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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Categories Cognition
If you need to solve a problem, there are a number of different problem-solving strategies that can help you come up with an accurate decision. Sometimes the best choice is to use a step-by-step approach that leads to the right solution, but other problems may require a trial-and-error approach.
Some helpful problem-solving strategies include: Brainstorming Step-by-step algorithms Trial-and-error Working backward Heuristics Insight Writing it down Getting some sleep
Table of Contents
While you can always make a wild guess or pick at random, that certainly isn’t the most accurate way to come up with a solution. Using a more structured approach allows you to:
There are many tools and strategies that can be used to solve problems, and some problems may require more than one of these methods in order to come up with a solution.
The problem-solving strategy that works best depends on the nature of the problem and how much time you have available to make a choice. Here are eight different techniques that can help you solve whatever type of problem you might face.
Coming up with a lot of potential solutions can be beneficial, particularly early on in the process. You might brainstorm on your own, or enlist the help of others to get input that you might not have otherwise considered.
Also known as an algorithm, this approach involves following a predetermined formula that is guaranteed to produce the correct result. While this can be useful in some situations—such as solving a math problem—it is not always practical in every situation.
On the plus side, algorithms can be very accurate and reliable. Unfortunately, they can also be time-consuming.
And in some situations, you cannot follow this approach because you simply don’t have access to all of the information you would need to do so.
This problem-solving strategy involves trying a number of different solutions in order to figure out which one works best. This requires testing steps or more options to solve the problem or pick the right solution.
For example, if you are trying to perfect a recipe, you might have to experiment with varying amounts of a certain ingredient before you figure out which one you prefer.
On the plus side, trial-and-error can be a great problem-solving strategy in situations that require an individualized solution. However, this approach can be very time-consuming and costly.
This problem-solving strategy involves looking at the end result and working your way back through the chain of events. It can be a useful tool when you are trying to figure out what might have led to a particular outcome.
It can also be a beneficial way to play out how you will complete a task. For example, if you know you need to have a project done by a certain date, working backward can help you figure out the steps you’ll need to complete in order to successfully finish the project.
Heuristics are mental shortcuts that allow you to come up with solutions quite quickly. They are often based on past experiences that are then applied to other situations. They are, essentially, a handy rule of thumb.
For example, imagine a student is trying to pick classes for the next term. While they aren’t sure which classes they’ll enjoy the most, they know that they tend to prefer subjects that involve a lot of creativity. They utilize this heuristic to pick classes that involve art and creative writing.
The benefit of a heuristic is that it is a fast way to make fairly accurate decisions. The trade-off is that you give up some accuracy in order to gain speed and efficiency.
Sometimes, the solution to a problem seems to come out of nowhere. You might suddenly envision a solution after struggling with the problem for a while. Or you might abruptly recognize the correct solution that you hadn’t seen before.
No matter the source, insight-based problem-solving relies on following your gut instincts. While this may not be as objective or accurate as some other problem-solving strategies, it can be a great way to come up with creative, novel solutions.
Sometimes putting the problem and possible solutions down in paper can be a useful way to visualize solutions. Jot down whatever might help you envision your options. Draw a picture, create a mind map, or just write some notes to clarify your thoughts.
If you’re facing a big problem or trying to make an important decision, try getting a good night’s sleep before making a choice. Sleep plays an essential role in memory consolidation, so getting some rest may help you access the information or insight you need to make the best choice.
Even with an arsenal of problem-solving strategies at your disposal, coming up with solutions isn’t always easy. Certain challenges can make the process more difficult. A few issues that might emerge include:
Becoming a good problem solver can be useful in a variety of domains, from school to work to interpersonal relationships. Important problem-solving skills encompass being able to identify problems, coming up with effective solutions, and then implementing these solutions.
According to a 2023 survey by the National Association of Colleges and Employers, 61.4% of employers look for problem-solving skills on applicant resumes.
Some essential problem-solving skills include:
Solving a problem is complex and requires the ability to recognize the issue, collect and analyze relevant data, and make decisions about the best course of action. It can also involve asking others for input, communicating goals, and providing direction to others.
If you’re ready to strengthen your problem-solving abilities, here are some steps you can take:
Before you can practice your problem-solving skills, you need to be able to recognize that there is a problem. When you spot a potential issue, ask questions about when it started and what caused it.
Instead of jumping right in to finding solutions, do research to make sure you fully understand the problem and have all the background information you need. This helps ensure you don’t miss important details.
Consider signing up for a class or workshop focused on problem-solving skill development. There are also books that focus on different methods and approaches.
The best way to strengthen problem-solving strategies is to give yourself plenty of opportunities to practice. Look for new challenges that allow you to think critically, analytically, and creatively.
If you have a problem to solve, there are plenty of strategies that can help you make the right choice. The key is to pick the right one, but also stay flexible and willing to shift gears.
In many cases, you might find that you need more than one strategy to make the choices that are right for your life.
Brunet, J. F., McNeil, J., Doucet, É., & Forest, G. (2020). The association between REM sleep and decision-making: Supporting evidences. Physiology & Behavior , 225, 113109. https://doi.org/10.1016/j.physbeh.2020.113109
Chrysikou, E. G, Motyka, K., Nigro, C., Yang, S. I. , & Thompson-Schill, S. L. (2016). Functional fixedness in creative thinking tasks depends on stimulus modality. Psychol Aesthet Creat Arts , 10(4):425‐435. https://doi.org/10.1037/aca0000050
Sarathy, V. (2018). Real world problem-solving. Front Hum Neurosci , 12:261. https://doi.org/10.3389/fnhum.2018.00261
Problem-solving is a mental process that involves discovering, analyzing, and solving problems. The ultimate goal of problem-solving is to overcome obstacles and find a solution that best resolves the issue.
The best strategy for solving a problem depends largely on the unique situation. In some cases, people are better off learning everything they can about the issue and then using factual knowledge to come up with a solution. In other instances, creativity and insight are the best options.
It is not necessary to follow problem-solving steps sequentially, It is common to skip steps or even go back through steps multiple times until the desired solution is reached.
In order to correctly solve a problem, it is often important to follow a series of steps. Researchers sometimes refer to this as the problem-solving cycle. While this cycle is portrayed sequentially, people rarely follow a rigid series of steps to find a solution.
The following steps include developing strategies and organizing knowledge.
While it may seem like an obvious step, identifying the problem is not always as simple as it sounds. In some cases, people might mistakenly identify the wrong source of a problem, which will make attempts to solve it inefficient or even useless.
Some strategies that you might use to figure out the source of a problem include :
After the problem has been identified, it is important to fully define the problem so that it can be solved. You can define a problem by operationally defining each aspect of the problem and setting goals for what aspects of the problem you will address
At this point, you should focus on figuring out which aspects of the problems are facts and which are opinions. State the problem clearly and identify the scope of the solution.
After the problem has been identified, it is time to start brainstorming potential solutions. This step usually involves generating as many ideas as possible without judging their quality. Once several possibilities have been generated, they can be evaluated and narrowed down.
The next step is to develop a strategy to solve the problem. The approach used will vary depending upon the situation and the individual's unique preferences. Common problem-solving strategies include heuristics and algorithms.
Heuristics are often best used when time is of the essence, while algorithms are a better choice when a decision needs to be as accurate as possible.
Before coming up with a solution, you need to first organize the available information. What do you know about the problem? What do you not know? The more information that is available the better prepared you will be to come up with an accurate solution.
When approaching a problem, it is important to make sure that you have all the data you need. Making a decision without adequate information can lead to biased or inaccurate results.
Of course, we don't always have unlimited money, time, and other resources to solve a problem. Before you begin to solve a problem, you need to determine how high priority it is.
If it is an important problem, it is probably worth allocating more resources to solving it. If, however, it is a fairly unimportant problem, then you do not want to spend too much of your available resources on coming up with a solution.
At this stage, it is important to consider all of the factors that might affect the problem at hand. This includes looking at the available resources, deadlines that need to be met, and any possible risks involved in each solution. After careful evaluation, a decision can be made about which solution to pursue.
After selecting a problem-solving strategy, it is time to put the plan into action and see if it works. This step might involve trying out different solutions to see which one is the most effective.
It is also important to monitor the situation after implementing a solution to ensure that the problem has been solved and that no new problems have arisen as a result of the proposed solution.
Effective problem-solvers tend to monitor their progress as they work towards a solution. If they are not making good progress toward reaching their goal, they will reevaluate their approach or look for new strategies .
After a solution has been reached, it is important to evaluate the results to determine if it is the best possible solution to the problem. This evaluation might be immediate, such as checking the results of a math problem to ensure the answer is correct, or it can be delayed, such as evaluating the success of a therapy program after several months of treatment.
Once a problem has been solved, it is important to take some time to reflect on the process that was used and evaluate the results. This will help you to improve your problem-solving skills and become more efficient at solving future problems.
It is important to remember that there are many different problem-solving processes with different steps, and this is just one example. Problem-solving in real-world situations requires a great deal of resourcefulness, flexibility, resilience, and continuous interaction with the environment.
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You can become a better problem solving by:
It's important to communicate openly and honestly with your partner about what's going on. Try to see things from their perspective as well as your own. Work together to find a resolution that works for both of you. Be willing to compromise and accept that there may not be a perfect solution.
Take breaks if things are getting too heated, and come back to the problem when you feel calm and collected. Don't try to fix every problem on your own—consider asking a therapist or counselor for help and insight.
If you've tried everything and there doesn't seem to be a way to fix the problem, you may have to learn to accept it. This can be difficult, but try to focus on the positive aspects of your life and remember that every situation is temporary. Don't dwell on what's going wrong—instead, think about what's going right. Find support by talking to friends or family. Seek professional help if you're having trouble coping.
Davidson JE, Sternberg RJ, editors. The Psychology of Problem Solving . Cambridge University Press; 2003. doi:10.1017/CBO9780511615771
Sarathy V. Real world problem-solving . Front Hum Neurosci . 2018;12:261. Published 2018 Jun 26. doi:10.3389/fnhum.2018.00261
By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."
Do you want to be a better problem-solver? Explore the skills you need to become more effective and confident at improving things for the better.
Are you human? Then you face problems every day!
Whether you’re trying to figure out where to go to lunch with a group of friends who have varying dietary issues, or you can’t figure out why your customer management system at work keeps shutting down, your problems throughout your life will range from major to minor, and everything in between.
Do you want to be a better problem solver? It’s not too late to gain the skills you need to become more effective and confident at improving things for the better.
In this article, we’ll look at problem-solving, its importance, and ten tips and strategies to become a better problem-solver.
Problem-solving is the process of breaking down challenges to find solutions. Typically it is a four-stage process of 1) identifying an issue, 2) establishing a plan, 3) executing the plan, and 4) finding a resolution. However, problem-solving can begin before a problem even occurs. For example, crisis management includes pre-planning for situations that could arise.
Problem-solving is important because it allows people to evaluate a problem, seek greater understanding, develop execution plans, overcome obstacles, and ultimately find a resolution.
Those resolutions lead to many benefits, including:
Here are some examples of common problems.
In the workplace: One familiar workplace problem leaders deal with is the lack of employee engagement . With good problem-solving skills, you can determine the root cause, where there may be a lack of understanding, the steps required to improve engagement, and how to get others involved in solving the issue.
In a crisis: One crisis situation you might find yourself in is discovering your significant other has just been in a car accident. With good problem-solving skills, you can quickly assess the situation and identify steps to contact authorities, get them to a hospital within their insurance network, and sort out the insurance details while also balancing what to do about the family details at home.
In everyday life: An everyday life problem you might deal with is what you’re having for dinner! (Depending on your household, this can sometimes turn into a crisis, right?!) With good problem-solving skills, you can assess what you have on hand already, how much time you have, what others might prefer, who’s cooking, when you’ll eat, and make a decision.
The characteristics and qualities of a good problem solver include the ability to understand the issue, rally others together, and empower appropriate players to execute a solution.
To do this well, problem solvers often have a knack for these skills:
Let’s look at how good problem solvers put these skills into action!
Get clear about what the problem is.
If the problem you’re trying to solve involves multiple people—and most likely it does—it’s important to get clear about what the problem is before you start trying to solve it. People often go around in circles trying to solve a problem until they realize they weren’t on the same page from the start. It’s a time-waster!
To clarify the problem, start with clarifying questions:
After you get clarity, you may discover multiple problems on the table. If you come to this realization, solve one of them at a time.
Once you’re clear about the problem, start identifying your next steps and the goal to solve the problem. To do this, you’ll want to identify your ideal outcome and the method to reach that outcome.
For example, your problem, outcome, and method might look something like this:
Problem: Our sales team is upset that they don’t get enough sales leads from marketing.
Ideal outcome: Our marketing system and process generates enough leads to increase sales over the next year.
Method: Analyze what’s not working in the current system and reorganize or implement a new lead-generating system.
To help you set better goals as you solve problems, check out this helpful resource:
Do you set the same goals over and over again? If you’re not achieving your goals – it’s not your fault! Let me show you the science-based goal-setting framework to help you achieve your biggest goals.
Often, there needs to be more clarity and communication at the root of many problems. To identify where something went wrong and how to solve it, gather data with questions for everyone involved. Try keeping your questions open-ended to avoid the risk of sounding accusatory with closed-ended, yes or no questions. Allow people to process and explain how they understand the issue.
Some open-ended questions you can ask to start solving a problem include:
Bonus Tip: If you’re a leader, it is especially important not to limit your questions to fellow senior leaders, especially if the problem affects the organization or a wider group. Ask questions at all levels.
Often, in hierarchically structured organizations, the employees working in the everyday processes know the issues but may feel unsure about how to bring them up. Ask! But be sure not to shoot the messenger; reward them for their feedback and support.
When you’re presented with a problem, it’s best to take a beat to assess the situation before you react. That is unless you’re facing a life-threatening situation like a house fire, physical attack, or baseball heading straight for your head. For the sake of this article, we’ll stick to solving general problems, not life-threatening problems.
