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Handbook on Problem Solving Skills

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In this paper we discuss how the interests and field theory promoted by public administration as a stakeholder in policy argumentation, directly arise from its problem solving activities, using the framework for public administration problem solving we proposed in [1,2]. We propose that calls for change of policy in public administration mainly arise from model-based diagnosis problem solving.

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Effective Problem-Solving Techniques in Business

Problem solving is an increasingly important soft skill for those in business. The Future of Jobs Survey by the World Economic Forum drives this point home. According to this report, complex problem solving is identified as one of the top 15 skills that will be sought by employers in 2025, along with other soft skills such as analytical thinking, creativity and leadership.

Dr. Amy David , clinical associate professor of management for supply chain and operations management, spoke about business problem-solving methods and how the Purdue University Online MBA program prepares students to be business decision-makers.

Why Are Problem-Solving Skills Essential in Leadership Roles?

Every business will face challenges at some point. Those that are successful will have people in place who can identify and solve problems before the damage is done.

“The business world is constantly changing, and companies need to be able to adapt well in order to produce good results and meet the needs of their customers,” David says. “They also need to keep in mind the triple bottom line of ‘people, profit and planet.’ And these priorities are constantly evolving.”

To that end, David says people in management or leadership need to be able to handle new situations, something that may be outside the scope of their everyday work.

“The name of the game these days is change—and the speed of change—and that means solving new problems on a daily basis,” she says.

The pace of information and technology has also empowered the customer in a new way that provides challenges—or opportunities—for businesses to respond.

“Our customers have a lot more information and a lot more power,” she says. “If you think about somebody having an unhappy experience and tweeting about it, that’s very different from maybe 15 years ago. Back then, if you had a bad experience with a product, you might grumble about it to one or two people.”

David says that this reality changes how quickly organizations need to react and respond to their customers. And taking prompt and decisive action requires solid problem-solving skills.

What Are Some of the Most Effective Problem-Solving Methods?

David says there are a few things to consider when encountering a challenge in business.

“When faced with a problem, are we talking about something that is broad and affects a lot of people? Or is it something that affects a select few? Depending on the issue and situation, you’ll need to use different types of problem-solving strategies,” she says.

Using Techniques

There are a number of techniques that businesses use to problem solve. These can include:

• Five Whys : This approach is helpful when the problem at hand is clear but the underlying causes are less so. By asking “Why?” five times, the final answer should get at the potential root of the problem and perhaps yield a solution.
• Gap Analysis : Companies use gap analyses to compare current performance with expected or desired performance, which will help a company determine how to use its resources differently or adjust expectations.
• Gemba Walk : The name, which is derived from a Japanese word meaning “the real place,” refers to a commonly used technique that allows managers to see what works (and what doesn’t) from the ground up. This is an opportunity for managers to focus on the fundamental elements of the process, identify where the value stream is and determine areas that could use improvement.
• Porter’s Five Forces : Developed by Harvard Business School professor Michael E. Porter, applying the Five Forces is a way for companies to identify competitors for their business or services, and determine how the organization can adjust to stay ahead of the game.
• Six Thinking Hats : In his book of the same name, Dr. Edward de Bono details this method that encourages parallel thinking and attempting to solve a problem by trying on different “thinking hats.” Each color hat signifies a different approach that can be utilized in the problem-solving process, ranging from logic to feelings to creativity and beyond. This method allows organizations to view problems from different angles and perspectives.
• SWOT Analysis : This common strategic planning and management tool helps businesses identify strengths, weaknesses, opportunities and threats (SWOT).

“We have a lot of these different tools,” David says. “Which one to use when is going to be dependent on the problem itself, the level of the stakeholders, the number of different stakeholder groups and so on.”

Each of the techniques outlined above uses the same core steps of problem solving:

• Identify and define the problem
• Consider possible solutions
• Evaluate options
• Choose the best solution
• Implement the solution
• Evaluate the outcome

Data drives a lot of daily decisions in business and beyond. Analytics have also been deployed to problem solve.

