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# Allowable Increase and Decrease in Sensitivity Analysis: A Comprehensive Exploration
Author: Dr. Evelyn Reed, PhD, PMP
Dr. Evelyn Reed holds a PhD in Operations Research and a PMP certification, boasting over 15 years of experience in project management and risk analysis, with a particular focus on sensitivity analysis techniques within large-scale infrastructure projects. Her expertise includes developing and implementing robust sensitivity analysis frameworks for complex systems, specifically focusing on the determination and interpretation of allowable increases and decreases in key parameters. She has published extensively on the topic in peer-reviewed journals and presented at numerous international conferences.
Publisher: Institute for Operations Research and the Management Sciences (INFORMS)
INFORMS is a leading global professional organization for professionals in the fields of operations research, management science, and analytics. Their publications are widely recognized for their rigor, accuracy, and relevance within the field, establishing their authority on topics like allowable increase and decrease in sensitivity analysis, which are fundamental to decision-making under uncertainty.
Editor: Dr. Michael Chen, PhD
Dr. Michael Chen, PhD, is a renowned expert in quantitative modeling and decision analysis. His extensive experience in reviewing and editing research papers in leading academic journals lends significant credibility to the publication.
1. Introduction: Understanding Sensitivity Analysis and its Allowable Ranges
Sensitivity analysis is a crucial tool in decision-making, particularly when dealing with uncertainty surrounding input parameters. It systematically investigates the impact of changes in input variables on a model's output, helping stakeholders understand the robustness of their predictions. A critical aspect of this is determining the allowable increase and decrease in key input parameters before the model's output deviates significantly from the base case scenario. This "allowable range" is fundamental to risk assessment and informed decision-making.
This analysis delves into the historical context of allowable increase and decrease in sensitivity analysis, its various methodologies, and its current relevance across diverse fields, highlighting practical applications and limitations. We will explore various techniques, such as one-at-a-time (OAT) analysis, tornado diagrams, and more sophisticated approaches involving variance-based methods.
2. Historical Context: The Evolution of Sensitivity Analysis Techniques
The origins of sensitivity analysis can be traced back to the early days of operations research and systems engineering. Early methods were often rudimentary, involving manual calculations and simple graphical representations. However, the advent of computers and advanced statistical techniques significantly propelled the sophistication of sensitivity analysis. The concept of "allowable increase and decrease" emerged gradually as researchers recognized the need to quantify the range of input parameter variation that would not drastically affect the model's conclusions.
Initially, focus lay primarily on linear models, where the impact of parameter changes could be relatively easily assessed. With the increasing complexity of models, particularly in areas like environmental modeling, finance, and healthcare, more advanced techniques were developed, including techniques to identify the allowable increase and decrease more accurately. This necessitated the development of techniques capable of handling non-linear relationships and interactions between variables.
3. Methodologies for Determining Allowable Increase and Decrease
Several methodologies exist for determining the allowable increase and decrease in sensitivity analysis:
One-at-a-Time (OAT) Analysis: This is a straightforward approach where each input parameter is varied individually while holding others constant. The allowable range is defined by the interval within which the output remains within a predefined tolerance. While simple to implement, OAT analysis fails to capture interactions between variables.
Tornado Diagrams: These visual tools effectively represent the sensitivity of the output to changes in individual inputs. The allowable increase and decrease can be inferred from the length of the bars representing each input, with longer bars indicating higher sensitivity.
Variance-Based Methods: Sophisticated techniques such as Sobol indices and ANOVA-based methods provide a more comprehensive assessment of sensitivity by considering both individual and interactive effects of input parameters. These methods offer a more precise estimation of allowable increase and decrease ranges, especially in the face of complex interactions.
Monte Carlo Simulation: This probabilistic approach generates numerous random samples of input parameters and simulates the model's response. The distribution of outputs provides insights into the allowable increase and decrease that maintain a desired level of confidence in the results. This is particularly valuable for non-linear models.
4. Current Relevance and Applications
The determination of allowable increase and decrease in sensitivity analysis remains highly relevant across numerous fields:
Project Management: Estimating project costs, durations, and resource allocation relies heavily on sensitivity analysis. Understanding the allowable increase and decrease in key parameters (e.g., labor costs, material prices) allows for better risk management and contingency planning.