Common knee-jerk reactions include:
To avoid reacting or making a decision you’ll regret later, try a centering activity like:
No one is immune to problems. As much as you can, plan for potential problems down the road, even if you don’t think they’ll happen. You never know!
Generally, we like to think positively, but in this case, the question, “What’s the worst that can happen?” can help you prepare for all kinds of situations. This is where lessons from crisis management are beneficial in your problem-solving process.
In the readiness stage of crisis management, you’ll want to:
When you’re presented with a problem, your initial reaction may be to want to solve it as quickly as possible so that you can move past it and move on. However, when you get reactive to problems, you will more likely end up with bandaid solutions and even more issues down the road. Give yourself time to stay open to feedback and ideas as you investigate solutions.
To remain open, prime your brain to think objectively and creatively. There may be solutions in places you haven’t considered, even outside your industry or network.
Fun Bonus Tip: Ask a child what they would do! You might hear an outside-of-the-box idea you would never have come up with on your own. And while you may not use their idea, it could help get your juices flowing to come up with a solution!
Not all problems need to be solved by the leader. One of the most empowering things a leader can do is provide resources and space to allow people with the strengths and skills to do what needs to be done.
To identify the best players to solve the problem, ask yourself and others these questions:
Once you’ve identified the problem, figured out what needs to happen, and determined the best players to solve the problem, it’s time to create the execution plan and get started.
If you’re the leader, and you’ve determined who the best players are to solve the problem, it’s best to delegate the execution and resource them well. Micromanagement in this stage may create a whole new set of problems!
Chris McChesney identifies four disciplines of execution 1 https://pages.franklincovey.com/4d-landing-pages-execute-goals-create-breakthrough-results-guide-nw.html which include:
One thing that separates a good problem solver from an average one is that a good problem solver doesn’t ignore, run away from, deflect, or deny the problem exists. They face it head-on with humility and curiosity. You can do just that whether or not you have a leadership title.
“A leader is anyone who takes responsibility for finding the potential in people and processes and has the courage to develop that potential. Leadership is not about titles or the corner office. It’s about the willingness to step up, put yourself out there, and lean into courage.” –Brené Brown, Ph.D., MSW.
In Brené Brown’s book, Dare to Lead , she identifies four leadership skill sets of daring leaders:
Are you a courageous leader? Take Brené Brown’s Daring Leadership Assessment .
To be human is to have problems occasionally. But equipping yourself with problem-solving skills will make you far better off when they arise. Be good to your future self and train yourself to be ready with helpful resources and books, including:
In summary, take note of these tips to become a better problem solver:
For more support to become a better problem solver, check out our article How to Master Strategic Thinking Skills in 7 Simple Steps .
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Effective problem solving is all about using the right process and following a plan tailored to the issue at hand. Recognizing your team or organization has an issue isn’t enough to come up with effective problem solving strategies.
To truly understand a problem and develop appropriate solutions, you will want to follow a solid process, follow the necessary problem solving steps, and bring all of your problem solving skills to the table. We’ll forst look at what problem solving strategies you can employ with your team when looking for a way to approach the process. We’ll then discuss the problem solving skills you need to be more effective at solving problems, complete with an activity from the SessionLab library you can use to develop that skill in your team.
Let’s get to it!
What skills do i need to be an effective problem solver, how can i improve my problem solving skills.
Problem solving strategies are methods of approaching and facilitating the process of problem-solving with a set of techniques , actions, and processes. Different strategies are more effective if you are trying to solve broad problems such as achieving higher growth versus more focused problems like, how do we improve our customer onboarding process?
Broadly, the problem solving steps outlined above should be included in any problem solving strategy though choosing where to focus your time and what approaches should be taken is where they begin to differ. You might find that some strategies ask for the problem identification to be done prior to the session or that everything happens in the course of a one day workshop.
The key similarity is that all good problem solving strategies are structured and designed. Four hours of open discussion is never going to be as productive as a four-hour workshop designed to lead a group through a problem solving process.
Good problem solving strategies are tailored to the team, organization and problem you will be attempting to solve. Here are some example problem solving strategies you can learn from or use to get started.
Often, the first step to solving problems or organizational challenges is bringing a group together effectively. Most teams have the tools, knowledge, and expertise necessary to solve their challenges – they just need some guidance in how to use leverage those skills and a structure and format that allows people to focus their energies.
Facilitated workshops are one of the most effective ways of solving problems of any scale. By designing and planning your workshop carefully, you can tailor the approach and scope to best fit the needs of your team and organization.
Workshops are an effective strategy for solving problems. By using tried and test facilitation techniques and methods, you can design and deliver a workshop that is perfectly suited to the unique variables of your organization. You may only have the capacity for a half-day workshop and so need a problem solving process to match.
By using our session planner tool and importing methods from our library of 700+ facilitation techniques, you can create the right problem solving workshop for your team. It might be that you want to encourage creative thinking or look at things from a new angle to unblock your groups approach to problem solving. By tailoring your workshop design to the purpose, you can help ensure great results.
One of the main benefits of a workshop is the structured approach to problem solving. Not only does this mean that the workshop itself will be successful, but many of the methods and techniques will help your team improve their working processes outside of the workshop.
We believe that workshops are one of the best tools you can use to improve the way your team works together. Start with a problem solving workshop and then see what team building, culture or design workshops can do for your organization!
Great for:
By using design thinking principles and methods, a design sprint is a great way of identifying, prioritizing and prototyping solutions to long term challenges that can help solve major organizational problems with quick action and measurable results.
Some familiarity with design thinking is useful, though not integral, and this strategy can really help a team align if there is some discussion around which problems should be approached first.
The stage-based structure of the design sprint is also very useful for teams new to design thinking. The inspiration phase, where you look to competitors that have solved your problem, and the rapid prototyping and testing phases are great for introducing new concepts that will benefit a team in all their future work.
It can be common for teams to look inward for solutions and so looking to the market for solutions you can iterate on can be very productive. Instilling an agile prototyping and testing mindset can also be great when helping teams move forwards – generating and testing solutions quickly can help save time in the long run and is also pretty exciting!
Organizational challenges and problems are often complicated and large scale in nature. Sometimes, trying to resolve such an issue in one swoop is simply unachievable or overwhelming. Try breaking down such problems into smaller issues that you can work on step by step. You may not be able to solve the problem of churning customers off the bat, but you can work with your team to identify smaller effort but high impact elements and work on those first.
This problem solving strategy can help a team generate momentum, prioritize and get some easy wins. It’s also a great strategy to employ with teams who are just beginning to learn how to approach the problem solving process. If you want some insight into a way to employ this strategy, we recommend looking at our design sprint template below!
Some problems are best solved by introducing a major shift in perspective or by using new methodologies that encourage your team to think differently.
Props and tools such as Methodkit , which uses a card-based toolkit for facilitation, or Lego Serious Play can be great ways to engage your team and find an inclusive, democratic problem solving strategy. Remember that play and creativity are great tools for achieving change and whatever the challenge, engaging your participants can be very effective where other strategies may have failed.
LEGO Serious Play is a problem solving methodology designed to get participants thinking differently by using 3D models and kinesthetic learning styles. By physically building LEGO models based on questions and exercises, participants are encouraged to think outside of the box and create their own responses.
Collaborate LEGO Serious Play exercises are also used to encourage communication and build problem solving skills in a group. By using this problem solving process, you can often help different kinds of learners and personality types contribute and unblock organizational problems with creative thinking.
Problem solving strategies like LEGO Serious Play are super effective at helping a team solve more skills-based problems such as communication between teams or a lack of creative thinking. Some problems are not suited to LEGO Serious Play and require a different problem solving strategy.
Card decks and method kids are great tools for those new to facilitation or for whom facilitation is not the primary role. Card decks such as the emotional culture deck can be used for complete workshops and in many cases, can be used right out of the box. Methodkit has a variety of kits designed for scenarios ranging from personal development through to personas and global challenges so you can find the right deck for your particular needs.
Having an easy to use framework that encourages creativity or a new approach can take some of the friction or planning difficulties out of the workshop process and energize a team in any setting. Simplicity is the key with these methods. By ensuring everyone on your team can get involved and engage with the process as quickly as possible can really contribute to the success of your problem solving strategy.
Looking to peers, experts and external facilitators can be a great way of approaching the problem solving process. Your team may not have the necessary expertise, insights of experience to tackle some issues, or you might simply benefit from a fresh perspective. Some problems may require bringing together an entire team, and coaching managers or team members individually might be the right approach. Remember that not all problems are best resolved in the same manner.
If you’re a solo entrepreneur, peer groups, coaches and mentors can also be invaluable at not only solving specific business problems, but in providing a support network for resolving future challenges. One great approach is to join a Mastermind Group and link up with like-minded individuals and all grow together. Remember that however you approach the sourcing of external advice, do so thoughtfully, respectfully and honestly. Reciprocate where you can and prepare to be surprised by just how kind and helpful your peers can be!
Problem solving in large organizations with lots of skilled team members is one thing, but how about if you work for yourself or in a very small team without the capacity to get the most from a design sprint or LEGO Serious Play session?
A mastermind group – sometimes known as a peer advisory board – is where a group of people come together to support one another in their own goals, challenges, and businesses. Each participant comes to the group with their own purpose and the other members of the group will help them create solutions, brainstorm ideas, and support one another.
Mastermind groups are very effective in creating an energized, supportive atmosphere that can deliver meaningful results. Learning from peers from outside of your organization or industry can really help unlock new ways of thinking and drive growth. Access to the experience and skills of your peers can be invaluable in helping fill the gaps in your own ability, particularly in young companies.
A mastermind group is a great solution for solo entrepreneurs, small teams, or for organizations that feel that external expertise or fresh perspectives will be beneficial for them. It is worth noting that Mastermind groups are often only as good as the participants and what they can bring to the group. Participants need to be committed, engaged and understand how to work in this context.
Receiving advice from a business coach or building a mentor/mentee relationship can be an effective way of resolving certain challenges. The one-to-one format of most coaching and mentor relationships can really help solve the challenges those individuals are having and benefit the organization as a result.
A great mentor can be invaluable when it comes to spotting potential problems before they arise and coming to understand a mentee very well has a host of other business benefits. You might run an internal mentorship program to help develop your team’s problem solving skills and strategies or as part of a large learning and development program. External coaches can also be an important part of your problem solving strategy, filling skills gaps for your management team or helping with specific business issues.
Now we’ve explored the problem solving process and the steps you will want to go through in order to have an effective session, let’s look at the skills you and your team need to be more effective problem solvers.
Problem solving skills are highly sought after, whatever industry or team you work in. Organizations are keen to employ people who are able to approach problems thoughtfully and find strong, realistic solutions. Whether you are a facilitator , a team leader or a developer, being an effective problem solver is a skill you’ll want to develop.
Problem solving skills form a whole suite of techniques and approaches that an individual uses to not only identify problems but to discuss them productively before then developing appropriate solutions.
Here are some of the most important problem solving skills everyone from executives to junior staff members should learn. We’ve also included an activity or exercise from the SessionLab library that can help you and your team develop that skill.
If you’re running a workshop or training session to try and improve problem solving skills in your team, try using these methods to supercharge your process!
Active listening is one of the most important skills anyone who works with people can possess. In short, active listening is a technique used to not only better understand what is being said by an individual, but also to be more aware of the underlying message the speaker is trying to convey. When it comes to problem solving, active listening is integral for understanding the position of every participant and to clarify the challenges, ideas and solutions they bring to the table.
Some active listening skills include:
Active Listening #hyperisland #skills #active listening #remote-friendly This activity supports participants to reflect on a question and generate their own solutions using simple principles of active listening and peer coaching. It’s an excellent introduction to active listening but can also be used with groups that are already familiar with it. Participants work in groups of three and take turns being: “the subject”, the listener, and the observer.
All problem solving models require strong analytical skills, particularly during the beginning of the process and when it comes to analyzing how solutions have performed.
Analytical skills are primarily focused on performing an effective analysis by collecting, studying and parsing data related to a problem or opportunity.
It often involves spotting patterns, being able to see things from different perspectives and using observable facts and data to make suggestions or produce insight.
Analytical skills are also important at every stage of the problem solving process and by having these skills, you can ensure that any ideas or solutions you create or backed up analytically and have been sufficiently thought out.
Nine Whys #innovation #issue analysis #liberating structures With breathtaking simplicity, you can rapidly clarify for individuals and a group what is essentially important in their work. You can quickly reveal when a compelling purpose is missing in a gathering and avoid moving forward without clarity. When a group discovers an unambiguous shared purpose, more freedom and more responsibility are unleashed. You have laid the foundation for spreading and scaling innovations with fidelity.
Trying to solve problems on your own is difficult. Being able to collaborate effectively, with a free exchange of ideas, to delegate and be a productive member of a team is hugely important to all problem solving strategies.
Remember that whatever your role, collaboration is integral, and in a problem solving process, you are all working together to find the best solution for everyone.
Marshmallow challenge with debriefing #teamwork #team #leadership #collaboration In eighteen minutes, teams must build the tallest free-standing structure out of 20 sticks of spaghetti, one yard of tape, one yard of string, and one marshmallow. The marshmallow needs to be on top. The Marshmallow Challenge was developed by Tom Wujec, who has done the activity with hundreds of groups around the world. Visit the Marshmallow Challenge website for more information. This version has an extra debriefing question added with sample questions focusing on roles within the team.
Being an effective communicator means being empathetic, clear and succinct, asking the right questions, and demonstrating active listening skills throughout any discussion or meeting.
In a problem solving setting, you need to communicate well in order to progress through each stage of the process effectively. As a team leader, it may also fall to you to facilitate communication between parties who may not see eye to eye. Effective communication also means helping others to express themselves and be heard in a group.