“We have specific classes around storytelling with data and how you convince your audience to understand what the data is,” David says. “Your audience has to trust the data, and only then can you use it for real decision-making.”

Data can be a powerful tool for identifying larger trends and making informed decisions when it’s clearly understood and communicated. It’s also vital for performance monitoring and optimization.

How Is Problem Solving Prioritized in Purdue’s Online MBA?

The courses in the Purdue Online MBA program teach problem-solving methods to students, keeping them up to date with the latest techniques and allowing them to apply their knowledge to business-related scenarios.

“I can give you a model or a tool, but most of the time, a real-world situation is going to be a lot messier and more valuable than what we’ve seen in a textbook,” David says. “Asking students to take what they know and apply it to a case where there’s not one single correct answer is a big part of the learning experience.”

Make Your Own Decision to Further Your Career

An online MBA from Purdue University can help advance your career by teaching you problem-solving skills, decision-making strategies and more. Reach out today to learn more about earning an online MBA with Purdue University .

If you would like to receive more information about pursuing a business master’s at the Mitchell E. Daniels, Jr. School of Business, please fill out the form and a program specialist will be in touch!

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MQ quasi-interpolation-based level set method for structural topology optimization

• Original Article
• Published: 04 July 2024

Cite this article

• Chen-Dong Yang 1 , 2 ,
• Jian-Hu Feng 1 ,
• Jiong Ren 2 &
• Ya-Dong Shen 3  

Parametric level set method (PLSM) using interpolation method, such as radial basis function (RBF) interpolation, exposes high computational cost and poor stability when solving structural topology optimization (STO) problems with large-scale nodes. However, the quasi-interpolation method can approximate the level set function (LSF) and its generalized functions without solving any system of linear equations. With this good property, this paper utilizes multiquadric (MQ) quasi-interpolation to parameterize the LSF and innovatively introduces it into the STO problem. Moreover, the MQ quasi-interpolation is utilized to compute the element density, which makes the level set band method (LSBM) more rigorous. The proposed methods were compared with the PLSM based on compactly supported radial basis functions (CSRBFs). The results show that the approximation accuracy, computational efficiency and stability of the evolution process of the proposed methods are better than those of CSRBFs when the shape parameter takes a suitable small value.

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A. G. M. Michell, LVIII. The limits of economy of material in frame-structures, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science , 8 (47) (1904) 589–597.

Article   Google Scholar  

M. P. Bendsøe and N. Kikuchi, Generating optimal topologies in structural design using a homogenization method, Computer Methods in Applied Mechanics and Engineering , 71 (2) (1988) 197–224.

Article   MathSciNet   Google Scholar  

M. P. Bendsøe, Optimal shape design as a material distribution problem, Structural Optimization , 1 (4) (1989) 193–202.

D. J. Munk, G. A. Vio and G. P. Steven, Topology and shape optimization methods using evolutionary algorithms: a review, Structural and Multidisciplinary Optimization , 52 (3) (2015) 613–631.

L. Xia, Q. Xia and X. Huang, Bi-directional evolutionary structural optimization on advanced structures and materials: a comprehensive review, Archives of Computational Methods in Engineering , 25 (2) (2018) 437–478.

J. A. Sethian and A. Wiegmann, Structural boundary design via level set and immersed interface methods, Journal of Computational Physics , 163 (2) (2000) 489–528.

M. Y. Wang, X. Wang and D. Guo, A level set method for structural topology optimization, Computer Methods in Applied Mechanics and Engineering , 192 (1–2) (2003) 227–246.

T. Belytschko, S. P. Xiao and C. Parimi, Topology optimization with implicit functions and regularization, International Journal for Numerical Methods in Engineering , 57 (8) (2003) 1177–1196.

S. Mukherjee, D. Lu and B. Raghavan, Accelerating largescale topology optimization: state-of-the-art and challenges, Archives of Computational Methods in Engineering , 28 (7) (2021) 1–23.

S. Xu, J. Liu and B. Zou, Stress constrained multi-material topology optimization with the ordered SIMP method, Computer Methods in Applied Mechanics Engineering , 373 (2021) 113453.

