FREJ EA & ROSELLI LRP. 2021. Combining holistic and decomposition paradigms in preference modeling with the flexibility of FITradeoff. Central European Journal of Operations Research, 29(1): 7-47. ). This is a key flexibility feature of the method, which can fasten the decision process, saving time and effort from decision-makers.
The FITradeoff method has recently been applied in order to solve MCDM problems that have covered a wide variety of themes, including facility location ( Dell’Ovo et al. 2017 DELL’OVO M, FREJ EA, OPPIO A, CAPOLONGO S, MORAIS DC & DE ALMEIDA AT. 2017. Multicriteria Decision Making for Healthcare Facilities Location with Visualization Based on FITradeoff Method. In: International Conference on Decision Support System Technology. p. 32-44. Cham: Springer . ; Sousa Ribeiro et al., 2021 SOUSA RIBEIRO ML, PEIXOTO ROSELLI LR, ASFORA FREJ E, DE ALMEIDA A & COSTA MORAIS D. 2021. Using the FITradeoff method to solve a shopping mall location problem in the northeastern countryside of Brazil. Control & Cybernetics, 50(1). ). Table 1 presents an overview of some practical applications developed with the FITradeoff multicriteria method, demonstrating its high potential of use.
Thumbnail Table 1 Applications of the FITradeoff method.
The list presented in Table 1 is not intended to be exhaustive; it aims to illustrate the applicability potential of the FITradeoff method and therefore to enhance the motivation for using this method to address the facility location problem presented in this paper. De Almeida et al (2023 DE ALMEIDA AT, FREJ EA, ROSELLI LRP & COSTA APCS. 2023. A summary on fitrade-off method with methodological and practical developments and future perspectives. Pesquisa Operacional , 43: 268356. ) present an overview of all practical applications and methodological developments made with the FITradeoff method. Neuroscience studies have also been applied to investigate issues about the behavior of decision-makers when applying the FITradeoff method (Da Silva et al., 2022a SILVA ALCDL, CABRAL SEIXAS COSTA AP & DE ALMEIDA AT. 2022a. Analysis of the cognitive aspects of the preference elicitation process in the compensatory context: a neuroscience experiment with FITradeoff. International Transactions in Operational Research , v. 31. ; Roselli & De Almeida, 2021 ROSELLI LRP & DE ALMEIDA AT. 2021. The use of the success-based decision rule to support the holistic evaluation process in FITradeoff. International Transactions in Operational Research . ).
The problem addressed in this paper emerges in the context of a well-established network of technical schools in Brazil, which is seeking to place a new unit in the state of Piauí, in the northeast region of the country. This is a branch of the largest franchise business of technical education in the private sector in Brazil. Choosing the best location to place the school is an important decision that leads to several consequences in the long term. Hence, a structured analysis should be conducted considering the multiple and conflicting factors inherently involved in the problem. Considering this, the central research question addressed in this research is how to choose the best location for placing a private sector technical school considering all short-term and long-term consequences and by taking into account all conflicting objectives involved.
The main contribution of the present paper, therefore, relies, on solving a practical real-life decision-making problem of the educational sector in a developing country, based on the construction of a well-structured 9-step methodology. In the proposed model, we deeply explore a new feature of a well-known MCDM method, the FITradeoff method, with a view to its benefits and implications for the decision process. We also show that improvements in the performance of the method are achieved based on the integration of preference modeling paradigms, leading to time and effort saving of DMs.
This paper is organized as follows. Section 2 introduces the main concepts and the mathematical model of the FITradeoff method. Section 3 presents the decision model proposed for structuring the decision-making process, which is divided into three main phases: the preliminary phase, in which the main elements of the MCDM problem are defined; the preference modeling phase, in which the FITradeoff method is applied for eliciting the DM’s preferences; and the finalization phase, in which a sensitivity analysis is performed and the final recommendation is made. Finally, Section 4 discusses the results obtained and presents the main conclusions.
Preference modeling is a critical issue in MCDM/A methods. This is because the elicitation of preferences can be a hard task for DMs, depending on the amount of preferential information required in the process to find a solution ( Kirkwood and Sarin 1985 KIRKWOOD CW & SARIN RK. 1985. Ranking with partial information: A method and an application. Operations Research, 33(1): 38-48. ; Kirkwood and Corner 1993 KIRKWOOD CW & CORNER JL. 1993. The effectiveness of partial information about attribute weights for ranking alternatives in multiattribute decision making. Organizational Behavior and Human Decision Processes, 54(3): 456-476. ; Athanassopoulos and Podinovki 1997 ATHANASSOPOULOS AD & PODINOVSKI VV. 1997. Dominance and potential optimality in multiple criteria decision analysis with imprecise information. Journal of the Operational Research Society, 48(2): 142-150. ). In order to reduce the cognitive effort demanded of DMs, several authors have proposed multicriteria decision-making (MCDM) methods for dealing with partial/incomplete/imprecise information about DMs’ preferences ( Park and Kim 1997 PARK KS & KIM SH. 1997. Tools for interactive multiattribute decision-making with incompletely identified information. European Journal of Operational Research, 98(1): 111-123. ; Malakooti 2000 MALAKOOTI B. 2000. Ranking and screening multiple criteria alternatives with partial information and use of ordinal and cardinal strength of preferences. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 30(3): 355-368. ; Salo and Hamalainen 2001 SALO AA & HAMALAINEN RP. 2001. Preference ratios in multiattribute evaluation (PRIME)elicitation and decision procedures under incomplete information. