Multi-Dimensional Problem Solving

10 years ago today - on April 2, 2014 - my dear friend and thought partner Patrick McCreesh and I began exchanging texts identifying a "re-humanization renaissance" as a common thread uniting many of the contemporary change approaches and technologies (like design thinking, appreciative inquiry, and wellness). A global pandemic and instantaneous remote work experiment added a new layer where the people side of the organization could not be unseen. And then just last week, I delivered a keynote at an HR conference about resolving the presumed paradox of being both more productive and more human centric at the same time. I've worked on this content for some years, even failed to write a book about it in 2022, but last week I introduced a new perspective that I think may have value and be widely applicable. Resolving a presumed paradox requires expanding a dimension; it takes moving from linear trade-off thinking to a multi-dimensional view (2x2) that provides a goal/quadrant for optimizing what seem like opposing forces. I created this animation to show how we can expand the solution set and resolve paradoxes by adding a dimension. What other paradoxes - besides "more productive and more human centric, at the same time" can you unpack by expanding a dimension? #UnpackingParadoxes #ChangeSuccess #ProductiveAndHumanCentric

Solving guestimates can come in handy at any point in your career: for case competitions, consulting interviews, and even later down your career. Practice these techniques with complex, multi-faceted problems and gradually integrate more sophisticated methods like Monte Carlo simulations and regression analysis. With time and practice, your ability to deconstruct and analyze intricate real-world problems will improve dramatically. Use this guidebook as a starting point and refine your process with each new problem you tackle. Some extra tips: ✅Advanced Uncertainty Quantification Monte Carlo Simulations: Run thousands of iterations with randomized inputs to generate a distribution of outcomes. This not only gives you an expected value but also a confidence interval. Fuzzy Logic: When precise probabilities aren’t available, apply fuzzy logic to handle ambiguous data and provide a range of likely values. ✅Sensitivity Analysis & Variance Decomposition Identify Key Drivers: Use sensitivity analysis to determine which assumptions have the largest impact on your final estimate. Techniques like variance-based decomposition can quantify this effect. Scenario Testing: Create best-case, worst-case, and base-case scenarios to see how changes in critical inputs influence the overall result. This helps in understanding the risk and uncertainty in your model. ✅Dimensional Analysis & Scaling Laws Unit Consistency: Always verify that your calculations make sense dimensionally. This serves as a built-in error check and ensures that different components of your estimate are comparable. Scaling Relations: Leverage known scaling laws or dimensionless numbers to connect small-scale data with larger, more complex systems. ✅Data Fusion & Cross-Validation Multiple Data Sources: Combine insights from surveys, historical data, industry reports, and expert opinions. Cross-referencing these sources can help pinpoint where your assumptions are most reliable. Benchmarking: Validate your estimates against known benchmarks or historical trends. This can highlight potential biases and guide you in recalibrating your model. ✅Continuous Iteration & Back-Casting Historical Comparison: Test your estimation method by applying it to past events (back-casting) where you already know the outcome. Adjust your approach based on these tests. Iterative Improvement: Don’t settle on your first model. Iterate through multiple versions, improving assumptions and incorporating new insights each time. For a change, I've used a carousel to explain the key points of solving such problems and it can help you a lot if you're an MBA students and are prepping for placements and/or case competitions. Let me know in the comments below if you prefer this style of posts over simple text based ones! #consulting #guesstimates #prep #placements #mba #career #iim #management #mbb #linkedin #india

In AI, particularly in optimization, it’s not just about finding solutions, it’s about finding optimal solutions in a multi-objective world. Optimization in real-world applications isn’t as straightforward as minimizing one objective. You’re often dealing with multiple, conflicting goals, and that’s where the complexity kicks in. ⚖️ Multi-objective optimization: How do you balance between minimizing cost and maximizing performance? Techniques like Pareto efficiency and evolutionary algorithms help find the sweet spot. 📉 When dealing with high-dimensional data, have you considered dimensionality reduction methods like PCA or t-SNE to improve the tractability of your optimization problem? 🤯 For complex constraints, Lagrangian relaxation and dual decomposition allow us to break problems into solvable sub-problems without sacrificing solution quality. I reiterate, optimization is not just about solving: it’s about trade-offs, decomposition, and balancing competing objectives. What’s your approach to tackling multi-objective optimization problems? Let’s dive into the theory and methods in the comments👇 #Optimization #MultiObjectiveOptimization #ParetoFront #DimensionalityReduction #AI #OperationsResearch #AdvancedAlgorithms