J. Yan, Q. Sui and Z. Fan, Multi-material and multiscale topology design optimization of thermoelastic lattice structures, CMES-Computer Modeling in Engineering Sciences , 130 (2) (2022) 967–986.

T. Ben, P. Zhang and L. Chen, Vibration reduction of reactor using global magneto-structural topology optimization, IEEE Transactions on Applied Superconductivity , 32 (6) (2022) 1–5.

O. Sigmund and K. Maute, Topology optimization approaches, Structural Multidisciplinary Optimization , 48 (6) (2013) 1031–1055.

F. Gibou, R. Fedkiw and S. Osher, A review of level-set methods and some recent applications, Journal of Computational Physics , 353 (2018) 82–109.

S. Wang and M. Y. Wang, Radial basis functions and level set method for structural topology optimization, International Journal for Numerical Methods in Engineering , 65 (12) (2006) 2060–2090.

Z. Luo, M. Y. Wang and S. Wang, A level set-based parameterization method for structural shape and topology optimization, International Journal for Numerical Methods in Engineering , 76 (1) (2008) 1–26.

H. Li, Z. Luo and L. Gao, An improved parametric level set method for structural frequency response optimization problems, Advances in Engineering Software , 126 (2018) 75–89.

N. P. van Dijk, K. Maute and M. Langelaar, Level-set methods for structural topology optimization: a review, Structural and Multidisciplinary Optimization , 48 (3) (2013) 437–472.

P. D. Dunning and H. A. Kim, Introducing the sequential linear programming level-set method for topology optimization, Structural and Multidisciplinary Optimization , 51 (3) (2015) 631–643.

J. Hyun and H. A. Kim, Level-set topology optimization for effective control of transient conductive heat response using eigenvalue, International Journal of Heat and Mass Transfer , 176 (2021) 121374.

H. Li, M. Yu and P. Jolivet, Reaction-diffusion equation driven topology optimization of high-resolution and feature-rich structures using unstructured meshes, Advances in Engineering Software , 180 (2023) 103457.

Y. Liu, C. Yang and P. Wei, An ODE-driven level-set density method for topology optimization, Computer Methods in Applied Mechanics and Engineering , 387 (2021) 114159.

C. D. Yang, J. H. Feng and Y. D. Shen, Step-size adaptive parametric level set method for structural topology optimization, Journal of Mechanical Science and Technology , 36 (10) (2022) 5153–5164.

Y. Wang, Z. Kang and P. Liu, Velocity field level-set method for topological shape optimization using freely distributed design variables, International Journal for Numerical Methods in Engineering , 120 (13) (2019) 1411–1427.

C. D. Yang, J. H. Feng and Y. D. Shen, Two interpolation matrix triangularization methods for parametric level set-based structural topology optimization, International Journal of Computational Methods , 19 (10) (2022) 2250024.

Z. Sun and Y. Gao, A meshless quasi-interpolation method for solving hyperbolic conservation laws based on the essentially non-oscillatory reconstruction, International Journal of Computer Mathematics , 100 (6) (2023) 1303–1320.

R. C. Mittal, S. Kumar and R. Jiwari, A cubic B-spline quasiinterpolation method for solving two-dimensional unsteady advection diffusion equations, International Journal of Numerical Methods for Heat & Fluid Flow , 30 (9) (2020) 4281–4306.

R. C. Mittal, S. Kumar and R. Jiwari, A comparative study of cubic B-spline-based quasi-interpolation and differential quadrature methods for solving fourth-order parabolic PDEs, Proceedings of the National Academy of Sciences, India Section A: Physical Sciences , 91 (3) (2021) 461–474.

R. C. Mittal, S. Kumar and R. Jiwari, A cubic B-spline quasiinterpolation algorithm to capture the pattern formation of coupled reaction-diffusion models, Engineering with Computers , 38 (S2) (2022) 1375–1391.

R. K. Beatson and M. J. D. Powell, Univariate multiquadric approximation: quasi-interpolation to scattered data, Constructive Approximation , 8 (3) (1992) 275–288.