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans , 31(6): 533-545. ; Cook and Kress 2002 COOK WD & KRESS M. 2002. A linear value function in mixed MCDM problems with incomplete preference data: An extreme point approach. INFOR: Information Systems and Operational Research, 40(4): 331-346. ; Mustajóki et al. 2005 MUSTAJOKI J, HÄMÄLÄINEN RP & SALO A. 2005. Decision support by interval SMART/SWING incorporating imprecision in the SMART and SWING methods. Decision Sciences, 36(2): 317-339. ; Salo and Punkka 2005 SALO AA & PUNKKA A. 2005. Rank inclusion in criteria hierarchies. European Journal of Operational Research, 163(2): 338-356. ; Sarabando and Dias 2010 SARABANDO P & DIAS LC. 2010. Simple procedures of choice in multicriteria problems without precise information about the alternatives’ values. Computers & Operations Research , 37(12): 2239-2247. ; Danielson et al. 2014 DANIELSON M, EKENBERG L & HE Y. 2014. Augmenting ordinal methods of attribute weight approximation. Decision Analysis, 11(1): 21-26. ). The Flexible and Interactive Tradeoff (FITradeoff) method ( de Almeida et al. 2016 DE ALMEIDA AT, ALMEIDA JA, COSTA APCS & ALMEIDA-FILHO AT. 2016. A New Method for Elicitation of Criteria Weights in Additive Models: Flexible and Interactive Tradeoff. European Journal of Operational Research, 250(1): 179-191. ; De Almeida et al., 2021 DE ALMEIDA AT, FREJ EA & ROSELLI LRP. 2021. Combining holistic and decomposition paradigms in preference modeling with the flexibility of FITradeoff. Central European Journal of Operations Research, 29(1): 7-47. ) was created in this context based on the entire axiomatic foundation of the traditional tradeoff procedure ( Keeney and Raiffa 1976 KEENEY RL & RAIFFA H. 1976. Decision analysis with multiple conflicting objectives. New York: Wiley & Sons. ), but improving its applicability for the DM by using a flexible process which asks less cognitively demanding elicitation questions. The computation of potentially optimal alternatives is conducted by linear programming, and graphical visualization of partial results is available for the DM at any step during the elicitation process. According to a literature review of partial information methods conducted by Da Silva et al. (2022b SILVA LBL, FREJ EA, DE ALMEIDA AT, FERREIRA RJP & MORAIS DC. 2022b. A review of partial information in additive multicriteria methods. IMA Journal of Management Mathematics. ), the FITradeoff method differs from other partial information methods in the literature due to the way in which the elicitation process is carried out: in a flexible manner, interactively, and with a structured protocol based on tradeoffs.
Solving multicriteria decision problems when the DM has a compensatory rationality leads to the use of unique criterion of synthesis methods ( de Almeida et al. 2015 DE ALMEIDA AT, CAVALCANTE CAV, ALENCAR MH, FERREIRA RJP, ALMEIDA-FILHO AT & GARCEZ TV. 2015. Multicriteria and Multi-objective Models for Risk, Reliability and Maintenance Decision Analysis . vol. 231 of International Series in Operations Research & Management Science. New York: Springer. ), which work based on value/utility functions for aggregating criteria. Within the scope of Multiattribute Value Theory (MAVT - Keeney and Raiffa 1976 KEENEY RL & RAIFFA H. 1976. Decision analysis with multiple conflicting objectives. New York: Wiley & Sons. ), alternatives are scored straightforwardly according to an additive aggregation function of the criteria (1). Each alternative has a global value v ( A j ), which is computed by the weighted sum of the n criteria scaling constants - or weights - w i and the consequence value of alternative A j in criterion i , v i ( x i j ), normalized in a 0-1 scale. The values of the scaling constants w i are also normalized, according to (2).
v A j = ∑ i = 1 n w i v i x i j (1)
∑ i = 1 n w i = 1 (2)
A critical issue related to additive aggregation models is the establishment of criteria scaling constants w i . Traditional utility/value methods that work based on complete information usually ask DMs to provide precisely detailed information about their preferences, which is a hard, cognitively demanding task ( Weber 1987 WEBER M. 1987. Decision making with incomplete information. European Journal of Operational Research, 28(1): 44-57. ). This leads to a tedious and time-consuming elicitation process, which DMs are not always willing to undergo ( Salo and Hamalainen 1992 SALO AA & HÄMÄLÄ INEN RP. 1992. Preference assessment by imprecise ratio statements. Operations Research, 40(6): 1053-1061. ; Belton and Stewart 2002 BELTON V & STEWART T. 2002. Multiple criteria decision analysis: an integrated approach. Springer Science & Business Media. ). In this context, the Flexible and Interactive Tradeoff (FITradeoff) method ( de Almeida et al. 2016 DE ALMEIDA AT, ALMEIDA JA, COSTA APCS & ALMEIDA-FILHO AT. 2016. A New Method for Elicitation of Criteria Weights in Additive Models: Flexible and Interactive Tradeoff. European Journal of Operational Research, 250(1): 179-191. ) was developed so as to facilitate the decision-making process for DMs, while keeping the entire axiomatic structure of MAVT. The FITradeoff method is suitable for solving problems in the scope of the choice problematic ( De Almeida et al., 2016 DE ALMEIDA AT, ALMEIDA JA, COSTA APCS & ALMEIDA-FILHO AT. 2016. A New Method for Elicitation of Criteria Weights in Additive Models: Flexible and Interactive Tradeoff. European Journal of Operational Research, 250(1): 179-191. ), ranking problematic ( Frej et al., 2019 FREJ EA, DE ALMEIDA AT & COSTA APCS. 2019. Using data visualization for ranking alternatives with partial information and interactive tradeoff elicitation. Operational Research, 19, 5: 909-931. ); sorting problematic ( Kang et al., 2020 KANG THA, FREJ EA & DE ALMEIDA AT. 2020. Flexible and interactive tradeoff elicitation for multicriteria sorting problems. Asia Pacific Journal of Operational Research , 37: 2050020. ) and portfolio problematic ( Frej et al., 2021 FREJ EA, EKEL P & DE ALMEIDA AT. 2021. A benefit-to-cost ratio based approach for portfolio selection under multiple criteria with incomplete preference information. Information Sciences, 545: 487-498. ; Marques et al., 2022 MARQUES AC, FREJ EA & DE ALMEIDA AT. 2022. Multicriteria decision support for project portfolio selection with the FITradeoff method. Omega, 111: 102661. )
FITradeoff works with partial information about the DMs’ preferences. The elicitation process is easier due to the amount and kind of information required. Throughout an interactive process, the two paradigms of preference modeling, elicitation by decomposition and holistic evaluations, are combined within the FITradeoff decision process ( De Almeida et al., 2021 DE ALMEIDA AT, FREJ EA & ROSELLI LRP. 2021. Combining holistic and decomposition paradigms in preference modeling with the flexibility of FITradeoff. Central European Journal of Operations Research, 29(1): 7-47. ). In the elicitation by decomposition, which is conducted based on the classical tradeoff procedure, the DMs are asked to state their preference regarding two consequences at each interaction, considering tradeoffs amongst criteria. This is an advantage if compared to the traditional tradeoff procedure ( Keeney and Raiffa 1976 KEENEY RL & RAIFFA H. 1976. Decision analysis with multiple conflicting objectives. New York: Wiley & Sons. ), in which the DM has to identify the exact indifference point which makes two consequences indifferent to each other. Holistic evaluations, however, consist of comparisons between elements in the alternatives space, instead of the consequences space. In the choice problematic, the DM has two possibilities: select the best alternative among a subset of potentially optimal alternatives, or eliminate the worst alternative among a subset of them. This analysis is conducted with the help of graphical visualization tools provided in the FITradeoff Decision Support System. A key flexibility feature of this method is the possibility to alternate between these two types of preference modeling, in accordance with the DM’s wishes and desires ( De Almeida et al., 2021 DE ALMEIDA AT, FREJ EA & ROSELLI LRP. 2021. Combining holistic and decomposition paradigms in preference modeling with the flexibility of FITradeoff. Central European Journal of Operations Research, 29(1): 7-47. ).