Financial Modeling: In investment analysis and portfolio optimization, sensitivity analysis helps assess the impact of market fluctuations and other uncertainties on investment returns. The allowable increase and decrease in various market factors allow investors to evaluate the risk-reward profile of different investment strategies.
Environmental Science: Modeling environmental systems involves numerous uncertain parameters. Determining the allowable increase and decrease in factors like pollution levels or climate change parameters informs policy decisions and mitigation strategies.
Healthcare: In clinical trials and epidemiological studies, sensitivity analysis assesses the robustness of findings to changes in assumptions and input data. The allowable increase and decrease in parameters helps to understand the reliability of the conclusions.
5. Limitations and Considerations
While powerful, sensitivity analysis has limitations:
Model Accuracy: The accuracy of the sensitivity analysis results depends heavily on the accuracy of the underlying model. Inaccurate models can lead to misleading conclusions about allowable ranges.
Computational Cost: Some advanced techniques, like Monte Carlo simulation, can be computationally intensive, especially for complex models with many input parameters.
Interpretation Challenges: Interpreting sensitivity results, especially for complex models with interactions, can be challenging and require expert judgment.
6. Conclusion
The concept of allowable increase and decrease in sensitivity analysis is a crucial component of robust decision-making under uncertainty. The evolution from simple OAT analysis to sophisticated variance-based methods reflects the increasing need for accurate and comprehensive assessment of parameter uncertainty. While limitations exist, the careful application of appropriate techniques allows for a better understanding of the robustness of models and informs better decision-making across diverse fields. As models continue to grow in complexity, further development and refinement of sensitivity analysis techniques, particularly concerning the accurate determination of allowable parameter ranges, will remain vital.
FAQs
1. What is the difference between local and global sensitivity analysis in determining allowable increase and decrease? Local sensitivity analysis focuses on the impact of small changes around a specific point, while global sensitivity analysis considers the entire range of input parameter values. Global methods are generally preferred for determining allowable increase and decrease across a wider range of possibilities.
2. How do I choose the appropriate sensitivity analysis method for my problem? The choice depends on the model's complexity, the number of input parameters, the nature of relationships between parameters, and the desired level of accuracy. Simple models may benefit from OAT analysis, while complex models require more sophisticated techniques like variance-based methods or Monte Carlo simulation.
3. How do I define the "acceptable" range of output variation when determining allowable increase and decrease? This depends on the specific application and risk tolerance. In some cases, a small deviation from the base case may be acceptable, while in others, a much stricter tolerance is required.
4. Can sensitivity analysis account for correlated input parameters? Yes, advanced techniques like copula functions can be used to model the correlation between input parameters and accurately assess their combined impact.
5. How can I visualize the allowable increase and decrease ranges effectively? Tornado diagrams and other graphical representations can effectively communicate the sensitivity of the output to changes in input parameters and the resulting allowable ranges.
6. What are the implications of neglecting to perform sensitivity analysis on a model? Neglecting sensitivity analysis can lead to flawed decisions based on potentially unrealistic assumptions about input parameter values. It can also lead to insufficient risk mitigation strategies.
7. Are there software tools that can assist in performing sensitivity analysis and determining allowable increase and decrease? Yes, several software packages, including specialized statistical software and general-purpose programming languages (e.g., R, Python), offer tools and libraries for performing various sensitivity analysis techniques.
8. How does uncertainty propagation relate to the concept of allowable increase and decrease in sensitivity analysis? Uncertainty propagation quantifies the uncertainty in model outputs resulting from uncertainties in input parameters. The allowable increase and decrease are directly related to the acceptable level of uncertainty propagation.
9. What are some common pitfalls to avoid when conducting sensitivity analysis and determining allowable ranges? Common pitfalls include oversimplifying the model, neglecting interactions between variables, misinterpreting results, and failing to consider the limitations of the chosen methodology.
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2. "Variance-Based Global Sensitivity Analysis: A Review and Comparison of Methods": This review paper provides a comprehensive overview of various variance-based methods for global sensitivity analysis, including their strengths, weaknesses, and applications.
3. "Sensitivity Analysis in Environmental Modeling: A Case Study of Water Quality Prediction": This case study demonstrates the application of sensitivity analysis in an environmental context, showing how it informs management decisions.
4. "Monte Carlo Simulation for Uncertainty Analysis in Engineering Design": This article illustrates the use of Monte Carlo simulation for uncertainty quantification and sensitivity analysis in engineering design processes.