Z. M. Wu and R. Schaback, Shape preserving properties and convergence of univariate multiquadric quasi-interpolation, Acta Mathematicae Applicatae Sinica , 10 (4) (1994) 441–446.

L. Ling, Multivariate quasi-interpolation schemes for dimension-splitting multiquadric, Applied Mathematics and Computation , 161 (1) (2005) 195–209.

L. M. Ma and Z. M. Wu, Approximation to the k -th derivatives by multiquadric quasi-interpolation method, Journal of Computational and Applied Mathematics , 231 (2) (2009) 925–932.

R. Tsai and S. Osher, Level set methods and their applications in image science, Communications in Mathematical Sciences , 1 (4) (2003) 623–656.

MathSciNet   Google Scholar  

H. Li, P. Li and L. Gao, A level set method for topological shape optimization of 3D structures with extrusion constraints, Computer Methods in Applied Mechanics and Engineering , 283 (2015) 615–635.

G. Allaire, F. Jouve and A. M. Toader, Structural optimization using sensitivity analysis and a level-set method, Journal of Computational Physics , 194 (1) (2004) 363–393.

P. Wei, Z. Li and X. Li, An 88-line matlab code for the parameterized level set method based topology optimization using radial basis functions, Structural and Multidisciplinary Optimization , 58 (2) (2018) 831–849.

R. Beatson and L. Greengard, A short course on fast multipole methods, Wavelets, Multilevel Methods and Elliptic PDEs , 1 (1997) 1–37.

P. Wei, W. Wang and Y. Yang, Level set band method: A combination of density-based and level set methods for the topology optimization of continuums, Frontiers of Mechanical Engineering , 15 (3) (2020) 390–405.

J. A. Sethian, Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry Fluid Mechanics, Computer Vision, and Materials Science , Cambridge University Press, New York, USA (1999).

Google Scholar  

Download references

Acknowledgments

The authors gratefully acknowledge the financial support provided by the Science Foundation of Xi’ an Aeronautical Institute (Grant No. 2023KY1202) and the equipment support sponsored by the Big Data Laboratory of Xi’ an Aeronautical Institute.

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School of Science, Chang’an University, Xi’an, 710064, China

Chen-Dong Yang & Jian-Hu Feng

School of Science, Xi’an Aeronautical Institute, Xi’an, 710077, China

Chen-Dong Yang & Jiong Ren

School of Civil Engineering and Architecture, Nanyang Normal University, Nanyang, 473061, China

Ya-Dong Shen

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Correspondence to Jian-Hu Feng .

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Chen-Dong Yang is currently a doctoral student of the School of Science, Chang’an University, Xi’an, China, and a lecturer of the School of Science, Aeronautical Institute, Xi’an, China. His research interests include optimum structural design and mathematical optimization.

Jian-Hu Feng is a Professor of the School of Science, Chang’an University, Xi’an, China. He received his Ph.D. in Aero Engine of Northwestern Polytechnical University Xi’an, China. His research interests include optimum structural design, computational fluid dynamics and high-performance computing technology for scientific and engineering problems.

Jiong Ren is a Lecturer of the School of Science, Aeronautical Institute, Xi’an, China. She received her Ph.D. in School of Aeronautics of Northwestern Polytechnical University Xi’an, China. Her research interests include optimum structural design, computational fluid dynamics and high-performance computing technology for scientific and engineering problems.

Ya-Dong Shen is a Lecturer in the School of Civil and Architectural Engineering, Nanyang Normal University, Nanyang, China. He received Ph.D. in School of Science, Chang’an University, Xi’an, China. His research interests include optimum structural design and foundation treatment.

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Yang, CD., Feng, JH., Ren, J. et al. MQ quasi-interpolation-based level set method for structural topology optimization. J Mech Sci Technol (2024). https://doi.org/10.1007/s12206-024-0625-8

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Received : 30 October 2023

Revised : 21 February 2024

Accepted : 15 March 2024

Published : 04 July 2024

DOI : https://doi.org/10.1007/s12206-024-0625-8

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