Another benefit of this method is that the DMs give as much information as they are willing to because the elicitation process can be interrupted at any time, namely, whenever the DM thinks that the partial result provided is already enough for his/her purposes.
The FITradeoff method is operated by means of an interactive Decision Support System (DSS). After an intracriteria evaluation is performed, the DM conducts the ranking criteria weights. The DM can choose to conduct this process through an overall evaluation of the criteria or by making pairwise comparisons between consequences. As a result of this preliminary step, the inequalities in (3) are obtained.
w 1 ≥ w 2 ≥ … ≥ w i ≥ w i + 1 ≥ … ≥ w n (3)
Thereafter, the DM chooses how he/she wants to continue the elicitation process: elicitation by decomposition or holistic evaluation. In the elicitation by decomposition, pairs of consequences are presented to the DM. He/she has to choose which one is more valuable for him/her, by considering tradeoffs amongst adjacent criteria. For instance, let us assume that consequences F 1A and F 2 are put to the DM (see Figure 1 ). F 1A presents the worst possible outcome W for all criteria, except for criterion i , which has an intermediate outcome X i U . F 2 presents the worst possible outcome W for all criteria, except for criterion i + 1, which has the best possible outcome B i+1 .
If the DM prefers F 1A over F 2 , then the global value of F 1A according to (1) is greater than the global value of F 2 , and thus (4) is obtained. Now, let us assume that the DM is asked to compare F 1B and F 2 . F 1B is similar to F 1A , but the outcome of criterion i is set to X i L < X i U , in such a way that now F 2 is preferred over F 1B , and (5) is obtained.
w i v i X i U > w i + 1 (4)
w i v i X i L > w i + 1 (5)
Inequalities (2 - 5) act as constraints for a linear programming problem model that runs for each alternative at each interaction cycle, in order to verify if this alternative is potentially optimal for the problem, i.e., if this alternative can be optimal for at least one vector of weights within the weight space formed by inequalities (2 - 5). The objective function of the LPP model is to maximize the global value of alternative A j in (1), and, in order to verify the possible potential optimality of A j , the inequalities in (6) also act as constraints for this LPP model.
∑ i = 1 n w i v i x i j ≥ ∑ i = 1 n w i v i x i k , k = 1 , … m ; k ≠ j (6)
If the global value (1) of alternative A j can be greater or equal to the global value of all other m − 1 alternatives A k , k = 1 , . . . m ; k ≠ j for at least one vector of weights within the weight space (2 5), than A j can be considered as a potentially optimal alternative for the problem.
As the DM gives additional preference information during the process with the comparison of more consequences, more inequalities of (4) and (5) are obtained, so that the weight space is updated. In addition to those inequalities, when a holistic evaluation is made by the DM, an inequality of type (7) is also included in the mathematical model, updating the weight space. Assuming that a holistic judgment is made by the DM, in which he/she declares preference for alternative a p over alternative a q ; hence, the inequality in (7) aims to guarantee that the global value of a p is greater than the global value of a q ( De Almeida et al., 2021 DE ALMEIDA AT, FREJ EA & ROSELLI LRP. 2021. Combining holistic and decomposition paradigms in preference modeling with the flexibility of FITradeoff. Central European Journal of Operations Research, 29(1): 7-47. ).
∑ i = 1 n w i v i x i p ≥ ∑ i = 1 n w i v i x i q (7)
Whenever there is an update in the weight space, the LPP models run again in order to find the refined set of potentially optimal alternatives. The process finishes if a unique alternative is found as potentially optimal; this is the optimal alternative to the problem. The DM, however, can stop the elicitation process before the end, if he/she thinks that the current subset of potentially optimal alternatives (POAs) is already sufficient for him/her to make a choice at that point, aided by the graphical visualization provided by the DSS. This will be illustrated in Section 3.2. The FITradeoff steps explained above are summarized in Figure 2 for a problem with an initial set of alternatives A 0 .
The application of this Multi-Criteria Decision-Aid (MCDA) method in order to help solve the problem of choosing the best location for a technical school is presented in the next section.
The MCDA problem addressed in this paper concerns the location of a technical school in the city of Teresina, the capital of the state of Piauí, in the northeast region of Brazil. This school is a branch of the largest Brazilian franchise business of technical education in the private sector, founded in 2011. There are schools in all the five regions of Brazil. In total, there are 28 units in full operation around the country. Moreover, there are 17 new schools under construction. The schools offer more than 20 technical courses, including nursing, radiology, clinical analysis, management, construction skills, electro-technology, and health and safety at work. The aim of the brand is to attract young people between 18 and 35 years old, who have completed high school, and whose monthly income is up to R$2.000 (around 460 American dollars).