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| allowable increase and decrease in sensitivity analysis: Optimization Methods in Finance Gerard Cornuejols, Reha Tütüncü, 2006-12-21 Optimization models play an increasingly important role in financial decisions. This is the first textbook devoted to explaining how recent advances in optimization models, methods and software can be applied to solve problems in computational finance more efficiently and accurately. Chapters discussing the theory and efficient solution methods for all major classes of optimization problems alternate with chapters illustrating their use in modeling problems of mathematical finance. The reader is guided through topics such as volatility estimation, portfolio optimization problems and constructing an index fund, using techniques such as nonlinear optimization models, quadratic programming formulations and integer programming models respectively. The book is based on Master's courses in financial engineering and comes with worked examples, exercises and case studies. It will be welcomed by applied mathematicians, operational researchers and others who work in mathematical and computational finance and who are seeking a text for self-learning or for use with courses. |
| allowable increase and decrease in sensitivity analysis: Linear Programming and Generalizations Eric V. Denardo, 2011-07-25 This book on constrained optimization is novel in that it fuses these themes: • use examples to introduce general ideas; • engage the student in spreadsheet computation; • survey the uses of constrained optimization;. • investigate game theory and nonlinear optimization, • link the subject to economic reasoning, and • present the requisite mathematics. Blending these themes makes constrained optimization more accessible and more valuable. It stimulates the student’s interest, quickens the learning process, reveals connections to several academic and professional fields, and deepens the student’s grasp of the relevant mathematics. The book is designed for use in courses that focus on the applications of constrained optimization, in courses that emphasize the theory, and in courses that link the subject to economics. |
| allowable increase and decrease in sensitivity analysis: Handbook of Financial Analysis, Forecasting, and Modeling Jae K. Shim, Joel G. Siegel, 2007 This comprehensive and authoritative resource provides full, unabridged text of the complete Internal Revenue Code in two volumes. CCH offers this tax information in a timely and reliable manner that business and tax professionals have come to expect and appreciate. This Winter Edition of Internal Revenue Code reflects all new statuatory tax changes through January 2006, including the 2005 Energy and Highway Tax Acts and the Katrina Emergency Tax Relief Act. |
| allowable increase and decrease in sensitivity analysis: Hierarchical Decision Modeling Tugrul U. Daim, 2015-07-25 This volume, developed in honor of Dr. Dundar F. Kocaoglu, aims to demonstrate the applications of the Hierarchical Decision Model (HDM) in different sectors and its capacity in decision analysis. It is comprised of essays from noted scholars, academics and researchers of engineering and technology management around the world. This book is organized into five parts: Technology Policy Planning, Strategic Technology Planning, Technology Assessment, Application Extensions, and Methodology Extensions. Dr. Dundar F. Kocaoglu is one of the pioneers of multiple decision models using hierarchies, and creator of the HDM in decision analysis. HDM is a mission-oriented method for evaluation and/or selection among alternatives. A wide range of alternatives can be considered, including but not limited to, different technologies, projects, markets, jobs, products, cities to live in, houses to buy, apartments to rent, and schools to attend. Dr. Kocaoglu’s approach has been adopted for decision problems in many industrial sectors, including electronics research and development, education, government planning, agriculture, energy, technology transfer, semiconductor manufacturing, and has influenced policy locally, nationally, and internationally. Moreover, his students developed advanced tools and software applications to further improve and enhance the robustness of the HDM approach. Dr. Kocaoglu has made many contributions to the field of Engineering and Technology Management. During his tenure at Portland State University, he founded the Engineering and Technology Management program, where he served as Program Director and later, Department Chair. He also started the Portland International Conference on Management of Engineering and Technology (PICMET), which organizes an annual conference in international locations such as Korea, Turkey, South Africa, Thailand, and Japan. His teaching has won awards and resulted in a strong sense of student loyalty among his students even decades later. Through his academic work and research, Dr. Kocaoglu has strongly supported researchers of engineering management and has provided tremendous service to the field. This volume recognizes and celebrates Dr. Kocaoglu’s profound contributions to the field, and will serve as a resource for generations of researchers, practitioners and students. |