Bus Trip #feedback #communication #appreciation #closing #thiagi #team This is one of my favourite feedback games. I use Bus Trip at the end of a training session or a meeting, and I use it all the time. The game creates a massive amount of energy with lots of smiles, laughs, and sometimes even a teardrop or two.
Creative problem solving skills can be some of the best tools in your arsenal. Thinking creatively, being able to generate lots of ideas and come up with out of the box solutions is useful at every step of the process.
The kinds of problems you will likely discuss in a problem solving workshop are often difficult to solve, and by approaching things in a fresh, creative manner, you can often create more innovative solutions.
Having practical creative skills is also a boon when it comes to problem solving. If you can help create quality design sketches and prototypes in record time, it can help bring a team to alignment more quickly or provide a base for further iteration.
The paper clip method #sharing #creativity #warm up #idea generation #brainstorming The power of brainstorming. A training for project leaders, creativity training, and to catalyse getting new solutions.
Critical thinking is one of the fundamental problem solving skills you’ll want to develop when working on developing solutions. Critical thinking is the ability to analyze, rationalize and evaluate while being aware of personal bias, outlying factors and remaining open-minded.
Defining and analyzing problems without deploying critical thinking skills can mean you and your team go down the wrong path. Developing solutions to complex issues requires critical thinking too – ensuring your team considers all possibilities and rationally evaluating them.
Agreement-Certainty Matrix #issue analysis #liberating structures #problem solving You can help individuals or groups avoid the frequent mistake of trying to solve a problem with methods that are not adapted to the nature of their challenge. The combination of two questions makes it possible to easily sort challenges into four categories: simple, complicated, complex , and chaotic . A problem is simple when it can be solved reliably with practices that are easy to duplicate. It is complicated when experts are required to devise a sophisticated solution that will yield the desired results predictably. A problem is complex when there are several valid ways to proceed but outcomes are not predictable in detail. Chaotic is when the context is too turbulent to identify a path forward. A loose analogy may be used to describe these differences: simple is like following a recipe, complicated like sending a rocket to the moon, complex like raising a child, and chaotic is like the game “Pin the Tail on the Donkey.” The Liberating Structures Matching Matrix in Chapter 5 can be used as the first step to clarify the nature of a challenge and avoid the mismatches between problems and solutions that are frequently at the root of chronic, recurring problems.
Though it shares lots of space with general analytical skills, data analysis skills are something you want to cultivate in their own right in order to be an effective problem solver.
Being good at data analysis doesn’t just mean being able to find insights from data, but also selecting the appropriate data for a given issue, interpreting it effectively and knowing how to model and present that data. Depending on the problem at hand, it might also include a working knowledge of specific data analysis tools and procedures.
Having a solid grasp of data analysis techniques is useful if you’re leading a problem solving workshop but if you’re not an expert, don’t worry. Bring people into the group who has this skill set and help your team be more effective as a result.
All problems need a solution and all solutions require that someone make the decision to implement them. Without strong decision making skills, teams can become bogged down in discussion and less effective as a result.
Making decisions is a key part of the problem solving process. It’s important to remember that decision making is not restricted to the leadership team. Every staff member makes decisions every day and developing these skills ensures that your team is able to solve problems at any scale. Remember that making decisions does not mean leaping to the first solution but weighing up the options and coming to an informed, well thought out solution to any given problem that works for the whole team.
Lightning Decision Jam (LDJ) #action #decision making #problem solving #issue analysis #innovation #design #remote-friendly The problem with anything that requires creative thinking is that it’s easy to get lost—lose focus and fall into the trap of having useless, open-ended, unstructured discussions. Here’s the most effective solution I’ve found: Replace all open, unstructured discussion with a clear process. What to use this exercise for: Anything which requires a group of people to make decisions, solve problems or discuss challenges. It’s always good to frame an LDJ session with a broad topic, here are some examples: The conversion flow of our checkout Our internal design process How we organise events Keeping up with our competition Improving sales flow
Most complex organizational problems require multiple people to be involved in delivering the solution. Ensuring that the team and organization can depend on you to take the necessary actions and communicate where necessary is key to ensuring problems are solved effectively.
Being dependable also means working to deadlines and to brief. It is often a matter of creating trust in a team so that everyone can depend on one another to complete the agreed actions in the agreed time frame so that the team can move forward together. Being undependable can create problems of friction and can limit the effectiveness of your solutions so be sure to bear this in mind throughout a project.
Team Purpose & Culture #team #hyperisland #culture #remote-friendly This is an essential process designed to help teams define their purpose (why they exist) and their culture (how they work together to achieve that purpose). Defining these two things will help any team to be more focused and aligned. With support of tangible examples from other companies, the team members work as individuals and a group to codify the way they work together. The goal is a visual manifestation of both the purpose and culture that can be put up in the team’s work space.
Emotional intelligence is an important skill for any successful team member, whether communicating internally or with clients or users. In the problem solving process, emotional intelligence means being attuned to how people are feeling and thinking, communicating effectively and being self-aware of what you bring to a room.
There are often differences of opinion when working through problem solving processes, and it can be easy to let things become impassioned or combative. Developing your emotional intelligence means being empathetic to your colleagues and managing your own emotions throughout the problem and solution process. Be kind, be thoughtful and put your points across care and attention.
Being emotionally intelligent is a skill for life and by deploying it at work, you can not only work efficiently but empathetically. Check out the emotional culture workshop template for more!
As we’ve clarified in our facilitation skills post, facilitation is the art of leading people through processes towards agreed-upon objectives in a manner that encourages participation, ownership, and creativity by all those involved. While facilitation is a set of interrelated skills in itself, the broad definition of facilitation can be invaluable when it comes to problem solving. Leading a team through a problem solving process is made more effective if you improve and utilize facilitation skills – whether you’re a manager, team leader or external stakeholder.
The Six Thinking Hats #creative thinking #meeting facilitation #problem solving #issue resolution #idea generation #conflict resolution The Six Thinking Hats are used by individuals and groups to separate out conflicting styles of thinking. They enable and encourage a group of people to think constructively together in exploring and implementing change, rather than using argument to fight over who is right and who is wrong.
Being flexible is a vital skill when it comes to problem solving. This does not mean immediately bowing to pressure or changing your opinion quickly: instead, being flexible is all about seeing things from new perspectives, receiving new information and factoring it into your thought process.
Flexibility is also important when it comes to rolling out solutions. It might be that other organizational projects have greater priority or require the same resources as your chosen solution. Being flexible means understanding needs and challenges across the team and being open to shifting or arranging your own schedule as necessary. Again, this does not mean immediately making way for other projects. It’s about articulating your own needs, understanding the needs of others and being able to come to a meaningful compromise.
The Creativity Dice #creativity #problem solving #thiagi #issue analysis Too much linear thinking is hazardous to creative problem solving. To be creative, you should approach the problem (or the opportunity) from different points of view. You should leave a thought hanging in mid-air and move to another. This skipping around prevents premature closure and lets your brain incubate one line of thought while you consciously pursue another.
Working in any group can lead to unconscious elements of groupthink or situations in which you may not wish to be entirely honest. Disagreeing with the opinions of the executive team or wishing to save the feelings of a coworker can be tricky to navigate, but being honest is absolutely vital when to comes to developing effective solutions and ensuring your voice is heard.
Remember that being honest does not mean being brutally candid. You can deliver your honest feedback and opinions thoughtfully and without creating friction by using other skills such as emotional intelligence.
Explore your Values #hyperisland #skills #values #remote-friendly Your Values is an exercise for participants to explore what their most important values are. It’s done in an intuitive and rapid way to encourage participants to follow their intuitive feeling rather than over-thinking and finding the “correct” values. It is a good exercise to use to initiate reflection and dialogue around personal values.
The problem solving process is multi-faceted and requires different approaches at certain points of the process. Taking initiative to bring problems to the attention of the team, collect data or lead the solution creating process is always valuable. You might even roadtest your own small scale solutions or brainstorm before a session. Taking initiative is particularly effective if you have good deal of knowledge in that area or have ownership of a particular project and want to get things kickstarted.
That said, be sure to remember to honor the process and work in service of the team. If you are asked to own one part of the problem solving process and you don’t complete that task because your initiative leads you to work on something else, that’s not an effective method of solving business challenges.
15% Solutions #action #liberating structures #remote-friendly You can reveal the actions, however small, that everyone can do immediately. At a minimum, these will create momentum, and that may make a BIG difference. 15% Solutions show that there is no reason to wait around, feel powerless, or fearful. They help people pick it up a level. They get individuals and the group to focus on what is within their discretion instead of what they cannot change. With a very simple question, you can flip the conversation to what can be done and find solutions to big problems that are often distributed widely in places not known in advance. Shifting a few grains of sand may trigger a landslide and change the whole landscape.
A particularly useful problem solving skill for product owners or managers is the ability to remain impartial throughout much of the process. In practice, this means treating all points of view and ideas brought forward in a meeting equally and ensuring that your own areas of interest or ownership are not favored over others.
There may be a stage in the process where a decision maker has to weigh the cost and ROI of possible solutions against the company roadmap though even then, ensuring that the decision made is based on merit and not personal opinion.
Empathy map #frame insights #create #design #issue analysis An empathy map is a tool to help a design team to empathize with the people they are designing for. You can make an empathy map for a group of people or for a persona. To be used after doing personas when more insights are needed.
Being a good leader means getting a team aligned, energized and focused around a common goal. In the problem solving process, strong leadership helps ensure that the process is efficient, that any conflicts are resolved and that a team is managed in the direction of success.
It’s common for managers or executives to assume this role in a problem solving workshop, though it’s important that the leader maintains impartiality and does not bulldoze the group in a particular direction. Remember that good leadership means working in service of the purpose and team and ensuring the workshop is a safe space for employees of any level to contribute. Take a look at our leadership games and activities post for more exercises and methods to help improve leadership in your organization.
Leadership Pizza #leadership #team #remote-friendly This leadership development activity offers a self-assessment framework for people to first identify what skills, attributes and attitudes they find important for effective leadership, and then assess their own development and initiate goal setting.
In the context of problem solving, mediation is important in keeping a team engaged, happy and free of conflict. When leading or facilitating a problem solving workshop, you are likely to run into differences of opinion. Depending on the nature of the problem, certain issues may be brought up that are emotive in nature.
Being an effective mediator means helping those people on either side of such a divide are heard, listen to one another and encouraged to find common ground and a resolution. Mediating skills are useful for leaders and managers in many situations and the problem solving process is no different.
Conflict Responses #hyperisland #team #issue resolution A workshop for a team to reflect on past conflicts, and use them to generate guidelines for effective conflict handling. The workshop uses the Thomas-Killman model of conflict responses to frame a reflective discussion. Use it to open up a discussion around conflict with a team.
Solving organizational problems is much more effective when following a process or problem solving model. Planning skills are vital in order to structure, deliver and follow-through on a problem solving workshop and ensure your solutions are intelligently deployed.
Planning skills include the ability to organize tasks and a team, plan and design the process and take into account any potential challenges. Taking the time to plan carefully can save time and frustration later in the process and is valuable for ensuring a team is positioned for success.
3 Action Steps #hyperisland #action #remote-friendly This is a small-scale strategic planning session that helps groups and individuals to take action toward a desired change. It is often used at the end of a workshop or programme. The group discusses and agrees on a vision, then creates some action steps that will lead them towards that vision. The scope of the challenge is also defined, through discussion of the helpful and harmful factors influencing the group.
As organisations grow, the scale and variation of problems they face multiplies. Your team or is likely to face numerous challenges in different areas and so having the skills to analyze and prioritize becomes very important, particularly for those in leadership roles.
A thorough problem solving process is likely to deliver multiple solutions and you may have several different problems you wish to solve simultaneously. Prioritization is the ability to measure the importance, value, and effectiveness of those possible solutions and choose which to enact and in what order. The process of prioritization is integral in ensuring the biggest challenges are addressed with the most impactful solutions.
Impact and Effort Matrix #gamestorming #decision making #action #remote-friendly In this decision-making exercise, possible actions are mapped based on two factors: effort required to implement and potential impact. Categorizing ideas along these lines is a useful technique in decision making, as it obliges contributors to balance and evaluate suggested actions before committing to them.
Some problem solving skills are utilized in a workshop or ideation phases, while others come in useful when it comes to decision making. Overseeing an entire problem solving process and ensuring its success requires strong project management skills.
While project management incorporates many of the other skills listed here, it is important to note the distinction of considering all of the factors of a project and managing them successfully. Being able to negotiate with stakeholders, manage tasks, time and people, consider costs and ROI, and tie everything together is massively helpful when going through the problem solving process.
Working out meaningful solutions to organizational challenges is only one part of the process. Thoughtfully documenting and keeping records of each problem solving step for future consultation is important in ensuring efficiency and meaningful change.
For example, some problems may be lower priority than others but can be revisited in the future. If the team has ideated on solutions and found some are not up to the task, record those so you can rule them out and avoiding repeating work. Keeping records of the process also helps you improve and refine your problem solving model next time around!
Personal Kanban #gamestorming #action #agile #project planning Personal Kanban is a tool for organizing your work to be more efficient and productive. It is based on agile methods and principles.
Conducting research to support both the identification of problems and the development of appropriate solutions is important for an effective process. Knowing where to go to collect research, how to conduct research efficiently, and identifying pieces of research are relevant are all things a good researcher can do well.
In larger groups, not everyone has to demonstrate this ability in order for a problem solving workshop to be effective. That said, having people with research skills involved in the process, particularly if they have existing area knowledge, can help ensure the solutions that are developed with data that supports their intention. Remember that being able to deliver the results of research efficiently and in a way the team can easily understand is also important. The best data in the world is only as effective as how it is delivered and interpreted.
Customer experience map #ideation #concepts #research #design #issue analysis #remote-friendly Customer experience mapping is a method of documenting and visualizing the experience a customer has as they use the product or service. It also maps out their responses to their experiences. To be used when there is a solution (even in a conceptual stage) that can be analyzed.