The state of Piauí is the only state in the northeast region of Brazil whose capital does not have a branch of this school. The capital of this state, the city of Teresina, has a population of over 850 thousand inhabitants, which makes it attractive for the brand to locate its next branch there. Therefore, the franchise team has designated a franchisee to start the processes that will lead to the opening of a technical school in Teresina. This person has collected data about possible buildings in the city to set up the school. In this context, the decision problem here is to choose one of these buildings in which to locate the branch, by considering several factors that must be borne in mind when making such a long-term strategic decision.
The steps for solving the technical school location problem were defined based on the framework for resolving MCDM problems proposed by de Almeida et al. (2015 DE ALMEIDA AT, CAVALCANTE CAV, ALENCAR MH, FERREIRA RJP, ALMEIDA-FILHO AT & GARCEZ TV. 2015. Multicriteria and Multi-objective Models for Risk, Reliability and Maintenance Decision Analysis . vol. 231 of International Series in Operations Research & Management Science. New York: Springer. ), which is illustrated in Figure 3 . This model is divided into three main phases: the preliminary phase; the preference modeling phase and the finalization phase. Each of these phases is described in the following subsections for the context of the technical school location problem addressed here.
This preliminary phase consists basically of defining the main elements of the MCDM problem, which are: the DM and other actors who may exert influence on how the decision-making problem is tackled; defining the main objectives that the DM wants to achieve by solving this problem; defining the set of criteria, which derive from the objectives defined; defining the set of alternatives that will be evaluated with respect to those criteria; and, finally, choosing the most appropriate type of problematic: choice, ranking or sorting ( Roy 2005 ROY B. 2005. Paradigms and challenges. In: Multiple criteria decision analysis: state of the art surveys. p. 3-24. New York, NY: Springer. ).
The DM is the franchisee who was designated by the franchise to be responsible for the branch of Teresina. There are also other actors who exert influence on this process, such as the owner of the franchise, who acts as a specialist in this case, since he has extensive experience in locating facilities of this franchise all over Brazil. The entire decision-making process was aided by an analyst with a strong background in MCDM.
The main objectives involved in this decision are to have a school with as many registered students as possible, which has high visibility in the street and which the students can reach easily. There should also be services nearby. The owners want to maximize their profit margin, and thus the costs of refurbishing should be as low as possible, and the monthly rent should be at an affordable price. Moreover, as it is a long-term strategic decision, possible expansions of the school in the future also have to be considered. Therefore, another objective of this decision is to locate the school in an area in which it can grow. Based on these objectives, a total of 7 criteria were defined. These are described in detail in Table 2 .
Thumbnail Table 2 Description of the Criteria.
With regard to the alternatives to the problem, the DM contacted three realtors and talked with them about what he was expecting as to the characteristics of the building, which took into consideration all the criteria mentioned above. The realtors initially presented the DM with a list of 15 buildings. Table 3 presents the consequences matrix and shows the performance of these 15 alternatives evaluated with respect to the criteria.
Thumbnail Table 3 Consequence matrix with an initial set of alternatives.
The DM, however, noticed that, for 5 of these 15 alternatives, the value of the area is smaller than 1000m 2 (Buildings 3, 6, 7, 10, and 11). Therefore, these 5 alternatives are automatically eliminated from the decision process, because the criterion of area acts as a veto for this problem since buildings with an area below 1000m 2 do not allow for future expansions, as mentioned in Table 2 . Hence, the refined consequence matrix with the final set of alternatives with 10 buildings is presented in Table 4 .
Thumbnail Table 4 Consequence matrix with a final set of alternatives.
By analyzing Table 4 , it can be noticed that most buildings present a 0 on the ‘grace period’ criterion. One could wonder why not eliminate those buildings in a preliminary analysis, similar to what was conducted with buildings having less than 1000m 2 area. However, in this case, the DM is willing to accept buildings without a grace period, as long as they have good performances in other criteria since the analysis is conducted under a compensatory rationality, in which the DM considers tradeoffs between criteria, allowing a lower performance in one criterion to be compensated by higher performance in other criteria.
With the consequences matrix established, the last task of this preliminary phase is to identify the problematic of this MCDM problem. Given that, for the time being, the franchise wants to build only one school in the city, the choice problematic is the most adequate one for dealing with this problem.
The preference modeling phase was aided by the FITradeoff DSS. The first step of this phase is to rank the criteria scaling constants. The DSS gives the DM the option of making a holistic evaluation of the criteria or making a pairwise comparison. In this case, the DM chose to conduct a holistic evaluation. As a result, the following order was obtained:
w R e n t a l p r i c e ≥ w C o s t o f R e f u r b i s h m e n t ≥ w V i s i b i l i t y ≥ w A c c e s s i b i l i t y ≥ w G r a c e p e r i o d ≥ w a r e a ≥ w P r o x i m i t y t o s e r v i c e s
By following the steps in Figure 2 , the LPP model is run in order to define the set of potentially optimal alternatives at this stage. According to the simulation studies performed by Mendes et al (2020 MENDES JAJ, FREJ EA, DE ALMEIDA AT & ALMEIDA JA. 2020. Evaluation of Flexible and Interactive Tradeoff Method Based on Numerical Simulation Experiments. Pesquisa Operacional , v. 40: 1-25. ), the information on the ranking of criteria weights is sufficient to significantly reduce the set of potentially optimal alternatives.
After the ranking of criteria weights performed by the DM, of the 10 buildings considered in this evaluation, only four of them have been found to be potentially optimal alternatives for the problem: Buildings 1, 4, 12, 14. The DSS provides the DM with a graphical visualization of the alternatives in the POA subset, as shown in Figure 4 .
The bar graphs in Figure 4 show the performance of the alternatives in each criterion, normalized on a ratio scale of 0-1. Each color represents one potentially optimal alternative, and the criteria are ordered from left to right. The DM has the possibility, at this stage, to make a holistic evaluation of the set of potentially optimal alternatives, performing a direct comparison of these alternatives. Anderson and Dror (2001 ANDERSON RK & DROR M. 2001. An interactive graphic presentation for multiobjective linear programming. Applied Mathematics and Computation, 123(2): 229-248. ) discussed the use of graphics when making decisions, and Kasanen and Ostermark (1991 KASANEN E, OSTERMARK R & ZELENY M. 1991. Gestalt system of holistic graphics: New management support view of MCDM. Computers & Operations Research, 18(2): 233-239. ) make special mention of using these tools in a multicriteria decision-making/aiding process.