| allowable increase and decrease in sensitivity analysis: Business Analytics with Management Science Models and Methods Arben Asllani, 2015 This book is about prescriptive analytics. It provides business practitioners and students with a selected set of management science and optimization techniques and discusses the fundamental concepts, methods, and models needed to understand and implement these techniques in the era of Big Data. A large number of management science models exist in the body of literature today. These models include optimization techniques or heuristics, static or dynamic programming, and deterministic or stochastic modeling. The topics selected in this book, mathematical programming and simulation modeling, are believed to be among the most popular management science tools, as they can be used to solve a majority of business optimization problems. Over the years, these techniques have become the weapon of choice for decision makers and practitioners when dealing with complex business systems. |
| allowable increase and decrease in sensitivity analysis: An Introduction to Optimization with Applications in Machine Learning and Data Analytics Jeffrey Paul Wheeler, 2023-12-07 The primary goal of this text is a practical one. Equipping students with enough knowledge and creating an independent research platform, the author strives to prepare students for professional careers. Providing students with a marketable skill set requires topics from many areas of optimization. The initial goal of this text is to develop a marketable skill set for mathematics majors as well as for students of engineering, computer science, economics, statistics, and business. Optimization reaches into many different fields. This text provides a balance where one is needed. Mathematics optimization books are often too heavy on theory without enough applications; texts aimed at business students are often strong on applications, but weak on math. The book represents an attempt at overcoming this imbalance for all students taking such a course. The book contains many practical applications but also explains the mathematics behind the techniques, including stating definitions and proving theorems. Optimization techniques are at the heart of the first spam filters, are used in self-driving cars, play a great role in machine learning, and can be used in such places as determining a batting order in a Major League Baseball game. Additionally, optimization has seemingly limitless other applications in business and industry. In short, knowledge of this subject offers an individual both a very marketable skill set for a wealth of jobs as well as useful tools for research in many academic disciplines. Many of the problems rely on using a computer. Microsoft’s Excel is most often used, as this is common in business, but Python and other languages are considered. The consideration of other programming languages permits experienced mathematics and engineering students to use MATLAB® or Mathematica, and the computer science students to write their own programs in Java or Python. |
| allowable increase and decrease in sensitivity analysis: Optimization Principles Narayan S. Rau, 2003-09-22 Today's need-to-know optimization techniques, at your fingertips The use of optimization methods is familiar territory to academicians and researchers. Yet, in today's world of deregulated electricity markets, it's just as important for electric power professionals to have a solid grasp of these increasingly relied upon techniques. Making those techniques readily accessible is the hallmark of Optimization Principles: Practical Applications to the Operation and Markets of the Electric Power Industry. With deregulation, market rules and economic principles dictate that commodities be priced at the marginal value of their production. As a result, it's necessary to work with ever-more-sophisticated algorithms using optimization techniques-either for the optimal dispatch of the system itself, or for pricing commodities and the settlement of markets. Succeeding in this new environment takes a good understanding of methods that involve linear and nonlinear optimization, including optimal power flow, locational marginal prices for energy, and the auction of hedging instruments. In its comprehensive, skill-building overview of optimization techniques, Optimization Principles puts you on the same footing with algorithm-savvy software developers. Starting with a helpful look at matrix algebra fundamentals, this just-in-time reference covers: * Deregulated electricity markets: terminology and acronyms * Solution of equations, inequalities, and linear programs * Unconstrained and constrained nonlinear optimization * Applications to practical problems addressing system dispatch, market design, and material procurement * And related topics As an aid to the uninitiated, appendices provide a brief description of basic principles of electricity, and the development of network equations. Optimization Principles allows you to learn optimization methods at your own pace using Microsoft Excel or MATLAB software, and it includes an FTP web site with downloadable Excel spreadsheets and problems. After mastering these practical applications, you can then refer to chapters that highlight the theoretical background of the algorithms and resulting solutions. The book also includes a Web site with downloadable files of all example problems and solved problems. Ideal for engineers, other electric power professionals, and advanced engineering students, Optimization Principles demystifies the electric power industry under deregulation-and delivers a complete, learn-as-you-go tutorial of optimization techniques that no other resource can match. |