Managing risk is an often overlooked part of the problem solving process. Solutions are often developed with the intention of reducing exposure to risk or solving issues that create risk but sometimes, great solutions are more experimental in nature and as such, deploying them needs to be carefully considered.
Managing risk means acknowledging that there may be risks associated with more out of the box solutions or trying new things, but that this must be measured against the possible benefits and other organizational factors.
Be informed, get the right data and stakeholders in the room and you can appropriately factor risk into your decision making process.
Decisions, Decisions… #communication #decision making #thiagi #action #issue analysis When it comes to decision-making, why are some of us more prone to take risks while others are risk-averse? One explanation might be the way the decision and options were presented. This exercise, based on Kahneman and Tversky’s classic study , illustrates how the framing effect influences our judgement and our ability to make decisions . The participants are divided into two groups. Both groups are presented with the same problem and two alternative programs for solving them. The two programs both have the same consequences but are presented differently. The debriefing discussion examines how the framing of the program impacted the participant’s decision.
No single person is as good at problem solving as a team. Building an effective team and helping them come together around a common purpose is one of the most important problem solving skills, doubly so for leaders. By bringing a team together and helping them work efficiently, you pave the way for team ownership of a problem and the development of effective solutions.
In a problem solving workshop, it can be tempting to jump right into the deep end, though taking the time to break the ice, energize the team and align them with a game or exercise will pay off over the course of the day.
Remember that you will likely go through the problem solving process multiple times over an organization’s lifespan and building a strong team culture will make future problem solving more effective. It’s also great to work with people you know, trust and have fun with. Working on team building in and out of the problem solving process is a hallmark of successful teams that can work together to solve business problems.
9 Dimensions Team Building Activity #ice breaker #teambuilding #team #remote-friendly 9 Dimensions is a powerful activity designed to build relationships and trust among team members. There are 2 variations of this icebreaker. The first version is for teams who want to get to know each other better. The second version is for teams who want to explore how they are working together as a team.
The problem solving process is designed to lead a team from identifying a problem through to delivering a solution and evaluating its effectiveness. Without effective time management skills or timeboxing of tasks, it can be easy for a team to get bogged down or be inefficient.
By using a problem solving model and carefully designing your workshop, you can allocate time efficiently and trust that the process will deliver the results you need in a good timeframe.
Time management also comes into play when it comes to rolling out solutions, particularly those that are experimental in nature. Having a clear timeframe for implementing and evaluating solutions is vital for ensuring their success and being able to pivot if necessary.
Improving your skills at problem solving is often a career-long pursuit though there are methods you can use to make the learning process more efficient and to supercharge your problem solving skillset.
Remember that the skills you need to be a great problem solver have a large overlap with those skills you need to be effective in any role. Investing time and effort to develop your active listening or critical thinking skills is valuable in any context. Here are 7 ways to improve your problem solving skills.
Remember that your team is an excellent source of skills, wisdom, and techniques and that you should all take advantage of one another where possible. Best practices that one team has for solving problems, conducting research or making decisions should be shared across the organization. If you have in-house staff that have done active listening training or are data analysis pros, have them lead a training session.
Your team is one of your best resources. Create space and internal processes for the sharing of skills so that you can all grow together.
Once you’ve figured out you have a skills gap, the next step is to take action to fill that skills gap. That might be by asking your superior for training or coaching, or liaising with team members with that skill set. You might even attend specialized training for certain skills – active listening or critical thinking, for example, are business-critical skills that are regularly offered as part of a training scheme.
Whatever method you choose, remember that taking action of some description is necessary for growth. Whether that means practicing, getting help, attending training or doing some background reading, taking active steps to improve your skills is the way to go.
Problem solving can be complicated, particularly when attempting to solve large problems for the first time. Using a problem solving process helps give structure to your problem solving efforts and focus on creating outcomes, rather than worrying about the format.
Tools such as the seven-step problem solving process above are effective because not only do they feature steps that will help a team solve problems, they also develop skills along the way. Each step asks for people to engage with the process using different skills and in doing so, helps the team learn and grow together. Group processes of varying complexity and purpose can also be found in the SessionLab library of facilitation techniques . Using a tried and tested process and really help ease the learning curve for both those leading such a process, as well as those undergoing the purpose.
Effective teams make decisions about where they should and shouldn’t expend additional effort. By using a problem solving process, you can focus on the things that matter, rather than stumbling towards a solution haphazardly.
Some skills gaps are more obvious than others. It’s possible that your perception of your active listening skills differs from those of your colleagues.
It’s valuable to create a system where team members can provide feedback in an ordered and friendly manner so they can all learn from one another. Only by identifying areas of improvement can you then work to improve them.
Remember that feedback systems require oversight and consideration so that they don’t turn into a place to complain about colleagues. Design the system intelligently so that you encourage the creation of learning opportunities, rather than encouraging people to list their pet peeves.
While practice might not make perfect, it does make the problem solving process easier. If you are having trouble with critical thinking, don’t shy away from doing it. Get involved where you can and stretch those muscles as regularly as possible.
Problem solving skills come more naturally to some than to others and that’s okay. Take opportunities to get involved and see where you can practice your skills in situations outside of a workshop context. Try collaborating in other circumstances at work or conduct data analysis on your own projects. You can often develop those skills you need for problem solving simply by doing them. Get involved!
Learn from the best. Our library of 700+ facilitation techniques is full of activities and methods that help develop the skills you need to be an effective problem solver. Check out our templates to see how to approach problem solving and other organizational challenges in a structured and intelligent manner.
There is no single approach to improving problem solving skills, but by using the techniques employed by others you can learn from their example and develop processes that have seen proven results.
Using tried and tested exercises that you know well can help deliver results, but you do run the risk of missing out on the learning opportunities offered by new approaches. As with the problem solving process, changing your mindset can remove blockages and be used to develop your problem solving skills.
Most teams have members with mixed skill sets and specialties. Mix people from different teams and share skills and different points of view. Teach your customer support team how to use design thinking methods or help your developers with conflict resolution techniques. Try switching perspectives with facilitation techniques like Flip It! or by using new problem solving methodologies or models. Give design thinking, liberating structures or lego serious play a try if you want to try a new approach. You will find that framing problems in new ways and using existing skills in new contexts can be hugely useful for personal development and improving your skillset. It’s also a lot of fun to try new things. Give it a go!
Encountering business challenges and needing to find appropriate solutions is not unique to your organization. Lots of very smart people have developed methods, theories and approaches to help develop problem solving skills and create effective solutions. Learn from them!
Books like The Art of Thinking Clearly , Think Smarter, or Thinking Fast, Thinking Slow are great places to start, though it’s also worth looking at blogs related to organizations facing similar problems to yours, or browsing for success stories. Seeing how Dropbox massively increased growth and working backward can help you see the skills or approach you might be lacking to solve that same problem. Learning from others by reading their stories or approaches can be time-consuming but ultimately rewarding.
A tired, distracted mind is not in the best position to learn new skills. It can be tempted to burn the candle at both ends and develop problem solving skills outside of work. Absolutely use your time effectively and take opportunities for self-improvement, though remember that rest is hugely important and that without letting your brain rest, you cannot be at your most effective.
Creating distance between yourself and the problem you might be facing can also be useful. By letting an idea sit, you can find that a better one presents itself or you can develop it further. Take regular breaks when working and create a space for downtime. Remember that working smarter is preferable to working harder and that self-care is important for any effective learning or improvement process.
Now we’ve explored some of the key problem solving skills and the problem solving steps necessary for an effective process, you’re ready to begin developing more effective solutions and leading problem solving workshops.
Need more inspiration? Check out our post on problem solving activities you can use when guiding a group towards a great solution in your next workshop or meeting. Have questions? Did you have a great problem solving technique you use with your team? Get in touch in the comments below. We’d love to chat!
James Smart is Head of Content at SessionLab. He’s also a creative facilitator who has run workshops and designed courses for establishments like the National Centre for Writing, UK. He especially enjoys working with young people and empowering others in their creative practice.
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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.
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In Psychology, you get to read about a ton of therapies. It’s mind-boggling how different theorists have looked at human nature differently and have come up with different, often somewhat contradictory, theoretical approaches.
Yet, you can’t deny the kernel of truth that’s there in all of them. All therapies, despite being different, have one thing in common- they all aim to solve people’s problems. They all aim to equip people with problem-solving strategies to help them deal with their life problems.
Problem-solving is really at the core of everything we do. Throughout our lives, we’re constantly trying to solve one problem or another. When we can’t, all sorts of psychological problems take hold. Getting good at solving problems is a fundamental life skill.
What problem-solving does is take you from an initial state (A) where a problem exists to a final or goal state (B), where the problem no longer exists.
To move from A to B, you need to perform some actions called operators. Engaging in the right operators moves you from A to B. So, the stages of problem-solving are:
The problem itself can either be well-defined or ill-defined. A well-defined problem is one where you can clearly see where you are (A), where you want to go (B), and what you need to do to get there (engaging the right operators).
For example, feeling hungry and wanting to eat can be seen as a problem, albeit a simple one for many. Your initial state is hunger (A) and your final state is satisfaction or no hunger (B). Going to the kitchen and finding something to eat is using the right operator.
In contrast, ill-defined or complex problems are those where one or more of the three problem solving stages aren’t clear. For example, if your goal is to bring about world peace, what is it exactly that you want to do?
It’s been rightly said that a problem well-defined is a problem half-solved. Whenever you face an ill-defined problem, the first thing you need to do is get clear about all the three stages.
Often, people will have a decent idea of where they are (A) and where they want to be (B). What they usually get stuck on is finding the right operators.
When people first attempt to solve a problem, i.e. when they first engage their operators, they often have an initial theory of solving the problem. As I mentioned in my article on overcoming challenges for complex problems, this initial theory is often wrong.
But, at the time, it’s usually the result of the best information the individual can gather about the problem. When this initial theory fails, the problem-solver gets more data, and he refines the theory. Eventually, he finds an actual theory i.e. a theory that works. This finally allows him to engage the right operators to move from A to B.
These are operators that a problem solver tries to move from A to B. There are several problem-solving strategies but the main ones are:
When you follow a step-by-step procedure to solve a problem or reach a goal, you’re using an algorithm. If you follow the steps exactly, you’re guaranteed to find the solution. The drawback of this strategy is that it can get cumbersome and time-consuming for large problems.
Say I hand you a 200-page book and ask you to read out to me what’s written on page 100. If you start from page 1 and keep turning the pages, you’ll eventually reach page 100. There’s no question about it. But the process is time-consuming. So instead you use what’s called a heuristic.
Heuristics are rules of thumb that people use to simplify problems. They’re often based on memories from past experiences. They cut down the number of steps needed to solve a problem, but they don’t always guarantee a solution. Heuristics save us time and effort if they work.
You know that page 100 lies in the middle of the book. Instead of starting from page one, you try to open the book in the middle. Of course, you may not hit page 100, but you can get really close with just a couple of tries.
If you open page 90, for instance, you can then algorithmically move from 90 to 100. Thus, you can use a combination of heuristics and algorithms to solve the problem. In real life, we often solve problems like this.
When police are looking for suspects in an investigation, they try to narrow down the problem similarly. Knowing the suspect is 6 feet tall isn’t enough, as there could be thousands of people out there with that height.
Knowing the suspect is 6 feet tall, male, wears glasses, and has blond hair narrows down the problem significantly.
When you have an initial theory to solve a problem, you try it out. If you fail, you refine or change your theory and try again. This is the trial-and-error process of solving problems. Behavioral and cognitive trial and error often go hand in hand, but for many problems, we start with behavioural trial and error until we’re forced to think.
Say you’re in a maze, trying to find your way out. You try one route without giving it much thought and you find it leads to nowhere. Then you try another route and fail again. This is behavioural trial and error because you aren’t putting any thought into your trials. You’re just throwing things at the wall to see what sticks.
This isn’t an ideal strategy but can be useful in situations where it’s impossible to get any information about the problem without doing some trials.
Then, when you have enough information about the problem, you shuffle that information in your mind to find a solution. This is cognitive trial and error or analytical thinking. Behavioral trial and error can take a lot of time, so using cognitive trial and error as much as possible is advisable. You got to sharpen your axe before you cut the tree.
When solving complex problems, people get frustrated after having tried several operators that didn’t work. They abandon their problem and go on with their routine activities. Suddenly, they get a flash of insight that makes them confident they can now solve the problem.
I’ve done an entire article on the underlying mechanics of insight . Long story short, when you take a step back from your problem, it helps you see things in a new light. You make use of associations that were previously unavailable to you.
You get more puzzle pieces to work with and this increases the odds of you finding a path from A to B, i.e. finding operators that work.
No matter what problem-solving strategy you employ, it’s all about finding out what works. Your actual theory tells you what operators will take you from A to B. Complex problems don’t reveal their actual theories easily solely because they are complex.
Therefore, the first step to solving a complex problem is getting as clear as you can about what you’re trying to accomplish- collecting as much information as you can about the problem.
This gives you enough raw materials to formulate an initial theory. We want our initial theory to be as close to an actual theory as possible. This saves time and resources.
Solving a complex problem can mean investing a lot of resources. Therefore, it is recommended you verify your initial theory if you can. I call this pilot problem-solving.
Before businesses invest in making a product, they sometimes distribute free versions to a small sample of potential customers to ensure their target audience will be receptive to the product.
Before making a series of TV episodes, TV show producers often release pilot episodes to figure out whether the show can take off.
Before conducting a large study, researchers do a pilot study to survey a small sample of the population to determine if the study is worth carrying out.
The same ‘testing the waters’ approach needs to be applied to solving any complex problem you might be facing. Is your problem worth investing a lot of resources in? In management, we’re constantly taught about Return On Investment (ROI). The ROI should justify the investment.