In this study, the DM’s opinion was that the graph in Figure 4 still had too much information, and he was not able to perform a holistic evaluation at that point. Thus, he decided to continue the elicitation process, and therefore the question-and-answer procedure for comparing consequences in FITradeoff started. After the first and second questions had been answered, nothing had changed in the POA subset. After the third question, however, Building 4 was eliminated from the process, and therefore, only three alternatives remained in the POA set, namely, Buildings 1, 12, and 14. Figure 5 shows the graphical visualization provided by the DSS at this point.
By analyzing Figure 5 , it can be seen that Buildings 1 and 14 are tied in three criteria with the best possible performance: visibility, accessibility, and proximity to services. However, Building 14 has 0 months of grace, which is a great disadvantage for this alternative. And Building 1 is worse than Building 12 in rental price - the most important criterion -, grace period and area, for both of which Building 12 has a great advantage. By following this point of view, the DM decided to perform a holistic evaluation at this point and chose to consider Building 12 as the best one. Hence, the elicitation process has finished with three elicitation questions being answered by the DM.
At this stage, however, the DM demonstrated curiosity about what would be the final result if he followed the elicitation by decomposition process until the end. Hence, the analyst continued the elicitation process with him, just to analyze how the results would be. After 10 more questions had been answered, Building 14 was eliminated, and so only Buildings 1 and 12 remained in the set of POAs. Finally, after the eleventh question had been answered, Building 12 was found as the optimal alternative for this problem, which is in accordance with the holistic judgment performed by the DM after the third question. In Table 5 , there is a summary of the application of FITradeoff, with all questions and answers of the DM for each interaction cycle.
Thumbnail Table 5 Summary of FITradeoff application.
The first column has the number of questions (or interaction cycle). Columns 2 and 3 show the two consequences that the DM was asked to compare, as explained in Section 2: Consequence A has the worst outcome for all criteria, except for the criterion specified in column 2, which has an intermediate value; and Consequence B has the worst outcome for all criteria, except for the criterion specified in column 3, which has the best possible outcome. Column 4 shows the answer given by the DM in each comparison, namely, it shows whether his preference was for Consequence A or Consequence B. The fifth column shows how many potentially optimal alternatives were found by the LPPs for that current level of partial information obtained, and in column six there are the alternatives that belong to the POA set (Building is abbreviated to B).
After achieving a final solution for the problem, FITradeoff DSS also offers the possibility of performing a sensitivity analysis of the values of the consequences matrix. Therefore, the DM may be asked to choose a criterion or several criteria and to decide to vary their values by a certain percentage. For the present problem, the DM has chosen to vary two criteria: cost of refurbishment and grace period. The cost of refurbishment is estimated based on the current state of the building. Thus, this will depend on what needs to be done in order to make the buildings ready to undertake the academic and administrative activities of the school in line with the relevant legislation and other requirements. However these values in Table 4 were estimated by a civil engineer who visited all the buildings that were originally suggested as possible alternatives. These, quite appropriately, were of an order of magnitude nature, and therefore, the estimates for refurbishing the building selected now need to attempt to take full account of the detailed refurbishments that must now begin to be specified. These are likely to change while the refurbishment is being undertaken, and therefore, the DM may choose to vary the estimates for the costs of refurbishment by ± 20%. As for the grace period, the DM considered that he could still persuade the owners of the buildings to lengthen the grace period. Hence, he chose to vary the values of this criterion in − 10%. A total of 10.000 instances were run in FITradeoff DSS, and the results are shown in Table 6 .
Thumbnail Table 6 Results of sensitivity analysis with 10.000 instances
On analyzing Table 6 , it can be concluded that the result obtained in the elicitation process - Building 12 - is quite robust because this alternative remained the optimal one in almost 70% of the cases when the values of the cost of refurbishment and the grace period are varied. Building 1 is the optimal alternative with the second highest percentage of occurrence, which is in line with the results of Table 5 , which shows that this alternative remained potentially optimal until the tenth cycle. Building 14 and Building 4 were also found to be the optimal alternatives in a few of the instances but not nearly enough to make either of them competitive with Buildings 1 and 12.
Another way to verify the robustness of the result obtained is to analyze the range of possible criteria weight values for which Building 12 remains the optimal alternative. FITradeoff DSS provides a graph (see Figure 6 ) that shows the range of possible weight values that match the preference statements given by the DM in the elicitation process and that would lead to Building 12 being chosen as the optimal alternative.
By following the steps of the framework in Figure 3 , the final recommendation to the DM is to proceed to the next steps for renting Building 12. This building has an excellent rental price, which is a fundamental factor for the DM. It also offers the best possible grace period and the greatest area, which allows the school to expand on-site. The main weakness of this alternative is the high cost of refurbishment, but, on the other hand, this is to some extent offset by the long grace period of rental. Similarly, the visibility of the building is not very good, since it is not located on the main avenue of the city, as was previously desired by the actors. As a consequence, the franchisee and his working team will have to think about other ways to publicize it and attract students.
As to implementing the decision, the expectation is that the negotiation process with the owner of the building will be concluded within the next two months, following which refurbishment should take around 8 to 10 months, after which the school will be ready to start its activities.
This paper presented a multicriteria decision model to solve a technical school location problem in a city in the northeast region of Brazil. A 9-step model was proposed, and the whole process was aided by an analyst with a strong background in MCDM. The franchise has designated a franchisee to make the final decision and to conduct operations in the new school. A set of 10 alternative buildings was evaluated with respect to 7 criteria, and the preference modeling was conducted with the flexible and interactive tradeoff method, supported by a Decision Support System.
