Problem Solving Methods

Engineers Solve Problems Problem solving is a powerful human activity. Computers are useful tools in problem solving, but it is the human who actually solves the problem. It is impossible to teach specific facts that will always lead to a solution. The ability to solve problem comes from doing it. Many things must pull together to solve a problem.

Problem Solving Problem solving is a combination of experience, knowledge, process, and art Design process is a series of logical steps that when followed produce an optimal solution given time and resources as two constraints

Problem Solving; cont’ A problem is a situation, quantitative or otherwise, that confronts an individual or group of individuals, that requires resolution, and for which the individual sees no apparent path to the solution.

Problem Solving; cont’ Problem solving is a process, an activity whereby a best value is determined for an unknown, subject to a specific set of conditions. It is a means by which an individual uses previously acquired knowledge, skills and understanding to satisfy the demands of an unfamiliar situation.

What skills must be used when solving a problem? Knowledge Motivation Experience Communication Skills Learning Skills Group Skills

Problem Analysis A distinguishing characteristic of a qualified engineer is the ability to solve technical problems; both art and science Science; knowledge of mathematics, chemistry, physics, etc Art; proper judgment, experience, common sense, and know-how; to know when and how rigorously science should be applied and whether the resulting answer reasonably satisfies the original problem is an art

Techniques for Error Free Problem Solving Always draw a picture of the physical situation,if possible. State any assumptions made. Indicate all given properties on the diagram with their units. Convert units to a given unit system. Label unknown quantities with a question mark.

Skills used in Implementing Problem Solving Strategies Analysis Use logic to: Identify the system to be analyzed Identify the objective Identify relationships Divide the system into parts

Skills used in Implementing Problem Solving Strategies Synthesis Use creativity to: Develop ideas via brainstorming Evaluate the ideas by analysis when enough ideas have been generated

Skills used in Implementing Problem Solving Strategies Decision Making Use logic to compare the various ideas and select the “best” one(s) Generalization - Going from the specific to the broad use abstraction to: Aid in analysis, synthesis, and decision making

3.1 Types of Problems Research Problems Knowledge Problems Troubleshooting Problems Mathematics Problems Resource Problems Social Problems Design Problems

Difficulties in Problem Solving Most common difficulty: failure to use known information. To avoid this problem: Write the problem in primitive form and sketch an accurate picture of the setup (where applicable). Transform the primitive statements to simpler language. Translate verbal problems to more abstract mathematical statement(s) and figures, diagrams, charts, etc.

General Problem Solving Method Define and understand problem Sketch the problem Gather information Generate and evaluate potential solutions Use applicable theories and assumptions Refine and implement solution Verify and test solution

Define and Understand Understand what is being asked Describe input/output (I/O) what are you given knowns what are you trying to find unknowns Sketch the problem

Gather Information Collect necessary data List relevant equations/theories State all assumptions

CHECK YOUR WORK!! Don’t stop at getting an answer!! Think about whether the answer makes physical sense. you are the instructor and you have to turn in final grades. In your haste, you calculate the average of Susie’s grades (100, 70, 90) to be 78 and give Susie a C...

Getting It Right The problem solving process may be an iterative process. If at first you don’t succeed (i.e., the algorithm test fails), try again… The more thorough you are at each step of the problem solving process, the more likely you are to get it right the first time!!

Creative Problem Solving The nine dots shown are arranged in equally spaced rows and columns. Connect all nine points with four straight lines without lifting the pencil from the paper and without retracing any line. Individual Exercise (3 minutes)

Creative Problem Solving

Creative Problem Solving If you enjoy solving puzzles, you will enjoy engineering Crick and Watson figured DNA when they were young Engineers create from nature what did not exist before In this creative process, the engineer marshals skills in mathematics, materials, and other engineering discipline and from these resources create a new solution for a human need

Creative Problem Solving Engineering is not dull or stifling; send people to moon, communication from battlefield, etc Creative artists spent many years perfecting their skills Engineers need patience, practice, and gaining problem-solving techniques by training

Self-Questions for Problem Solving How important is the answer to a given problem? Would a rough, preliminary estimate be satisfactory or high degree accuracy demanded? How much time do you have and what resources are at your disposal? Data available or should be collected, equipments and personnel, etc

Self-Questions for Problem Solving What about the theory you intend to use? Can you use it now or must learn to use it? Is it state of the art? Can you make assumptions that simplify without sacrificing needed accuracy? Are other assumptions valid and applicable? Optimize time and resources vs reliability

Engineering Method Recognize and understand the problem (most difficult part) Accumulate data and verify accuracy Select the appropriate theory or principles Make necessary assumptions Solve the problem Verify and check results

Engineering Method Perfect solutions to real problems do not exist. Simplify the problem to solve it; steady state, rigid body, adiabatic, isentropic, static etc To solve a problem, use mathematical model; direct methods, trial-and-error, graphic methods, etc.