If the answer is yes, go ahead and formulate your initial theory based on extensive research. Find a way to verify your initial theory. You need this reassurance that you’re going in the right direction, especially for complex problems that take a long time to solve.
Problem solving boils down to getting your causal thinking right. Finding solutions is all about finding out what works, i.e. finding operators that take you from A to B. To succeed, you need to be confident in your initial theory (If I do X and Y, they’ll lead me to B). You need to be sure that doing X and Y will lead you to B- doing X and Y will cause B.
All obstacles to problem-solving or goal-accomplishing are rooted in faulty causal thinking leading to not engaging the right operators. When your causal thinking is on point, you’ll have no problem engaging the right operators.
As you can imagine, for complex problems, getting our causal thinking right isn’t easy. That’s why we need to formulate an initial theory and refine it over time.
I like to think of problem-solving as the ability to project the present into the past or into the future. When you’re solving problems, you’re basically looking at your present situation and asking yourself two questions:
“What caused this?” (Projecting present into the past)
“What will this cause?” (Projecting present into the future)
The first question is more relevant to problem-solving and the second to goal-accomplishing.
If you find yourself in a mess , you need to answer the “What caused this?” question correctly. For the operators you’re currently engaging to reach your goal, ask yourself, “What will this cause?” If you think they cannot cause B, it’s time to refine your initial theory.
Hi, I’m Hanan Parvez (MA Psychology). I’ve published over 500 articles and authored one book. My work has been featured in Forbes , Business Insider , Reader’s Digest , and Entrepreneur .
A clear problem statement is crucial for project success. It should describe the issue , its impact , and context without proposing solutions. Craft a concise statement that aligns stakeholders and guides research . Regularly review your problem statement to ensure solutions address the core issue .
Many people struggle to explain problems at work or in research projects. Research indicates that over two-thirds of projects don't succeed because the initial problem statement isn't clearly defined. Here, you'll learn how to create strong problem statements , setting your projects up for success from the start.
Every successful project or study relies on a clear explanation of the issue at hand. It guides teams toward a shared goal and prevents solving the wrong problem. A problem statement briefly describes an issue that needs fixing. It describes the present circumstances, the intended result, and the difference between them . It provides a brief overview of the issue without proposing any fixes.
Defining a problem statement.
For example, a healthcare project's problem statement might be:
"In 2019, late filing caused 61.6% of denied insurance claims, leading to $7.8 million in lost profit."
This explanation highlights the problem , its effects, and paves the way for further investigation.
Problem statements serve a crucial purpose beyond mere procedure. They serve several important functions:
"If I had an hour to solve a problem I'd spend 55 minutes thinking about the problem and five minutes thinking about solutions." — Albert Einstein
Einstein believed that most of the time spent solving a problem should be used to understand it, with only a small portion dedicated to finding solutions. Grasping the issue fully is crucial before attempting to resolve it.
Having covered the importance of problem statements, we'll now explore techniques for developing one that boosts your project's chances of success.
An effective problem statement needs to have these parts:
Keep in mind, an effective problem statement is brief (typically two sentences max) and immediately captures the reader's interest. It should inspire and motivate without suggesting a specific solution.
Despite good aims, people often make errors when describing problems. Watch out for these frequent mistakes:
Crafting a clear problem statement without these errors will set a strong foundation for your work.
An effective problem statement is only the beginning. True advancement occurs when you apply the statement to achieve concrete outcomes.
A well-defined problem statement can act as a roadmap for your study or project . It assists you in:
Keep in mind that your problem statement may evolve. Your understanding might grow, requiring adjustments to the statement . This back-and-forth process is normal and useful in research.
While your problem statement shouldn't include solutions, it's the starting point for finding them. Here's a way to move forward:
Constantly checking your problem statement during problem-solving keeps your work targeted and aligned with your initial aims.
Writing effective problem statements is a skill that can greatly improve the success rate of your projects and research. Clearly stating the problem paves the way for fresh ideas and valuable outcomes.
A good problem statement acts as your roadmap, guiding you through the tricky steps of solving issues. When you encounter a difficult situation, pause and consider if you've truly understood what the issue is. This approach will help you see things more clearly and know what to do next.
Which problem are you going to look at differently today?
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Whether it’s a toy-related conflict, a tough math equation, or negative peer pressure, kids of ALL ages face problems and challenges on a daily basis.
As parents or teachers, we can’t always be there to solve every problem for our children. In fact, this isn’t our job. Our job is to TEACH our children how to solve problems by themselves . This way, they can become confident , independent, and successful individuals.
Instead of giving up or getting frustrated when they encounter a challenge, kids with problem-solving skills manage their emotions, think creatively, and persist until they find a solution. Naturally, these abilities go hand-in-hand with a growth mindset .
Before you continue, we thought you might like to download our FREE Your Words Matter Volume 2 Kit . With these 10 one-page parenting guides, you will know exactly how to speak to your child to help them stand up for themselves, be more confident, and develop a growth mindset.
So HOW do you teach problem-solving skills to kids?
Well, it depends on their age . As cognitive abilities and the size of the child’s challenges grow/evolve over time, so should your approach to teaching problem-solving skills.
Read on to learn key strategies for teaching problem-solving to kids, as well as some age-by-age ideas and activities.
1. model effective problem-solving .
When YOU encounter a challenge, do a “think-aloud” for the benefit of your child. MODEL how to apply the same problem-solving skills you’ve been working on together, giving the real-world examples that she can implement in her own life.
At the same time, show your child a willingness to make mistakes . Everyone encounters problems, and that’s okay. Sometimes the first solution you try won’t work, and that’s okay too!
When you model problem-solving, explain that there are some things that are out of our control. As we're solving a problem at hand we should focus on the things we CAN actually control.
You and your child can listen to Episode 35 of the Big Life Kids Podcast to learn about focusing on what you can control.
Ask your kids for advice when you have a problem. This teaches them that it’s common to make mistakes and face challenges. It also gives them the opportunity to practice problem-solving skills.
Plus, when you indicate that their ideas are valued , they’ll gain the confidence to attempt solving problems on their own.
As difficult as it may be, allow your child to struggle, sometimes fail , and ultimately LEARN from experiencing consequences.
Now, let’s take a look at some age-specific strategies and activities. The ages listed below are general guidelines, feel free to choose any strategies or activities that you feel will work for YOUR child.
To step into a problem-solving mindset, young children need to first learn to manage their emotions . After all, it’s difficult for a small child to logically consider solutions to a problem if he’s mid-tantrum.
One way to accomplish this is by using the emotion coaching process outlined by John Gottman.
First, teach your kids that ALL emotions are acceptable. There are NO “bad” emotions. Even seemingly negative emotions like anger, sadness, and frustration can teach us valuable lessons. What matters is how we respond to these emotions.
Second, follow this process:
When your child struggles or feels frustrated, try a technique suggested by mom and parenting blogger Lauren Tamm . Simply say, “Show me the hard part.”
This helps your child identify the ROOT of the problem, making it less intimidating and easier to solve.
Repeat back what your child says, “So you’re saying…”
Once you both understand the real problem, prompt your child to come up with solutions . “There must be some way you can fix that…” or “There must be something you can do…”
Now that your child has identified “the hard part,” she’ll likely be able to come up with a solution. If not, help her brainstorm some ideas. You may try asking the question, “If you DID know, what would you think?” and see what she comes up with.
Allow your child to choose activities and games based on her interests . Free play provides plenty of opportunities to navigate and creatively solve problems.
Children often learn best through play. Playing with items like blocks, simple puzzles, and dress-up clothes can teach your child the process of problem-solving.
Even while playing, your child thinks critically: Where does this puzzle piece fit? What does this do? I want to dress up as a queen. What should I wear? Where did I put my tiara? Is it under the couch?
Read age-appropriate stories featuring characters who experience problems, such as:
Connect these experiences to similar events in your child’s own life, and ASK your child HOW the characters in these stories could solve their problems. Encourage a variety of solutions, and discuss the possible outcomes of each.
This is a form of dialogue reading , or actively ENGAGING your child in the reading experience. Interacting with the text instead of passively listening can “turbocharge” the development of literacy skills such as comprehension in preschool-aged children.
By asking questions about the characters’ challenges, you can also give your child’s problem-solving abilities a boost.
You can even have your child role-play the problem and potential solutions to reinforce the lesson.
For book suggestions, refer to our Top 85 Growth Mindset Books for Children & Adults list.
Come up with a simple problem-solving process for your child, one that you can consistently implement. For example, you might try the following five steps:
Consistently practice these steps so that they become second nature, and model solving problems of your own the same way. It's a good idea to reflect : What worked? What didn’t? What can you do differently next time?
Crafting is another form of play that can teach kids to solve problems creatively.
Provide your child with markers, modeling clay, cardboard boxes, tape, paper, etc. They’ll come up with all sorts of interesting creations and inventive games with these simple materials.
These “open-ended toys” don’t have a “right way to play,” allowing your child to get creative and generate ideas independently .
Asking open-ended questions improves a child’s ability to think critically and creatively, ultimately making them better problem-solvers. Examples of open-ended questions include:
Open-ended questions have no right answer and can’t be answered with a simple “Yes” or “No.”
You can ask open-ended questions even when your child isn’t currently solving a problem to help her practice her thinking skills, which will come in handy when she does have a problem to solve.
If you need some tips on how to encourage a growth mindset in your child, don't forget to download our FREE Your Words Matter Volume 2 Kit .
This strategy is a more advanced version of “Show me the hard part.”
The bigger your child gets, the bigger her problems get too. When your child is facing a challenge that seems overwhelming or insurmountable, encourage her to break it into smaller, more manageable chunks.
For instance, let’s say your child has a poor grade in history class. Why is the grade so low? What are the causes of this problem?
As usual, LISTEN as your child brainstorms, asking open-ended questions to help if she gets stuck.
If the low grade is the result of missing assignments, perhaps your child can make a list of these assignments and tackle them one at a time. Or if tests are the issue, what’s causing your child to struggle on exams?
Perhaps she’s distracted by friends in the class, has trouble asking for help, and doesn’t spend enough time studying at home. Once you’ve identified these “chunks,” help your child tackle them one at a time until the problem is solved.
Discuss the importance of embracing challenges and solving problems independently with the “broken escalator video.”
In the video, an escalator unexpectedly breaks. The people on the escalator are “stuck” and yelling for help. At this age, it’s likely that your child will find the video funny and immediately offer a solution: “Just walk! Get off the escalator!”
Tell your child that this is a simple example of how people sometimes act in difficult situations. Ask, “Why do you think they didn’t get off the escalator?” (they didn’t know how, they were waiting for help, etc.)
Sometimes, your child might feel “stuck” when facing problems. They may stop and ask for help before even attempting to find a solution. Encourage your child to embrace challenges and work through problems instead.
Provide your child or a group of children with materials such as straws, cotton balls, yarn, clothespins, tape, paper clips, sticky notes, Popsicle sticks, etc.
With just these materials, challenge your kids to solve unusual problems like:
This is a fun way to practice critical thinking and creative problem-solving. Most likely, it will take multiple attempts to find a solution that works, which can apply to just about any aspect of life.
When your child asks for a new toy, technology, or clothes, have her make a plan to obtain the desired item herself. Not only will your child have to brainstorm and evaluate solutions, but she’ll also gain confidence .
Ask your child HOW she can earn the money for the item that she wants, and encourage her as she works toward her goal .
Have your child write out their problems on paper and brainstorm some potential solutions.
But now, she takes this process a step further: After attempting each solution, which succeeded? Which were unsuccessful? Why ?
This helps your child reflect on various outcomes, learning what works and what doesn’t. The lessons she learns here will be useful when she encounters similar problems in the future.
Learning to play chess is a great way for kids to learn problem-solving AND build their brains at the same time. It requires players to use critical thinking, creativity, analysis of the board, recognize patterns, and more. There are online versions of the game, books on how to play, videos, and other resources. Don’t know how to play? Learn with your teen to connect and problem solve together!
Our teens and tweens are already tech-savvy and can use their skills to solve problems by learning to code. Coding promotes creativity, logic, planning, and persistence . There are many great tools and online or in-person programs that can boost your child’s coding skills.
This project has to be meaningful to your teen, for example starting a YouTube channel. Your teen will practice problem-solving skills as they’re figuring out how to grow their audience, how to have their videos discovered, and much more.
In the Big Life Journal - Teen Edition , there’s a section that guides them through planning their YouTube channel and beginning the problem-solving process.
Looking for a game plan that your teen can employ when faced with a problem? The SODAS method can be used for big or small problems. Just remember this simple acronym and follow these ideas:
Does your teen enjoy solving problems in a team? Have them join a group or club that helps them hone their skills in a variety of settings--from science and robotics to debating and international affairs. Some examples of groups include:
Looking for additional resources? The Bestseller’s Bundle includes our three most popular printable kits packed with science-based activities, guides, and crafts for children. Our Growth Mindset Kit, Resilience Kit, and Challenges Kit work together as a comprehensive system designed specifically for children ages 5-11.
I love, love, love the point about emotional coaching. It’s so important to identify how children are feeling about a problem and then approach the solutions accordingly.
Thank you for putting this together. I wrote an article on problem-solving specifically from the point of view of developing a STEM aptitude in kids, if you like to check it out – https://kidpillar.com/how-to-teach-problem-solving-to-your-kids-5-8-years/
I feel that these techniques will work for my kid.. Worthy.. Thank you
I love you guys
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1 School of Computer Science and Artificial Intelligence, Changzhou University, Changzhou, 213164 China
2 School of Information Science and Technology, Zhejiang Shuren University, Hangzhou, 310015 China
3 State Grid WenZhou Electric Power Supply Company, Wenzhou, 325035 China
The datasets generated and/or analysed during the current study are not publicly available due this study is going on but are available from the corresponding author on reasonable request.