In this application, the advantages of a combination of preference modeling paradigms could be observed. By performing a holistic evaluation in the middle of the process, the DM could have shortened the elicitation process. With only three elicitation questions answered (plus one holistic judgment), the DM was able to achieve an optimal solution for his problem. If the classical elicitation by decomposition was conducted until the end, a total of eleven elicitation questions would be necessary to find a final solution, which shows that incorporating holistic evaluations within the decision process makes it possible to shorten it, saving time and effort from decision makers. Future studies should, however, investigate deeper this phenomenon, i.e., how the incorporation of holistic evaluations in the decision process can reduce the amount of information provided by the DM when compared to the situation in which the classical elicitation by decomposition process is conducted from the beginning to the end. Simulation studies could be conducted in order to analyze the magnitude of the reduction in the number of elicitation questions when holistic evaluations are incorporated into the process.
The flexibility of the FITradeoff method allows the DM to alternate between these two types of preference elicitation, carrying the process in the way the DM feels more comfortable with. At the end of the process, Building 12 was shown to be quite a robust result according to the sensitivity analysis performed in FITradeoff DSS, and the DM was satisfied with the output of this application.
It is still possible to conduct a comparison with the classical tradeoff procedure, in terms of number of questions needed to find a solution. As a benchmarking for the number of questions answered in elicitation processes, we should remember what happens in the traditional tradeoff procedure. Considering that n is the number of criteria of the MCDM problem, the tradeoff procedure requires the DM to answer at least n − 1 questions, in order to build an equation system and thus find the values of the weights ( Keeney and Raiffa, 1976 KEENEY RL & RAIFFA H. 1976. Decision analysis with multiple conflicting objectives. New York: Wiley & Sons. ). However, in order to build these equations, the DM has to specify the exact points at which he/she is indifferent to two consequences. This information is much more difficult to provide, compared to the preference statements given when applying the FITradeoff method. Therefore, the ideal is to ask strict preference questions before reaching the indifference point ( de Almeida et al. 2016 DE ALMEIDA AT, ALMEIDA JA, COSTA APCS & ALMEIDA-FILHO AT. 2016. A New Method for Elicitation of Criteria Weights in Additive Models: Flexible and Interactive Tradeoff. European Journal of Operational Research, 250(1): 179-191. ), and thus the benchmarking for the number of questions would be 3( n − 1). For the problem of the technical school location addressed here, this would lead to 18 questions. Therefore, the 3 questions answered with the FITradeoff method resulted in the DM saving considerable time and effort compared to what the traditional tradeoff procedure would require, since he answered a smaller number of questions, which were also less cognitively demanding.
The number of questions necessary in FITradeoff to find a solution, however, is not a fixed value. It will depend on the data of the problem. The topology of the alternatives and also the distribution of criteria weights greatly influence this number. The closer the alternatives are to each other in terms of their performance, the higher the amount of information needed to choose only one of them as the optimal alternative, which consequently leads to the DM needing to answer a higher number of questions in the elicitation process. In order to avoid a tedious and very long process with many questions to be answered, the FITradeoff method provides flexibility features, such as the graphical visualization tool, which enables the DM to shorten the elicitation process. Another benefit of this method is that, during the elicitation process, the DM can also skip questions if he/she thinks that a question is too hard for him/her to answer. The FITradeoff DSS used in this application is available on request from the website http://www.fitradeoff.org.
To summarize, the originality of this work relied on solving a real-life decision problem of choosing the best location to place a technical school in the northeast region of Brazil, by proposing a structured decision model with the FITradeoff multicriteria method. The decision support provided to the franchisee with the model proposed in this paper was valuable in the sense that he could analyze several factors that have a high influence on the decision and were not previously considered for placing other units, stating his own tradeoffs between them. The preference modeling with the FITradeoff method is innovative when compared to other MCDM methods since it combines two preference modeling techniques in a flexible manner: decomposition elicitation and holistic judgments. MCDM methods in the literature usually work with one of those two types of preference elicitation ( De Almeida et al., 2021 DE ALMEIDA AT, FREJ EA & ROSELLI LRP. 2021. Combining holistic and decomposition paradigms in preference modeling with the flexibility of FITradeoff. Central European Journal of Operations Research, 29(1): 7-47. ), but FITradeoff combines both in a synergic manner, with the possibility of fastening the decision process. Moreover, it works with partial information about the DM's preferences, saving time and effort, and with a great potential to reduce inconsistencies during the process.
Please replace by The authors would like to acknowledge CNPq (grant numbers 312695/2020-9 and 311886/2022-1), FACEPE, and CAPES for the financial support for this research.
Figures | tables | formulas.
Application area | References |