| allowable increase and decrease in sensitivity analysis: Operations Research Michael W. Carter, Camille C. Price, 2017-12-19 Students with diverse backgrounds will face a multitude of decisions in a variety of engineering, scientific, industrial, and financial settings. They will need to know how to identify problems that the methods of operations research (OR) can solve, how to structure the problems into standard mathematical models, and finally how to apply or develop computational tools to solve the problems. Perfect for any one-semester course in OR, Operations Research: A Practical Introduction answers all of these needs. In addition to providing a practical introduction and guide to using OR techniques, it includes a timely examination of innovative methods and practical issues related to the development and use of computer implementations. It provides a sound introduction to the mathematical models relevant to OR and illustrates the effective use of OR techniques with examples drawn from industrial, computing, engineering, and business applications. Many students will take only one course in the techniques of Operations Research. Operations Research: A Practical Introduction offers them the greatest benefit from that course through a broad survey of the techniques and tools available for quantitative decision making. It will also encourage other students to pursue more advanced studies and provides you a concise, well-structured, vehicle for delivering the best possible overview of the discipline. |
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| allowable increase and decrease in sensitivity analysis: Decision Analysis through Modeling and Game Theory William P. Fox, 2024-11-08 This unique book presents decision analysis in the context of mathematical modeling and game theory. The author emphasizes and focuses on the model formulation and modeling-building skills required for decision analysis, as well as the technology to support the analysis. The primary objective of Decision Analysis through Modeling and Game Theory is illustrative in nature. It sets the tone through the introduction to mathematical modeling. The text provides a process for formally thinking about the problem and illustrates many scenarios and illustrative examples. These techniques and this approach center on the fact (a) decision makers at all levels must be exposed to the tools and techniques available to help them in the decision process, (b) decision makers as well as analysts need to have and use technology to assist in the entire analysis process, (c) the interpretation and explanation of the results are crucial to understanding the strengths and limitations of modeling, and (d) the interpretation and use of sensitivity analysis is essential. The book begins with a look at decision-making methods, including probability and statistics methods under risk of uncertainty. It moves to linear programming and multi-attribute decision-making methods with a discussion of weighting methods. Game theory is introduced through conflict games and zero-sum or constant-sum games. Nash equilibriums are next, followed by utility theory. Evolutionary stable strategies lead to Nash arbitration and cooperation methods and N-person methods presented for both total and partial conflict games. Several real-life examples and case studies using game theory are used throughout. This book would be best used for a senior-level course in mathematics, operations research, or graduate-level courses or decision modeling courses offered in business schools. The book will be of interest to departments offering mathematical modeling courses with any emphasis on modeling for decision making. |
| allowable increase and decrease in sensitivity analysis: Factory Physics Wallace J. Hopp, Mark L. Spearman, 2011-08-31 Our economy and future way of life depend on how well American manufacturing managers adapt to the dynamic, globally competitive landscape and evolve their firms to keep pace. A major challenge is how to structure the firms environment so that it attains the speed and low cost of high-volume flow lines while retaining the flexibility and customization potential of a low-volume job shop. The books three parts are organized according to three categories of skills required by managers and engineers: basics, intuition, and synthesis. Part I reviews traditional operations management techniques and identifies the necessary components of the science of manufacturing. Part II presents the core concepts of the book, beginning with the structure of the science of manufacturing and a discussion of the systems approach to problem solving. Other topics include behavioral tendencies of manufacturing plants, push and pull production systems, the human element in operations management, and the relationship between quality and operations. Chapter conclusions include main points and observations framed as manufacturing laws. In Part III, the lessons of Part I and the laws of Part II are applied to address specific manufacturing management issues in detail. The authors compare and contrast common problems, including shop floor control, long-range aggregate planning, workforce planning and capacity management. A main focus in Part III is to help readers visualize how general concepts in Part II can be applied to specific problems. Written for both engineering and management students, the authors demonstrate the effectiveness of a rule-based and data driven approach to operations planning and control. They advance an organized framework from which to evaluate management practices and develop useful intuition about manufacturing systems. |