Employee scheduling aims to assign employees to shifts to satisfy daily workload and constraints. Some employee scheduling problems and their variants have been proven NP-hard, and a series of works have been done. However, the existing algorithms consider the fixed work time, which may cause plenty of overstaffing and understaffing phenomenons. Hence, this paper proposes a fast-flexible strategy based approach (FFS) to solve it. FFS introduces the idea of soft work time, which allows the work time of employees can be adjusted in a range. Based on this, we set the flextime strategy to decide the specific work time of each employee every day. Besides, FFS adopts a pairwise-allocated strategy and proficiency average matrix to boost its efficiency and effectiveness. Finally, the extensive experimental evaluation shows that FFS is more effective and efficient than the baselines for solving the employee scheduling problem considering soft work time.
Employee scheduling aims at assigning the right employees to the right shifts at the right time, for satisfying the constraints and achieving the optimization of goals 1 . It widely arises in real-life scenarios such as health care 2 – 4 , retail stores 5 , 6 , transportation 7 , job shops 8 and call centers 9 – 11 . In most existing works, employees perform their duties according to the fixed period, which is composed of fixed start and end time points. However, the workload of different periods varies as time goes by, and employee scheduling considering fixed work time can not satisfy the varied workload well, and causes a lot of understaffing and overstaffing problems. In the following, we consider one representative motivation example.
In a call center, employees are assigned to shifts and serve the call arrivals as Fig. 1 a shows. In Fig. 1 a, three employees are assigned to the same shifts, suppose that the execution time of this shift is [7:30, 9:30], every 30 minutes is treated as a period and each one contains the number of call arrivals (treated as workload) as Fig. 1 b shows. Combined with these two figures, employee scheduling considering fixed work time causes some understaffing and overstaffing problems. For example, the period [7:30, 8:00] requires 2 employees to satisfy its workload, but there are 3 employees, which is over the requirement of workload and causes the overstaffing problem. Besides, the period [9:00, 9:30] asks for 4 employees, while it is assigned to 3 employees, and thus the understaffing problem arises. Hence, employee scheduling considering fixed work time can not satisfy the varied workload well. The execution time of a normal shift usually contains several hours, and the corresponding workload of different periods is even more drastic as Fig. 1 c shows, thus, the existing fixed work time scheduling causes plenty of overstaffing and understaffing phenomenons. In this paper, we introduce the idea of soft work time, which allows adjusting start and end time points. In real scenarios, there are several types of shifts with different execution times, and each one can adjust its start and end time points. When the number of assigned employees is over the requirement of workload, some employees can delay the start point of execution time or be earlier to end the work. Note that the adjustable periods exist at the start/end/meal point of the execution.
Illustration for motivation example.
However, the existing studies suffer from one or more drawbacks in solving such employee scheduling problems.
In our work, we consider the soft work time. Specifically, we consider two types of soft work time, i.e. the number of consecutive working days and the working duration of one day. To address this issue, we propose FFS, a polynomial-time method to address it. Specifically, FFS is divided into four steps. In the first step, FFS proposes a scheduling-cycle-based hard constraints control mechanism, to decide the soft consecutive working days. In the second step, FFS uses the gradient descent projection to estimate the number of employees required for each shift, according to workload and work time of each sharing period. It can implement coarse-grained pruning of the search space. In the third step, based on the estimated number of employees in the second step, FFS uses the pairwise-allocated strategy to find the suitable employee combinations and establishes the proficiency average matrix to further boost its efficiency. Thus, we generate the feasible assignments for each day in the whole scheduling horizon. In the fourth step, according to the workload coverage of each period, a flextime strategy is proposed to decide the specific work time of each employee performing his assigned shift.
In a nutshell, the key contributions of our paper are listed below.
The rest of this paper is organized as follows. Section " Preliminaries " introduces basic concepts and gives a formal definition of the problem. Section " Algorithm overview " elaborates on our approach FFS. Experimental results and our findings are reported in Sect. " Experiments ". Section " Related work " reviews related work. Finally, Sect. " Conclusion " concludes the paper with some directions for future work.
In this section, we first present a series of decisions, i.e. scheduling horizon, shifts, and employees. Then we introduce the scheduling constraints. Finally, we define the optimization goals.
We start with the description of each decision.
The scheduling horizon D is defined by
where d i ∈ D denotes a day. Each day has the same duration for work, and can be divided into ω same consecutive time periods, denoted by { t p i 1 , t p i 2 , ⋯ , t p i ω } . Each time period t p i j ∈ TP has a corresponding workload, denoted by W _ t p i j .
There are 5 types of shifts assigned to employees, each type of shift contains an execution time, they are denoted by,
Where i is the i th day; k is the k th employee; S F T k i is the assigned shift of k th employee for i th day; τ is the types of shifts which can be assigned to employees; in the { 1 , 2 , 3 , 4 , 5 , 0 } , { 1 , 2 , 3 , 4 , 5 } is the shifts for working and { 0 } is the rest day; T k i is the execution time for k th employee for i th day; T ks i is the start execution time for k th employee for i th day; T ke i is the end execution time for k th employee for i th day; T km i is the meal time for k th employee for i th day. One employee can be assigned to one shift at most. Each shift has an execution time, which contains a series of consecutive time periods. In addition, the execution time of each shift is unfixed. Specifically, the start and end time periods of execution time are selected in the first four time periods and the last four time periods.
There are t employees, each one has a proficiency, and each time period has a total proficiency, which is denoted by,
where k is the k th employee; p k is the proficiency of k th employee; t o t a l p _ t p i j is the total proficiency of time period t p i j for the employee assigned to working shifts.
(1) Average workload coverage Ave_Coverage . Ave_Coverage can be computed by the whole workload and total assigned employees’ proficiency (n days and each day ω time periods), which can be defined as below.
where t p i j is the j th time period of i th day; t o t a l p _ t p i j is the number of total assigned employee proficiency for t p i j ; W _ t p i j is the workload of t p i j ; n is the number of days in scheduling horizon; ω is the number of time periods in one day; t is the number of employees. No matter the average workload coverage of one day or one time period, it should be closest to 1. If coverage > 1, it means that the assigned proficiency is too much and more than the requirement of the workload, which causes the waste of employee proficiency. When coverage < 1, it means the assigned proficiency is too little and less than the requirement of the workload, where the workload can not be finished.
(2) Coverage fairness Coverage_Fairness can be computed by the whole workload and total assigned employees’ proficiency, which can be defined as below.
where t p i j is the j th time period of i th day; t o t a l p _ t p i j is the number of total assigned employee proficiency for t p i j ; W _ t p i j is the workload of t p i j ; Ave_Coverage is the average workload coverage for n days, which can be computed by Eq. ( 2 ); n is the number of days in scheduling horizon; ω is the number of time periods in one day; t is the number of employees. Coverage fairness should be minimal, which means the coverage fluctuation of time periods.
(1) Each employee consecutively works max days at most, but no less than min days, which can be defined as below.
minimal day constraint:
maximal day constraint:
(2) Each employee should have r rest days for the whole scheduling horizon and any two consecutive rest days are not allowed, which can be defined as below.
Traditional objective function gathers all objectives with weights, but the weights need more time to be adjusted. Hence, this paper used the TOPSIS to evaluate the indicated solutions without weights. More details are presented as our other work 15 .
Where function TOPSIS measures two optimization objectives to generate a score at the same time, here, the score is higher, the quality of the result is better, the score is lower the quality of the result is worse.
To generate a feasible schedule with flexible work time, a naive way to address this problem is to traverse all the potential schedules, and select the best result among them as the final solution. However, such a method requires prohibitive computation consumption, since the number of potential schedules grows exponentially as the number of employees increases.
The overview of our approach.
Hence, we propose a fast-flextime strategy based approach (FFS) to efficiently search for a feasible schedule, which is a polynomial-time method. For ease of understanding the main idea of FFS, the pseudo-code of algorithm overview is presented in Algorithm 1. To be more specific, we generate the employee assignment over days (line 1), and the employee assignment of each day is generated by four modules, namely, satisfying constraints SATISFY_CONSTRAINTS () (line 2), estimating employee number ESTIMATE_NUMBER () (line 3), searching feasible assignments SEARCH_ASSIGNMENT () (line 4) and deciding flexible work time DECIDE_FLEXTIME () (line 5).
To ensure the availability of the generated schedule, SATISFY_CONSTRAINTS () is required to meet the hard constraints. Its pseudo-code is presented in Algorithm 2. SATISFY_CONSTRAINTS () takes a set of employees ( E ), the certain day ( d i ) and the number of days in scheduling horizon ( D ) as input, and output is available employee set ( available_E ).
SATISFY_CONSTRAINT ( E , d i ,| D |).
To achieve satisfying hard constraints, SATISFY_HCONSTRAINT () adopts the constraint control mechanism based on scheduling cycle ( SC ), which is composed of ξ consecutive workdays and a rest day, e.g. the shift sequence ( sft_1 , sft_2 , rest-day ) contains 2 working days and 1 rest-day, which can compose a SC . The types of such SC are dependent on max and min . Since H 2 asks each employee works max days at most, but no less than min days, we get ξ ∈ [ min , min ]. Suppose that min =2, max =4, the scheduling cycles contain three types, i.e. 2W+1R (2 workdays and 1 rest-day), 3W+1R (3 workdays and 1 rest-day) and 4W+1R (4 workdays and 1 rest-day).
Then SATISFY_CONSTRAINTS() computes the DCT of each employee (line 3), which can be divided into 3 categories: the number of days before the first rest-day q , the number of days in all types of scheduling cycles ∑ a g · G , and the left days t , as Fig. 2 shows.
Classification of time points in DCT.
Note that the first rest day of each employee does not belong to any type of scheduling cycle, and H 3 asks for r rest day for each employee in the scheduling horizon. Hence, the total number of scheduling cycles for each employee is r - 1 . Besides, as for t , due to the minimal number of consecutive workdays are set to min days, as long as t ≤ m i n , employees will be assigned to shifts in these t days, and the total number of rest-days for each employee are fixed to r days.
The formal for computing DCT is as below.
According to the above operations, SATISFY_HCONSTRAINT () module computes DCT of each employee. Since the serial number of rest days is different for each employee, their DCT is different. For each employee e k ∈ E , SATISFY_HCONSTRAINT () will check the return value ( sign(g) ), and identify the availability of employees. Here, SATISFY_HCONSTRAINT () traverses previous max shifts for each employee, and the number of workdays in this shift sequence is marked as NUM , which is treated as a trigger to search for suitable SC. There may exist three situations:
The available employees of d i are generated by SATISFY_HCONSTRAINT (). Suppose that the number of available employees is β , given five types of shifts (defined in Para.1 Page 3), if we assign directly available employees to shifts, each employee can be assigned to anyone in these five types of shifts, and thus, the number of potential assignments is 5 β , i.e. exponential. To avoid such a situation, we invoke the procedure ESTIMATE_NUMBER () (as algorithm 3 shows), which takes available employees and the workload of each time period in d i as inputs, and the output is the estimated number of employees required for each shift of d i . In the following, we give an example to show how it works, combined with Algorithm 3.
Estimate_number( available_E , W_tp i j ).
First, according to the work time of each shift, we count the sharing work time periods share_TP among different shifts. For instance, given three shifts of d i , i.e. sft_1 , sft_2 , sft_5 and their work time are [ t p i 1 , t p i 18 ], [ t p i 2 , t p i 22 ] and [ t p i 13 , t p i 30 ], respectively, These work time are divided into different share time periods as Fig. 3 shows (line 1), e.g. share_TP 1 =[ t p i 1 , t p i 2 ), share_TP 2 =[ t p i 2 , t p i 13 ). Then we compute the average workload AW_share_TP z of each sharing work time period share_TP z (line 2). Next, we establish the workload function as follows (line 3) to estimate the workload of each shift of d i .
Example of computing sharing work time among shifts.
Where AW_share_TP z represents the average workload of share_TP z , λ is a parameter for checking whether share_TP z belongs to the work time of the corresponding shift, W_sft_t is the workload of sft_t .
Note that if share_TP z belongs to the work time of sft_t , λ = 1 ; Otherwise, λ = 0 . Thus, Eq. ( 11 ) represents that the average workload of share_TP z is composed of the workload of each shift. However, estimating the workload of each shift by solving Eq. ( 11 ) is so strict that there may not exist a feasible solution, since the number of sharing work time periods is regularly larger than the type of shifts ( z ≥ t ), Eq. ( 11 ) is an overdetermined function 16 . Hence, we adopt the projected gradient methods to generate the solution of Eq. ( 11 ), where an error Δ b is introduced. Eq. ( 11 ) is converted into Δ b + A W _ s h a r e _ T P z = ∑ t = 1 5 λ W _ s f t _ t , where Δ b should follow that (1) the variance of any two sub-errors is the same, and (2) any two sub-errors are independent 16 . For easing to remember, we denote λ W _ s f t _ t and A W _ s h a r e _ T P z by Ax and B , where A is a matrix composed of λ , x is the estimated workload for each shift of d i and B denotes the workload of each sharing time period. Thus, we get Eq. ( 12 ) from Eq. ( 11 ).
Note that we vary the value of x and make the error Δ b as small as possible. Thus, we use the least square method to reach this goal, which is achieved as below.
where | | Δ b | | reaches the minimum, x is the feasible solution. To get the solution x , we introduce the projected gradient method, which is defined below.
where P C ( x ) denotes the projection operator, C represents the solution space for x , μ is the step length and ∇ f ( x k ) is the gradient vector. The workload of each sharing time period must be greater than 0, hence C = R + n . In this way, we estimate the workload for each shift EW_sft_t (line 4).
However, the proficiencies of all available employees may not satisfy the workloads of shifts. Hence, we need to confirm the total proficiency by total_AP and ∑ EW_sft_t as below.
where total_AP is the total proficiency of all available employees, and ∑ 1 5 E W _ s f t _ t is the total workload of all shifts for d i .