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Logistics & Supply Chain | FREJ EA, ROSELLI LRP, ALMEIDA J & DE ALMEIDA AT. 2017. A Multicriteria Decision Model for Supplier Selection in a Food Industry Based on FITradeoff Method. Mathematical Problems in Engineering.); CYRENO MW, ROSELLI LRP & DE ALMEIDA AT. 2022. Using the FITradeoff Method for Solving a Truck Acquisition Problem at a Midsize Carrier. In: CABRAL SEIXAS COSTA AP, PAPATHANASIOU J, JAYAWICKRAMA U & KAMISSOKO D (Eds.), Decision Support Systems XII: Decision Support Addressing Modern Industry, Business, and Societal Needs. ICDSST 2022. Lecture Notes in Business Information Processing, vol. 447. Cham: Springer.), LUGO SR, B, ALMEIDA J & NISHINO N. 2023. A Circular Food Economy Multicriteria Decision Problem Based on the FITtradeoff Method. Pesquisa Operacional , 43(spe1): 263528.); CARVALHO RCLC, ROSELLI LRP & FIGUEIRA JR. 2023. Assigning priorities for raw material of a large pet food producer in the context of supply disruption. Pesquisa Operacional, 43(spe1): 263605.) |
Portfolio Selection | FREJ EA, EKEL P & DE ALMEIDA AT. 2021. A benefit-to-cost ratio based approach for portfolio selection under multiple criteria with incomplete preference information. Information Sciences, 545: 487-498.); MARQUES AC, FREJ EA & DE ALMEIDA AT. 2022. Multicriteria decision support for project portfolio selection with the FITradeoff method. Omega, 111: 102661.); CYRENO MW & ROSELLI LR. 2023. Application of the FITradeoff Method in a Portfolio Problem in the Context of Reverse Logistics for Wholesale. Pesquisa Operacional , 43(spe1): 263604.) |
Facility Location | DELL’OVO M, FREJ EA, OPPIO A, CAPOLONGO S, MORAIS DC & DE ALMEIDA AT. 2017. Multicriteria Decision Making for Healthcare Facilities Location with Visualization Based on FITradeoff Method. In: International Conference on Decision Support System Technology. p. 32-44. Cham: Springer .); SOUSA RIBEIRO ML, PEIXOTO ROSELLI LR, ASFORA FREJ E, DE ALMEIDA A & COSTA MORAIS D. 2021. Using the FITradeoff method to solve a shopping mall location problem in the northeastern countryside of Brazil. Control & Cybernetics, 50(1).) |
Agricultural Sector | RODRÍGUEZ JMM, FREJ EA, KANG THA & DE ALMEIDA AT. 2023. Outsourcing laboratory services from a Colombian agricultural research company using the FITradeoff method under multiple stakeholders analysis. Pesquisa Operacional , 43: 258518.); ÁLVAREZ CARRILLO PA, ROSELLI LRP, FREJ EA & DE ALMEIDA AT. 2018. Selecting na agricultural technology package based on the flexible and interactive tradeoff method. Annals of Operations Research, p. 1-16.) |
Energy Sector | FOSSILE DK, FREJ EA, COSTA SEG, LIMA EP & DE ALMEIDA AT. 2020. Selecting the most viable renewable energy source for Brazilian ports using the FITradeoff method. Journal of Cleaner Production, 260: 121107.); KANG THA, SOARES JÚNIOR AMC & DE ALMEIDA AT. 2018. Evaluating electric power generation technologies: A multicriteria analysis based on the FITradeoff method, Energy.) |
Technology Information Sector | GUSMÃO APH & MEDEIROS CP. 2016. A model for selecting a strategic information system using the FITradeoff. Mathematical Problems in Engineering, ID 7850960.) |
Production Management | PERGHER I, FREJ EA, ROSELLI LRP & DE ALMEIDA AT. 2020. Integrating simulation and FITradeoff method for scheduling rules selection in job-shop production systems. International Journal of Production Economics, 227: 107669.) |
Project Management | SANTOS AG, PESSOA LAMP, MOTA CMM & FREJ E. 2023. A fitradeoff-based approach for strategic decisions on military budget. Pesquisa Operacional , 43(spe1): 262789.) |
Industry 4.0 | FERREIRA D, GUSMÃO APH & ALMEIDA JA. 2024. A multicriteria model for assessing maturity in industry 4.0 context. Journal of Industrial Information Integration, 100579.) |
Tourism Management | CZEKAJSKI M, WACHOWICZ T & FREJ EA. 2023. Exploring the combination of holistic evaluation and elicitation by decomposition in FITradeoff: prioritizing cultural tourism products in Poland. Pesquisa Operacional , 43: 263454.) |
Negotiation Analysis | FREJ EA, MORAIS DC & DE ALMEIDA AT. 2022. Negotiation Support Through Interactive Dominance Relationship Specification. Group Decision And Negotiation.) |
Criteria | Description | Preference |
---|---|---|
The monthly cost of renting a building (R$). This value is a fixed cost that will be paid every month. It has a direct impact on the profit margin of the branch. | Minimize | |
Cost of refurbishing the building to make it ready for the school’s activities (R$). The lower this cost, the lower the payback time of this investment. | Minimize | |
Total area of the property (m ). The minimum desirable size for the area is 1000m ; otherwise, further expansions would not be possible. | Maximize | |
Related to the number of services nearby, such as hospitals and restaurants. These services are convenient for the students. This criterion is measured on a verbal scale from 1 to 3: 1there are no services nearby; 2 there are a few services nearby; 3 there are many services nearby. | Maximize | |
Related to the level of visibility of the location of the building. This is important because around 30% of the enrollments come from pedestrians passing by the school. This criterion is measured on a verbal scale from 1 to 5: 1very low visibility; 2 low visibility; 3 medium visibility; 4 high visibility; 5 very high visibility. | Maximize | |
This is the grace period on rental payment that the owners of some buildings offer the franchisee, measured in months. This criterion is important because the grace period directly impacts the total investment of the branch. | Maximize | |
Related to the facility of access for the students and teachers. Wide streets, bike paths, parking lots, and especially access by public transport are desirable. Around 90% of the students go to the school by public transport. This criterion is measured on a verbal scale from 1 to 5: 1very low accessibility; 2 low accessibility; 3 medium accessibility; 4 high accessibility; 5 very high accessibility. | Maximize |
Alternatives | Rental price (R$) | Cost of Re-furbishment (R$) | Area (m2) | Proximity to Services | Visibility | Grace period (months) | Accessibility |
---|---|---|---|---|---|---|---|
22000 | 450000 | 1080 | 3 | 5 | 6 | 5 | |
60000 | 350000 | 1770 | 3 | 5 | 0 | 5 | |
10000 | 1000000 | 3 | 5 | 12 | 5 | ||
14000 | 300000 | 1600 | 1 | 2 | 0 | 3 | |
40000 | 1000000 | 2000 | 2 | 3 | 3 | 2 | |
30000 | 800000 | 2 | 3 | 3 | 2 | ||
20000 | 500000 | 2 | 3 | 0 | 3 | ||
40000 | 500000 | 1500 | 3 | 4 | 3 | 4 | |
20000 | 700000 | 1075 | 2 | 3 | 0 | 3 | |
25000 | 350000 | 3 | 5 | 0 | 5 | ||
25000 | 800000 | 2 | 3 | 0 | 3 | ||
15000 | 450000 | 2500 | 2 | 4 | 12 | 4 | |
25000 | 100000 | 1000 | 1 | 1 | 0 | 3 | |
30000 | 200000 | 1600 | 3 | 5 | 0 | 5 | |
30000 | 100000 | 1000 | 2 | 2 | 0 | 3 |
Alternatives | Rental price (R$) | Cost of Refurbishment (R$) | Area (m2) | Proximity to Services | Visibility | Grace period (months) | Accessibility |