Standards of Problem Presentation Engineers should have ability to present information with great clarity in a neat, careful manner Poor engineering documents can be legal problems in courts Follow standard forms such as shown in the textbooks

Building Effective Leadership Skills Creating Your Own Leadership Legacy

Background/Overview Effective leadership skills are needed more than ever to stay ahead of the competition. Through the examples of five leadership legends, you will hear ideas and strategies that you can incorporate into your personal leadership style to help drive winning results in your organization. Historically, the training of actuaries has underserved the leadership component. Using effective leadership skills can help actuaries be more impactful, and better influence the businesses they support.

The essence of leadership is service to others On a basic level, as a leader, you exist to: Inspire others to strive for excellence Ensure the work environment is safe, challenging, and fair Teach, mentor, provide guidance True leaders put the welfare of the group ahead of their own self-interest “Selfless” does not mean “hands-off” Great leaders enhance institutional capability by driving the actions of others to achieve greatness Leadership is all about helping others to succeed.

The perceived complexity of leadership arises from its seemingly overwhelming number of duties Create and establish strategies Ensure effectiveness and efficiency Communicate openly and often Build solid relationships Act with integrity and fairness Provide counsel and direction Exert influence in the absence of ownership Foster collaboration Motivate, coach and develop others Produce results, meet objectives and exceed goals How can a leader avoid being overwhelmed by this complexity?

Focusing on a few key qualities and incorporating them into every action simplifies the act of leading others, and increases leadership effectiveness There is no standardized approach to effective leadership Your effectiveness as a leader is directly proportional to how well the key qualities you focus on align with your values and your personality My five qualities of a great leader are: Maintains and demonstrates strong convictions Develops and communicates a clear, winning vision Creates a high performance culture Convinces rather than controls Continually learns

Maintain and Demonstrate Strong Convictions Leadership Profile: Joan of Arc

Maintaining and demonstrating strong convictions gives leaders their credibility Integrity Lead by example Personal accountability Strive for excellence “Play for your paycheck” “Bring your ‘A’ game every day” “Average is defined as the best of the worst, or the worst of the best”

Develop and Communicate a Clear, Winning Vision Leadership Profile: Martin Luther King, Jr.

A clear, compelling, winning vision is the cornerstone of building organizational success Establish and articulate a clear vision of the future for your business to inspire commitment from others: Should be “stretch,” but not “folly” Include measurable indicators of progress and success Develop compelling long-term business strategies to achieve the vision: Built with a strong understanding of the external environment Takes into account perspectives and capabilities of your organization and those with which it interacts Ensure broad strategies are translated into clear and effective operating plans and tactical initiatives

Create a High Performance Culture Leadership Profile: Herbert D Create a High Performance Culture Leadership Profile: Herbert D. Kelleher, Southwest Airlines

A High Performing Culture engages, challenges, and fully leverages employees, which promotes innovation and continuous improvement Build your team to win! Assess, then stretch/challenge top players Seek to Redeploy, Rehabilitate, or, if needed, Remove underperformers Hire winners Execute aggressive performance management as part of your overall talent management strategy Set clear performance objectives and expectations Monitor and document performance; reward success, and hold people accountable for poor performance Provide direct, helpful feedback Take corrective action when necessary Pay for performance, pay for potential Drive a culture of open and fast communication to support rapid response to changing business conditions Build inclusion, leverage diversity Continually raise the bar – don’t get complacent

Convince Rather Than Control Leadership Profile: William Wallace - “Braveheart”

Any leader can get work done by barking orders…

…But the enlightened leader convinces people to engage in the right behaviors, gains buy-in, and gives them choices while influencing them to perform at a high level Clearly articulate your point of view and persuade employees to accept your proposal and/or recommendation Project self-confidence without arrogance Develop effective and constructive strategies for influencing important decisions, sometimes shifting the organization’s direction or way of looking at things Use high-impact, efficient communication vehicles to get your points across

Continuous Learning Leadership Profile: Jack Welch

The Profession of Leadership requires continuous learning, just like Actuarial Regularly conduct an honest self-assessment Initiate efforts to develop skills that will enhance performance in current role and/or accelerate readiness for future roles Take full advantage of available learning and development programs, e.g., executive development programs, courses, professional certifications Solicit feedback and guidance from mentors or coaches, then genuinely listen to feedback and apply learnings Seek challenges that provide opportunities for on-the-job development of critical knowledge and skills Ask questions to learn from others with different knowledge, experience or perspective

Summary The essence of leadership is service to others Don’t be overwhelmed by the seemingly endless number of tasks and obligations leadership requires Rather, focus on a few core attributes as you practice the profession of leadership, like these: Have strong convictions Develop and communicate a clear, winning vision Create a high performance culture Convince rather than control Be a continuous learner What qualities of a great leader would you add to this list?

Some Final Thoughts Your role as a leader is more critical than ever Identify a take-away to work on towards building more effective leadership skills What will be your leadership legacy?

Open Discussion