🔔 #ALERT Knowledge Augmented Complex Problem Solving with Large Language Models: A Survey ➡️ Complex problem solving is framed from both cognitive science (human-centered trace) and computational theory (algorithm design) perspectives. ➡️ Key challenges for LLMs in this space are multi-step reasoning, effective domain knowledge integration, and reliable result verification. ➡️ Methodologies discussed include enhancing Chain-of-Thought reasoning via data synthesis and self-correction, leveraging external knowledge bases (RAG, KGs), and employing diverse verification tools (LLM-as-a-judge, symbolic, experimental). ➡️ The survey maps these challenges and advancements to specific domains: software engineering, mathematics, data science, and scientific research, highlighting domain-specific complexities. ➡️ Future directions emphasize addressing data scarcity, reducing computational costs, improving knowledge representation, and developing more robust evaluation frameworks for complex, open-ended problems. Large Language Models demonstrate capabilities for complex problem solving by approximating human-like reasoning and integrating computational tools. However, deploying them effectively in real-world scenarios requires overcoming significant hurdles. The survey highlights that while progress has been made in areas like multi-step reasoning through techniques like Chain-of-Thought and self-correction, challenges remain in handling complex sequences and ensuring high accuracy. Integrating specialized domain knowledge is critical, moving beyond pre-training to using external sources and agent-based approaches. Furthermore, reliable verification of solutions, especially in domains lacking clear outcomes, necessitates a combination of LLM-based, symbolic, and experimental methods. The path forward involves refining these core capabilities and tailoring solutions to the unique demands of different technical fields. If you are keeping track of where the industry and the implementation of the AI is at! This article from ANTgroup and Zhejiang University is for you. #LLMs #TechnicalSurvey #ProblemSolving #ArtificialIntelligence

Problem Solving: The Art of Navigating Complexity in the AI Era I've learned that in enterprise settings, problems rarely come with neat definitions or clear boundaries. They're messy, interconnected, and often evolving as we work on them, and solutions dont appear magically; you have to work on them from multiple perspectives. While AI excels at solving well-defined problems, the uniquely human skill lies in unpacking complexity by breaking down ambiguous challenges into workable components. This means becoming comfortable with uncertainty, asking better questions, and resisting the urge to jump to solutions. It's like compound interest for problem-solving; the more you invest in understanding the problem space, the greater your returns in solution effectiveness. The most effective problem solvers I work with have mastered four capabilities:   1. Deconstructing multi-layered problems into manageable pieces   2. Studying the problem from different perspectives.   3. Iterating rapidly between hypothesis and testing, and   4. Synthesizing insights across domains and stakeholders. However, I've discovered that AI can serve as an exceptional thought partner in this iterative process. When facing complex challenges, I utilize AI to stress-test my hypotheses, explore potential blind spots I might miss, and rapidly prototype various solutions to the problem. It's like having an always-on collaborator, and a whole slew of subject matter experts in different domains who can help you think through multiple scenarios simultaneously. The future belongs to leaders who can dance with ambiguity while maintaining human agency in defining problems and making decisions. With AI as our thought partner, every one of us can now possess superpowers, accessing knowledge in any domain and accelerating thinking cycles that once took weeks and months to complete, now into minutes and hours. Foundry for AI by Rackspace (FAIR™) D Scott Sanders Ben Blanquera #ProblemSolving #AI #Leadership #CriticalThinking #EnterpriseSolutions #FutureOfWork #ComplexSystems

QUANTUM THINKING IN LEADERSHIP: THE POWER OF STRATEGIC PARALLELISM In traditional problem-solving, leaders often follow a linear, trial-and-error approach—testing different paths one by one until they find the best solution. It is methodical but time-consuming. Now, imagine applying quantum thinking to leadership and decision-making. Instead of exploring options sequentially, what if we could project multiple possibilities simultaneously, assessing different scenarios in parallel before converging on the best outcome? STRATEGIC PARALLELISM Effective leaders do not operate in a strictly linear fashion. They cultivate multiple perspectives, consider diverse strategies at once, and adapt dynamically. They create teams and networks that function as “parallel agents,” exploring different solutions simultaneously while staying aligned with a unified mission. THE LEADERSHIP ADVANTAGE Like quantum computing, high-impact leadership minimizes wasted effort. Instead of pursuing every possibility with equal weight, top performers leverage insight, intuition, and systems thinking to reduce complexity and accelerate decision-making. KEY LESSONS FOR LEADERS ► Build teams capable of independent exploration while maintaining strategic alignment. ► Embrace uncertainty, allowing multiple ideas to coexist before committing to a single path. ► Recognize that the most successful leaders are not those who take the longest route, but those who make the smartest leaps. In an era of increasing complexity, linear problem-solving is a limitation. Leaders who embrace strategic parallelism—like quantum systems—will drive transformation at an exponential pace. What strategies do you use to explore multiple paths without losing focus? #Leadership #HumanResources #OrganizationalDevelopment #ChangeManagement #ManagementConsulting #PersonalDevelopment #LATAM #StrategicThinking #DecisionMaking