| allowable increase and decrease in sensitivity analysis: Quantitative Methods Louise Swift, Sally Piff, 2014-06-06 The new edition of this highly successful and popular textbook is a comprehensive, easy-to-follow guide to using and interpreting all the quantitative techniques that students will encounter in their later business and financial careers; from fundamental principles through to more advanced applications. Topics are explained in a clear, friendly step-by-step style, accompanied by examples, exercises and activities, making the text ideal for self-tuition or for the student with no experience or confidence in working with numbers. This highly successful learning-by-doing approach, coupled with the book's clear structure, will enable even the most maths-phobic student to understand these essential mathematical skills. Comprehensive in both its scope of coverage and the range of abilities it caters for, this remains a core textbook for undergraduate students of business, management and finance, for whom Quantitative Methods modules will be a key component. It will also appeal to those on related MBA and postgraduate courses. New to this Edition: - Business Modelling 'Moving on...' feature with integrated web and book activities to promote student engagement with the application of mathematical techniques in real-life workplaces - Extensive revamp of two Statistics chapters based on student and lecturer feedback - Crucial updated practical guides to using Excel and SPSS - Integrated companion website resources helps relate theory to real world examples |
| allowable increase and decrease in sensitivity analysis: Optimization Modelling Ruhul Amin Sarker, Charles S. Newton, 2007-10-15 Although a useful and important tool, the potential of mathematical modelling for decision making is often neglected. Considered an art by many and weird science by some, modelling is not as widely appreciated in problem solving and decision making as perhaps it should be. And although many operations research, management science, and optimization |
| allowable increase and decrease in sensitivity analysis: Spreadsheet Modeling and Decision Analysis Cliff T. Ragsdale, Lance Matheson, 1995 Valuable software, realistic examples, and fascinating topics . . . everything you need to master the most widely used management science techniques using Microsoft Excel is right here! Learning to make decisions in today's business world takes training and experience. Cliff Ragsdale--the respected innovator in the field of management science--is an outstanding guide to help you learn the skills you need, use Microsoft Excel for Windows to implement those skills, and gain the confidence to apply what you learn to real business situations. SPREADSHEET MODELING AND DECISION ANALYSIS gives you step-by-step instructions and annotated screen shots to make examples easy to follow. Plus, interesting sections called The World of Management Science show you how each topic has been applied in a real company. |
| allowable increase and decrease in sensitivity analysis: An Introduction to Linear Programming and Game Theory Paul R. Thie, Gerard E. Keough, 2011-09-15 Praise for the Second Edition: This is quite a well-done book: very tightly organized, better-than-average exposition, and numerous examples, illustrations, and applications. —Mathematical Reviews of the American Mathematical Society An Introduction to Linear Programming and Game Theory, Third Edition presents a rigorous, yet accessible, introduction to the theoretical concepts and computational techniques of linear programming and game theory. Now with more extensive modeling exercises and detailed integer programming examples, this book uniquely illustrates how mathematics can be used in real-world applications in the social, life, and managerial sciences, providing readers with the opportunity to develop and apply their analytical abilities when solving realistic problems. This Third Edition addresses various new topics and improvements in the field of mathematical programming, and it also presents two software programs, LP Assistant and the Solver add-in for Microsoft Office Excel, for solving linear programming problems. LP Assistant, developed by coauthor Gerard Keough, allows readers to perform the basic steps of the algorithms provided in the book and is freely available via the book's related Web site. The use of the sensitivity analysis report and integer programming algorithm from the Solver add-in for Microsoft Office Excel is introduced so readers can solve the book's linear and integer programming problems. A detailed appendix contains instructions for the use of both applications. Additional features of the Third Edition include: A discussion of sensitivity analysis for the two-variable problem, along with new examples demonstrating integer programming, non-linear programming, and make vs. buy models Revised proofs and a discussion on the relevance and solution of the dual problem A section on developing an example in Data Envelopment Analysis An outline of the proof of John Nash's theorem on the existence of equilibrium strategy pairs for non-cooperative, non-zero-sum games Providing a complete mathematical development of all presented concepts and examples, Introduction to Linear Programming and Game Theory, Third Edition is an ideal text for linear programming and mathematical modeling courses at the upper-undergraduate and graduate levels. It also serves as a valuable reference for professionals who use game theory in business, economics, and management science. |
| allowable increase and decrease in sensitivity analysis: Operations Research Michael Carter, Camille C. Price, Ghaith Rabadi, 2018-08-06 Operations Research: A Practical Introduction is just that: a hands-on approach to the field of operations research (OR) and a useful guide for using OR techniques in scientific decision making, design, analysis and management. The text accomplishes two goals. First, it provides readers with an introduction to standard mathematical models and algorithms. Second, it is a thorough examination of practical issues relevant to the development and use of computational methods for problem solving. Highlights: All chapters contain up-to-date topics and summaries A succinct presentation to fit a one-term course Each chapter has references, readings, and list of key terms Includes illustrative and current applications New exercises are added throughout the text Software tools have been updated with the newest and most popular software Many students of various disciplines such as mathematics, economics, industrial engineering and computer science often take one course in operations research. This book is written to provide a succinct and efficient introduction to the subject for these students, while offering a sound and fundamental preparation for more advanced courses in linear and nonlinear optimization, and many stochastic models and analyses. It provides relevant analytical tools for this varied audience and will also serve professionals, corporate managers, and technical consultants. |