When t o t a l _ A P ≤ ∑ 1 5 E W _ s f t _ t , all the available employees can be assigned to shifts and the number of available proficiency totalap_d i is set to total_AP (lines 5-7). When t o t a l _ A P ≥ ∑ 1 5 E W _ s f t _ t , not all available employees can be assigned to shifts for satisfying S 1 , thus the number of available proficiency totalap_ d i is set to ∑ 1 5 E W _ s f t _ t (lines 7-8).
Based on these, we estimate the number of proficiency ap_sft_t for each shift according to the ratios among EW_sft_t (line 9), and compute the estimated number of employees required for each shift people_sft_t by ap_sft_t and the average proficiency of all available employees average_AP (lines 10-11), then return people_sft_t (line 12).
According to the estimated number of employees for each shift of d i , SEARCH_ASSIGNMENT () requires to select employees and assign them to the corresponding shifts, which should follow the principle that the average proficiency of employee combinations for each shift should be maximally close to average_AP , since the closer to average_AP the average proficiency of employee combinations is, the smaller the values of | 1 - A v e _ C o v e r a g e | and C o v e r a g e _ F a i r n e s s are. Hence, we adopt the pairwise-allocated strategy to achieve this goal, and introduce the proficiency average matrix to boost its efficiency. In the sequel, combined with the procedure SEARCH_ASSIGNMENT () as Algorithm 4 shows, we present more details with the following example as Fig. 4 shows, where there are 7 available employees and their proficiencies are 11, 13.4, 17.3, 12.7, 15.6, 16.1, 14.2, SEARCH_ASSIGNMENT () assigns the estimated number of employees to the corresponding shifts.
Dividing the proficiencies set into two subsets.
SEARCH_ASSIGNMENTS ( available_E , People_ d i ).
First, the proficiencies of all available employees are sorted in ascending order (line 1), and they are divided into two subsets (i.e. AP_1 and AP_2 ) according to average_AP (line 2), where AP_1 ={11, 12.7, 13.4, 14.2} and AP_2 ={15.6, 16.1, 17.3}. Then we compute the available value of any two proficiency in AP to establish the proficiency average matrix ( PAM ) as Fig. 5 shows (line 3), which is defined as a square matrix of available_E . Next, we take the first proficiencies of AP_1 and AP_2 , denoted by { L 1, R1 }={11, 15.6} (lines 4-6). Subsequently, we sort People_sft_t in an ascending order, which stores the estimated number of each shift, and starts with the least number of shifts (lines 6-7).
The example of establishing the average proficiency matrix.
Subsequently, we get the corresponding employee combination ec 1 ={ e 1 , e 5 } (lines 8-9), and its the average proficiency average_ec 1 (= 11 + 15.6 2 = 13.3 ) is a trigger to find the next employee combination e c 2 . To ensure the average proficiency of e c 1 and e c 2 be as close to average_AP as possible, the expected average proficiency of e c 2 E p 2 = 2 × a v e r a g e _ A P - a v e r a g e _ e c 1 = 15.4 (line 10). Pairwise-allocated strategy searches the value that is closest to Ep 2 (=15.4) in this PAM . It is worth noting that for satisfying the hard constraint H 1 (i.e. each employee is assigned to at most one shift per day ), the employees in e c 2 are selected from the available employees except e 1 and e 5 (lines 11, 13) as Fig. 6 shows, and based on this, e c 2 = { e 6 , e 7 } , since the average proficiency of e 6 and e 7 is 15.15, which is closet to E p 2 (= 15.4 line 10) (line 12).
The example of searching e c 2 .
In the sequel, the pairwise-allocated strategy computes the expected average proficiency of e c i ( i ≥ 3 ) and locates e c i in the same way until the total number of employees in the selected groups equals the estimated number (line 14). Note that, if the estimated number of employees is odd, the last employee is treated as a group, whose selection way also follows the principle that the average proficiency of this group should be maximally close to the expected average proficiency (lines 15-16).
Then, we select the first proficiency in A P _ 1 and the second proficiency A P _ 2 , denoted by { L 1, R 2}={11, 16.1}, and the corresponding employee group e c 1 = { e 1 , e 6 } is utilized to generate the next candidate assignment until all combinations of proficiency between AP_1 and AP_2 are listed.
In the end, we introduce the TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution, TOPSIS 17 ) to evaluate the selected assignments, where each one will be scored by TOPSIS. The assignment with the highest score is treated as the feasible schedule (line 17). Traditional multiple-objective optimization algorithms usually use the linear weighted method, which uses weights to transform different optimization objectives into one. However, weight setting requires a large amount of domain knowledge and expert experience, and needs a lot of time to choose suitable weights. Compared with these, TOPSIS rarely considers the weights among the optimization objectives, and this is the reason for choosing TOPSIS. The more details are explained in reference 17 .
To maximally satisfy the workload of each time period for each day, the assignments generated from Sect. " Searching feasible schedule " require deciding the flexible work time of each shift. To achieve this goal, we invoke the procedure DECIDE_FLEXTIME () (as Algorithm 5 shows), which takes the feasible assignment ( fa ) as the input, and the output is the feasible schedule with flexible work time ( fs ).
First, according to the feasible assignment fa , we compute the total average proficiency of fa (lines 1-2). Based on these, we compute the coverage of each time period for the assignment of d i , and get the employee sets for each shift, i.e. E_sft_t (lines 3-5). Next, we get the corresponding proficiency sets for these employee sets, and sort the proficiencies of them in ascending order (line 6).
Then we need to confirm the flexible work time of each shift (lines 7-8), which is divided into three categories, i.e. the start work time periods, the end work time periods and the meal break, hence we propose three corresponding strategies to deal with these.
DECIDE_FLEXTIME ( available_E , ap , fs ).
Strategy 1: (The flexible start work time periods) The time periods for flexible start work are [ t p i 1 , t p i 4 ], we need to compare the coverages of these time periods with Average_fs in turn. For each coverage C i j of the time period t p i j ∈ [ t p i 1 , t p i 4 ], if C i j ≥ A v e r a g e _ f s , we remove the proficiency in P_sft_t in turn. The reason is that the workloads of these time periods are small, and removing the proficiency from smallest to largest will make coverage maximally get close to Average_fa , on the premise of decreasing the influence on the coverage of these time periods (lines 9-10). In addition, if e k is working in the time period t p i j - 1 , he can not be set to rest in t p i j .
Strategy 2: (flexible end work time periods) The time periods for flexible end work are [ t p i 27 , t p i 30 ] and we compare coverages of these time periods with Average_fs in decreasing order in turn, then we do the same operations (lines 11-12) in strategy 1. Similarly, if e k is working in the time period t p i j + 1 , he can not be set to rest in t p i j .
Strategy 3: (flexible meal break) Different from the start and end work time periods, each employee must have a meal break, when he can have lunch or supper. In addition, the meal break is divided into lunch meal time and dinner meal time, hence we should identify which one belongs to the shift sft_t of e k (line 13-14,18). Based on these, if sft_t contains the lunch meal time, we select the higher coverage ratio of the time periods t p i 7 , t p i 8 , t p i 9 and t p i 10 , denoted by c i j (line 15). Next, we set employees in E_sft_t starting with the largest proficiency, the corresponding proficiency is removed, and C i j is renewed (lines 16-17). Then we check the adjacent time periods of t p i j to have a longer meal time (line 18). If sft_t contains the dinner meal time, we do the same operations on the time periods of the dinner meal, i.e, [ t p i 19 , t p i 21 ] (lines 19-23).
Thus, each employee assigned to shifts of d i has flexible work time and meal break, and is added to the assignment of d i in the feasible schedule ( fs ) (line 22). Finally, when the assignments of all days in the scheduling horizon are performed DECIDE_FLEXTIME (), fs is treated as the feasible schedule with flexible work time and returned (line 23).
This subsection discusses each module of our approach in terms of time complexities by the book with the title “New Generation Computer algorithm” 18 . Then, the existing algorithms are compared to our algorithm with time complexity.
SATISFY_CONSTRAINTS This module is composed of two parts: dynamic combination table (DCT) computation and DCT query. Since the dynamic combination tablets can be generated in advance, this part of time complexity is negligible. In the part of the DCT query, due to the number of types of scheduling cycles being constant, hence its time complexity is O (1).
ESTIMATED_NUMBER This module is composed of a sequential structure, where the highest time complexity is the Gradient Descent Projection (GDP). Although its time complexity is hard to evaluate, this computation can be processed in advance. As for other operations in this module, the computation is constant and the time complexity is O (1).
SEARCH_ASSIGNMENT In this module, the available employees are divided into two sub-sets. In the worst case, the number of first employee combinations is ( n 2 ) 2 . The next employee combination will be selected by whose proficiency can make the first one’s proficiency closest to the average proficiency O (1). Thus, the time complexity of this module is O ( n 2 ) .
DECIDE_FLEXTIME This module decides the work time of each employee in sequential order. Hence, its time complexity is O (n).
Based on these, the time complexity of our approach is O ( m · n 2 ), where m is the number of days on the scheduling horizon.
Our problem is a new one, the heuristic algorithm is designed for a specific problem, hence the existing heuristic algorithm is unsuitable for our problem, only general algorithms such as meta-heuristic algorithms can adapt to our problem. However, due to randomness of the generated results, the meta-heuristic algorithm (NSGA-II 19 , IPSO 20 , PICEA-g 21 , MOEAD 9 and GF 22 ) are required to run multiple times for deciding final results with rather high quality. Besides, they usually generate initial individuals and adopt evolutionary mechanisms to generate new individuals, then compare them to choose the better ones. Due to the mechanism of choosing, their time complexity is different. NSGA-II and MOEAD are O ( β · n 2 ) and O ( β n T ) , where β denotes the number of individuals of one generation, and T is the number of neighborhoods. IPSO is O ( n !), PICEA-g is O ( n 3 ) . GF is a novel general framework, which gathers the existing meta-heuristic algorithms whose time complexity ranges from O ( β n T ) to O ( n !). As for the MILP, we use the Gurobi solver 9.1 and the solution is a branch and bound method, the time complexity is O ( n !).
In general, the time complexity of our algorithm is less than others.
In this section, we experimentally evaluate the efficiency and effectiveness of our proposed solution FFS against the state-of-the-art. We implement our algorithm in Python, and adopt the Python implementations of all competitors based on the following methods: Mixed-Integer Linear Programming (MILP 12 ), Improved Particle Swam Optimization (IPSO 20 ), A Fast and Elitist Multiobjective Genetic Algorithm (NSGA-II 19 ), the Preference-inspired Co-evolutionary Algorithm Using Goal Vectors (PICEA-g 21 ), Multi-objective Evolutionary Algorithm based Decomposition (MOEAD 9 ) and a general multi-objective algorithm framework (GF 22 ), which are listed in Table 1 . The MILP adopts Gurobi solver 9.1 23 to generate solutions. NSGA-II 19 , MOEAD 9 and PICEA-g 21 are three multi-objective evolutionary algorithms (MOEAs), and MILP 12 belongs to the mathematical methods, the IPSO 20 is the heuristic algorithms, and the GF 22 is one of novel general framework for solving multi-objective optimization problems.
The data sets used in experiments.
Methods | Category | Year |
---|---|---|
NSGA-II | Meta-Heuristic | 2021 |
MOEAD | Meta-Heuristic | 2020 |
MILP | Mathematical | 2020 |
IPSO | Meta-Heuristic | 2020 |
PICEA-g | MOEA | 2021 |
GF | Meta-Heuristic | 2020 |
Besides, to compare the performance of FFS and five methods with the considerations of fairness and accuracy, we (1) report the response time of each method by generating the same feasible schedule results, and (2) report the TOPSIS score of each method under the same response time. all evaluations in this section are performed based on a mixture of real and synthetic data sets. The real part is provided by the call center of China Telecom company, which is the call arrivals of six months from July 2020 to Dec. 2020. The synthetic part is the employees, which are synthesized from the real employees of a call center in China Telecom company. Both of these parts are listed in Table 2 , where the number of employees is the real-life data. We synthesize five employee sets for each month, whose number of employees are 40, 60, 80, 100 and 120, respectively. We synthesize these employee sets by randomly choosing part of employees in real life as the added or reduced employees. In addition, each employee in these employee sets has a proficiency. Note that each experiment runs 10 times by randomly choosing the corresponding quantity of employees, and reports the average result. All the experiments are conducted on a server machine with an Intel Intel(R) Xeon(R) CPU E5-2637 3.50 GHz processor and 8GB RAM, running Windows 10 with Python 3.8.
Datasets | Days | Call arrivals | Employee number |
---|---|---|---|
July 2020 | 30 | 37,691 | 81 |
Aug. 2020 | 31 | 38,037 | 60 |
Sept. 2020 | 31 | 35,991 | 76 |
Oct. 2020 | 30 | 37,110 | 70 |
Nov. 2020 | 31 | 38,133 | 86 |
Dec. 2020 | 30 | 36,510 | 79 |
We totally set 6 sets of experiments to evaluate the performance of FFS and five alternatives, the parameters in each experiment are illustrated in Table 3 , where the same quality means that five alternatives aim at generating a schedule with the quality same to that of FFS generating and report their response time, same run-time means that their response time is set to be same to that of FFS generating a schedule and report the quality of their schedules. EXP1 to EXP4 evaluate the overall performance difference among FFS and five alternatives by varying the number of employees and datasets. EXP5 and EXP6 evaluate the internal performance difference by removing the flextime-strategy, pairwise-allocated strategy and proficiency in turn.
The parameters used in experiments.
EXPs | Data sets | Employee quantity | Same run-time | Same quality |
---|---|---|---|---|
EXP1 | – | 80 | ||
EXP2 | – | 80 | ||
EXP3 | Oct. | 80 | ||
EXP4 | Oct. | 80 | ||
EXP5 | Oct. | – | ||
EXP6 | Oct. | – | ||
EXP7 | – | 80 | ||
EXP8 | Oct. | 80 |
Exp 1: search efficiency.