---|---|---|---|---|---|---|---|
22000 | 450000 | 1080 | 3 | 5 | 6 | 5 | |
60000 | 350000 | 1770 | 3 | 5 | 0 | 5 | |
14000 | 300000 | 1600 | 1 | 2 | 0 | 3 | |
40000 | 1000000 | 2000 | 2 | 3 | 3 | 2 | |
40000 | 500000 | 1500 | 3 | 4 | 3 | 4 | |
20000 | 700000 | 1075 | 2 | 3 | 0 | 3 | |
15000 | 450000 | 2500 | 2 | 4 | 12 | 4 | |
25000 | 100000 | 1000 | 1 | 1 | 0 | 3 | |
30000 | 200000 | 1600 | 3 | 5 | 0 | 5 | |
30000 | 100000 | 1000 | 2 | 2 | 0 | 3 |
Cycle | Consequence A | Consequence B: Best of | Answer | # P.O.A | P. O. A set |
---|---|---|---|---|---|
0 | ordering criteria scaling constants | 4 | B 1, B 4, B 12, B 14 | ||
1 | 37000 of Rental price (R$) | Proximity to Services | A | 4 | B 1, B 4, B 12, B 14 |
2 | 37000 of Rental price (R$) | Cost of Reform (R$) | B | 4 | B 1, B 4, B 12, B 14 |
3 | 550000 of Cost of Refurbishment (R$) | Visibility | B | 3 | B 1, B 12, B 14 |
4 | 3 of Visibility | Accessibility | A | 3 | B 1, B 12, B 14 |
5 | 3 of Accessibility | Grace period (months) | B | 3 | B 1, B 12, B 14 |
6 | 6 of Grace period (months) | Area (m ) | A | 3 | B 1, B 12, B 14 |
7 | 1750 of Area (m ) | Proximity to Services | A | 3 | B 1, B 12, B 14 |
8 | 25500 of Rental price (R$) | Cost of Reform (R$) | A | 3 | B 1, B 12, B 14 |
9 | 325000 of Cost of Refurbishment (R$) | Visibility | A | 3 | B 1, B 12, B 14 |
10 | 2 of Visibility | Accessibility | B | 2 | B 1, B 12 |
11 | 4 of Accessibility | Grace period (months) | B | 1 | B 12 |
Optimal alternative | % Occurrence |
---|---|
Building 12 | 69.57% |
Building 1 | 23.72% |
Building 14 | 6.7% |
Building 4 | 0.01% |
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Man united suffered a 2-1 defeat at brighton in their second premier league game of the new season with a familiar erik ten hag problem re-emerging.
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One major Manchester United issue reared its ugly head again during Saturday's 2-1 defeat at Brighton .
It's been a busy summer at Old Trafford with the arrival of three new defenders, Leny Yoro, Matthijs de Ligt and Noussair Mazraoui as well as a new striker in Joshua Zirkzee. Around £138million in transfer fees has been spent to strengthen Erik ten Hag 's squad as new sporting director Dan Ashworth looks to transform how the club buys and sells players.
It's too early to say whether Ashworth's work has had any effect and at least one more signing is set to be made before the window closes on August 30. Paris Saint-Germain's Manuel Ugarte has agreed personal terms with United and the Reds are now close to a breakthrough with PSG .
READ MORE: Chelsea star Cole Palmer backed to complete Man United transfer on one condition
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But one central problem remains which Ten Hag has yet to fix, two games into his third season at the club. United succumbed to defeat at the Amex Stadium from a late stoppage-time winner, scored by Brighton's Joao Pedro.
It followed the late equaliser scored by Bernardo Silva at Wembley in the Community Shield against Manchester City . United went on to lose that fixture as well, on penalties.
Since the start of Ten Hag's first season in charge back in 2022/23, United have lost more games to goals scored in the 90th minute or later than any other English top-flight side (six). It's a startling statistic considering that they had only lost two such matches in the first 30 Premier League campaigns combined.
And with another concentration lapse on Saturday costing United yet again, questions have to be asked of both the manager and players as to why this keeps happening. Is Ten Hag making the right substitutions to see out a close game? Are the players doing enough to stay switched on?
A combination of both is probably why this keeps happening. A lack of goals scored by United players is also a factor.
So many games won by Ten Hag's team have been by a single-goal margin. With so many United results on a knife edge, it's no wonder that wins so quickly turn into draws and draws turn into defeats.
It's an issue which another big summer of big spending hasn't solved. No one should panic at the club after one defeat and there were some positive signs.
However, Ten Hag won't take United far if he and the players continue to make poor decisions at the same major moments which cost United so many results. Improvement takes time but it will remain Groundhog Day at Old Trafford until United's major flaw is fixed.
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David Beckham, Roy Keane, Paul Scholes, Ryan Giggs – perhaps the finest midfield quartet in the history of the British game. Peter Schmeichel and Jaap Stam, two of the rocks at the back upon which the Treble triumph was built. The fab four up front - Andy Cole, Dwight Yorke, Teddy Sheringham, Ole Gunnar Solskjaer.
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Perhaps the data collection method wasn't effective, or the strategy needs more time to show results. ... Even if the strategy didn't solve the problem, what insights did you gain that could inform future inquiries? Adopt the same growth mindset you encourage in your students in order to view setbacks as learning opportunities. Inquiry is a ...
Generative AI easily handles a variety of business tasks, but can it develop creative solutions to problems? Yes, although some of the best ideas emerge when humans and AI work together, according to research by Jacqueline Ng Lane, Karim Lakhani, Miaomiao Zhang, and colleagues.
In this work, an efficient and stable exponential time difference method is presented for solving boundary layer problems. By combining exponential time difference schemes with spatial direct discontinuous Galerkin discretization based on exponential boundary layer approximations, the proposed algorithm not only may admit large time step sizes but also could provide good spatial approximations ...
The FITradeoff method is suitable for solving problems in the scope of the choice problematic (De Almeida et al., 2016 DE ALMEIDA AT, ALMEIDA JA, COSTA APCS & ALMEIDA-FILHO AT. 2016. A New Method for Elicitation of Criteria Weights in Additive Models: Flexible and Interactive Tradeoff. European Journal of Operational Research, 250(1): 179-191.
Manchester United have a major problem even £138m transfer splurge won't solve Man United suffered a 2-1 defeat at Brighton in their second Premier League game of the new season with a familiar ...