The first set of experiments verifies the performance of FFS by varying datasets, compared with the other six alternative methods. The result is shown in Fig. 7 a. The first observation is that FFS has the shortest response time in all cases, with MILP, GF and NSGA-II in the second place, and MOEAD, PICEA-g and IPSO are the worst. Specifically, FFS outperforms MILP, GF and NSGA-II by one order of magnitude, and is faster than PICEA-g, IPSO and MOEAD two orders of magnitudes. The reason is that MILP needs to consider all the potential assignments, and even if adopting a series of fast computing sub-algorithms such as the simplicissimum method, MILP remains to be time-consuming. GF adopts the universe methods to solve this problem, but they lack of optimization strategy for our problem. As for NSGA-II, it adopts a fast non-dominated sorted strategy to speed up the convergence of solutions. MOEAD, PICEA-g, and IPSO require enough generation operations to get the feasible solutions, due to their random nature of query strategies; while FFS adopts the pairwise-allocated strategy to effectively shrink the number of potential assignments, which makes the feasible assignment query execute in a small solution space. The second observation is that FFS achieves the most stable performance and MOEAD fluctuates most greatly. The reason is that FFS effectively reduces the number of potentially feasible assignments, owing to pairwise-allocated strategy. While MOEAD requires the operations of mutation and crossover to generate the new assignments, and select ones with the quality higher than old assignments. However, the operations of mutation and crossover contain the nature of randomness, which results in the instability of newly generated solutions.
Overall effectiveness and efficiency with different data sets.
EXP 2 runs under the condition of running the same time and reports the TOPSIS score of each method as illustrated in Fig. 7 b. It is seen that when changing the datasets, the TOPSIS score of FFS changes slightly, and gets the highest TOPSIS score. It is because, the flextime strategy of FFS according to the coverage ratio of each time period changes the work time of each employee, which follows the principle that each employee should have r rest days for each month and can not be assigned to rest day for two consecutive days. Thus, it ensures that two optimization goals (i.e. Ave_Coverage and Coverage_Fairness ) can be closer to the optimal values. In addition, pairwise-allocated strategy in FFS selects suitable employee combinations according to the soft constraint S 1 , and assigns them to the corresponding shifts. Hence, the TOPSIS score performs best. As for the NSGA-II, MOEAD and PICEA-g, these MOEAs usually require a large number of generations to ensure the quality of their solutions, but the time cost of this experiment is little, which limits the number of generations and the solutions of MOEAs can not be guaranteed to be high-quality. The MILP also faces a similar situation, which considers all the potential schedules and requires enough computations to support its search sub-algorithms, but the limited time cost weakens the quality of its solution. As for the IPSO, it is easy to fall into local-optimal status, hence, when the first solution is high-quality, it will get some better solutions than MOEAD, NSGA-II, MILP and PICEA-g. However, when the quality of the initial solution is low, it may have low-quality solutions in the final. All of these deeply influence the quality of the generated schedule, and lead to that the quality of solutions from our approach is superior to that of others.
The third set of experiments evaluates the impact of the number of employees on search efficiency. The result is depicted in Fig. 8 a. The first observation is that the response time of FFS slightly increases as the number of employees grows. It is because that, for FFS , the search space shrunken by pairwise-allocated strategy gets larger with the increasing number of employees, and FFS spends more time searching the suitable employee groups. The second observation is that the time cost of MILP and GF increases as the number of employees grows. The reason is that the number of potential feasible schedules increases exponentially for MILP and GF, although they contain a series of pruning techniques to reduce the search space, it remains to be pretty large and the growth of employee number adds to their response time. The third observation is that the response time of MOEAD, NSGA-II and PICEA-g fluctuates with the increase in the number of employees. The reason is that, they randomly initialize individuals, and generate the feasible schedule based on the search strategy with the nature of randomness, which leads to unstably of their generated schedules. To reach the quality of a fixed schedule, they have to spend more generations to find a suitable schedule, and are presented in the fluctuation of response time. As for IPSO, it is easy to fall into local-optimal, the time cost of running one is pretty short, but the quality of the generated schedule can not reach the fixed schedule, it will run again until it does. Thus, the total time cost is comparatively higher than others.
Overall effectiveness and efficiency with the number of employees.
Figure 8 b shows the result of each method by varying the number of employees. It is observed that the TOPSIS score of FFS increases as the number of employees grows. It is because more employees mean more potential employee combinations, and thus, there is a higher possibility for FFS selecting the employee groups whose proficiency is nearest to the workload of shifts. Hence, the TOPSIS of FFS will increase with the number of employees growing. However, since the time cost is limited to that of FFS costing and it is too short, all alternatives’ query strategies are time-consuming, which results in a low number of generations and computations for MOEAs, IPSO and MILP. Thus, their generated schedules are of low quality. In view of these, the TOPSIS score of FFS is the highest in all cases.
Exp 5: internal performance vs. different datasets.
The fifth set of experiments evaluates the internal impact of the performance of pairwise-allocated PA strategy and proficiency average matrix PAM by varying the datasets. We compare FFS with five alternative methods, i.e. FFS-NoFlextime , FFS-NoPAM and Enumeration , respectively. FFS-NoPAM removes the Average Proficiency Matrix PAM , and Enumeration enumerates all potential schedules. The result is illustrated in Fig. 9 a. It is observed that FFS is faster than FFS-NoPAM and Enumeration on all datasets. In particular, FFS is faster than FFS-NoPAM by two orders of magnitudes, and outperforms Enumeration by 3 orders of magnitude in average, respectively. This is because, compared to Enumeration , FFS and FFS-NoPAM contain PA , which greatly reduces the number of potential schedules. This indicates that PA effectively shrinks the search range and improves efficiency. In addition, FFS adopts the proficiency average matrix ( PAM ) to boost the efficiency, and based on PAM , FFS outperforms FFS-NoPAM one order of magnitude, which indicates that PAM further improve the efficiency of search.
The sixth set of experiments explores the internal effect for FFS by varying the number of employees. The result is plotted in Fig. 9 b. The first observation is that the response time of Enumeration is exponential, the reason is that the number of employee assignments grows exponentially as the number of employees increases, and the corresponding response time for Enumeration generating a schedule presents exponentially. The second observation is that the response time of FFS and FFS-NoPAM still remains low and stable, the reason lies in two aspects: first, they pre-estimate the number of employees for each shift of each day for pre-pruning a large number of potential schedules, which provides a pretty small range for searching the feasible schedule; second, they adopt the pairwise-allocated strategy to assign employees to shifts, where they only need few average proficiency computations instead of computing all employee combinations. The third observation is that the response time of FFS is less than that of FFS-NoPAM . The reason is that, FFS uses the proficiency average matrix to boost the efficiency of the pairwise-allocated strategy. PAM provides the average proficiency of all employees, which prunes the process of computing average proficiency among employees, and PA selects the suitable employee group with only a few computations.
EXP 7 aims to explore the impact of the performance of flextime strategy on different datasets. The result is shown in Fig. 10 a. It is seen that FFS has a higher TOPSIS score than FFS-NOFlextime . The reason is that the flextime strategy sets the flexible work time for each employee, which makes the assigned proficiency satisfy the workloads of different time periods in a fine-grained way. Then more satisfying workloads will present with higher TOPSIS scores.
TOPSIS score of FFS by varying parameters.
The eighth set of experiments aims to explore the impact of the performance of the flextime strategy by varying the number of employees. The result is shown in Fig. 10 b. Similar to EXP7, FFS has a better TOPSIS score than FFS-NoFlextime , and it is because that FFS adopts the flextime strategy to adjust the work time of employees for each day, the understaffing and overstaffing phenomenons have been improved.
Employee scheduling problem is of significant importance in industries, such as healthcare, retail, and manufacturing. It made a great deal of progress in the past decades, and can be classified into three categories.
The first category is the mathematical methods, which model their employee scheduling problems and adopt open solvers such as LP 24 , 25 , IP 26 , 27 and MIP 28 solvers to generate feasible schedules. Basán et al. 29 proposed a novel MILP-based decomposition method, for solving employee scheduling problems arising in manufacturing environments. However, this method requires a large amount of domain knowledge to model the problem. Meng et al. 12 proposed four mixed integer linear programming (MILP) models as well as a constraint programming (CP) model to address the distributed flexible job shop scheduling problem with minimizing optimization goals. However, these works stressed the global result of the optimization objectives, but ignored the balance between the local result of each optimization objective on each day. Lunardi et al. 30 present mixed integer linear programming and constraint programming models to address a flexible job shop scheduling problem with sequence flexibility in which precedence constraints among operations of a job. Although this work is performed well on small, medium, and large-sized instances, it generates the schedule with a one-day scheduling horizon, which arises in certain scenarios. A longer scheduling horizon (i.e. a week, a month, or longer) is a more regular phenomenon for most scenarios, and it means more difficult challenges such as temporal constraints. Our approach sets the hard constraints for these temporal constraints, and adopts a series of strategies to address the employee scheduling problem effectively and efficiently.
Although this category of the method has high effectiveness, a large amount of computation leads to low efficiency and high responding time. These methods do not provide the allocated strategy and search strategy as FFS does, and limit themselves to similar trips or other mathematical methods.
The second category is the meta-heuristic algorithm (MHA), which is one type of general algorithm and is suitable for solving most employee scheduling problems. Hence it has been treated as one of the most used algorithms 31 – 33 . Plenty of meta-heuristic algorithms have been developed for searching the PARETO solutions and attracted an increasing number of interests 34 , 35 . The Non-dominated Sorting Genetic Algorithm (NSGA-II 19 ) and Multi-objective Evolutionary algorithm based on decomposition (MOEA/D 9 ) are two classical MHAs. The PARETO-based rank and crowding distance are proposed to assign the fitness values to each individual, while MOEA/D transforms a multi-objective optimization problem into several single-objective sub-problems, then EA searches the optimal solutions of these sub-problems in parallel 36 . Yuan et al. 37 proposed an improved Non-dominated Sorting Genetic Algorithm (NSGA-II) algorithm, which presents a novel evaluation function based on ranking level and crowding degree, then the variable proportion-based elitist retention is designed to help generate the optimal solution. However, this method continues to require a large number of generation operations for generating stable and high-quality PARETO solutions. Wang et al. 38 proposed a hybrid multi-objective evolutionary algorithm based on decomposition (HMOEA/D) to solve the problem. They set a cooperative search operator to generate new solutions, and design an adaptive selection strategy based on the reference point for using the local search operators to enhance exploitation ability.
However, MHAs usually have high time complexity, and due to the randomness of initial conditions and search strategy, they often need to run repeatedly to generate relatively stable results. Our approach adopts the pairwsie-allocated strategy to search for a high-quality schedule, establishes a proficiency average matrix to boost its efficiency, and optimizes the quality of the schedule by flextime strategy.
The third category is the heuristic method, which usually is designed for specific problems. It adopts a series of heuristic strategies to reduce the search space, which aims to speed up the search efficiency and is required to lose part of the result quality. Li et al. 39 propose a hybrid of iterated greedy and simulated annealing algorithms (IGSA algorithm) to address the flexible scheduling problem, where an improved construction heuristic considering the problem features is proposed to balance the exploration abilities and time complexity. Alzaqebah et al. 40 present an improved Bee Colony Optimization algorithm for the flexible work time scheduling problem, where a self-adaptive mechanism is used to adaptively select the neighborhood structure to enhance the local intensification capability of the algorithm and to help the algorithm escape from a local optimum. However, this method requires a large number of iteration operations to ensure the feasibility of the generated schedule, which is time-consuming. Khaniyev et al. 41 address the operating room scheduling problem with the conflicting priorities and preferences of various stakeholders and the inherent uncertainty of surgery duration. They propose a hybrid heuristic algorithm, which defines the objective function in terms of auxiliary functions with a recursive pattern to exactly analyze the optimal surgery duration. However, this method needs too much domain knowledge to build the heuristic models, and high time consumption.
However, heuristic algorithms can be used to solve specific problems, when the problem is changed, the existing algorithm may not be suitable for the new one.
This paper proposes FFS , a polynomial-time solution for soft work time scheduling problems. FFS uses the pairwise-allocated strategy to pre-estimate the number of employees for each shift of each day, which effectively shrinks the number of potential assignments, and the proficiency average matrix is established for boosting its efficiency. In addition, it proposes the flextime strategy to decide the soft work time of each employee for each day, which makes the assigned proficiency satisfy the workload of each time period for each day better. Extensive experimental evaluation shows that FFS is more effective and efficient than the baselines (i.e. MILP , IPSO and MOEAD ), as EXP1-EXP6 shows. Besides, we test the performance of flextime-strategy in improving the effectiveness of FFS , as EXP7-EXP8 shows. Hence, FFS outperforms the state-of-the-art in our problem.
This work was supported by the National Natural Science Foundation of China (Grant No. 82011530399), the Zhejiang Province Key Research and Development Program (Grant No. 2021C01189), Leading talents of Science and Technology Innovation in Zhejiang Province (Grant No. 2020R52042), Zhejiang-Netherlands Joint Laboratory for Digital Diagnosis and Treatment of oral diseases, and Major Scientific Research Innovation (team) Project “Research and Application of Multi-objective Collaborative Intelligent Control Method”.
K.M.: Conceptualization, Investigation, Methodology, Data curation, Validation, and Writing-Original draft preparation. C.Y.: Data curation, Validation, Supervisor, Resources, Funding acquisition, and Writing-Reviewing and Editing. H.X.: Resources, Validation, Funding Acquisition, and Reviewing. H.L.: Resources, Funding acquisition and Validation. F.H.: Methodology, Validation, Data curation, Supervision, Funding acquisition, and Writing-Reviewing and Editing.
Competing interests.
The authors declare no competing interests.
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Decomposed diffusion sampler for accelerating large-scale inverse problems.
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