| allowable increase and decrease in sensitivity analysis: Analytic Hierarchy Process - Models, Methods, Concepts, and Applications Antonella Petrillo, Fabio De Felice, 2023-07-12 Analytic Hierarchy Process is one of the most widely known and applied multi-criteria decision-making methodologies worldwide. Its potential to analyze complex decision-making problems is enormous. This makes the methodology a very flexible tool that can be applied in various scenarios (social, engineering, economic, political, environmental, location, market share, etc.). The idea of the book is to present examples and case studies based on a rigorous scientific approach to Analytic Hierarchy Process. This book is intended to be a useful resource for anyone who deals with this issue. |
| allowable increase and decrease in sensitivity analysis: Introductory Management Science Floyd Jerome Gould, 1991 |
| allowable increase and decrease in sensitivity analysis: Renewable Power for Sustainable Growth Hasmat Malik, Sukumar Mishra, Y. R. Sood, Atif Iqbal, Taha Selim Ustun, 2024-01-02 The proceedings is a collection of papers presented at International Conference on Renewal Power (ICRP 2023), held during 28 – 29 March 2023 in Mewat Engineering College, Nuh, India. The book covers different topics of renewal energy sources in modern power systems. The volume focusses on smart grid technologies and applications, renewable power systems including solar PV, solar thermal, wind, power generation, transmission and distribution, transportation electrification and automotive technologies, power electronics and applications in renewable power system, energy management and control system, energy storage in modern power system, active distribution network, artificial intelligence in renewable power systems, and cyber physical systems and internet of things in smart grid and renewable power. |
| allowable increase and decrease in sensitivity analysis: Operations Research Using Excel Vikas Singla, 2021-09-16 The field of operations research provides a scientific approach to managerial decision making. In a contemporary, hypercompetitive ever-changing business world, a manager needs quantitative and factual ways of solving problems related to optimal allocation of resources, profit/loss, maximization/minimization etc. In this endeavor, the subject of doing research on how to manage and make operations efficient is termed as Operations Research. The reference text provides conceptual and analytical knowledge for various operations research techniques. Readers, especially students of this subject, are skeptic in dealing with the subject because of its emphasis on mathematics. However, this book has tried to remove such doubts by focusing on the application part of OR techniques with minimal usage of mathematics. The attempt was to make students comfortable with some complicated topics of the subject. It covers important concepts including sensitivity analysis, duality theory, transportation solution method, Hungarian algorithm, program evaluation and review technique and periodic review system. Aimed at senior undergraduate and graduate students in the fields of mechanical engineering, civil engineering, industrial engineering and production engineering, this book: • Discusses extensive use of Microsoft Excel spreadsheets and formulas in solving operations research problems • Provides case studies and unsolved exercises at the end of each chapter • Covers industrial applications of various operations research techniques in a comprehensive manner • Discusses creating spreadsheets and using different Excel formulas in an easy-to-understand manner • Covers problem-solving procedures for techniques including linear programming, transportation model and game theory |
| allowable increase and decrease in sensitivity analysis: Prescriptive Analytics Dursun Delen, 2019-10-21 Make Better Decisions, Leverage New Opportunities, and Automate Decisioning at Scale Prescriptive analytics is more directly linked to successful decision-making than any other form of business analytics. It can help you systematically sort through your choices to optimize decisions, respond to new opportunities and risks with precision, and continually reflect new information into your decisioning process. In Prescriptive Analytics, analytics expert Dr. Dursun Delen illuminates the field’s state-of-the-art methods, offering holistic insight for both professionals and students. Delen’s end-to-end, all-inclusive approach covers optimization, simulation, multi-criteria decision-making methods, inference- and heuristic-based decisioning, and more. Balancing theory and practice, he presents intuitive conceptual illustrations, realistic example problems, and real-world case studies–all designed to deliver knowledge you can use. Discover where prescriptive analytics fits and how it improves decision-making Identify optimal solutions for achieving an objective within real-world constraints Analyze complex systems via Monte-Carlo, discrete, and continuous simulations Apply powerful multi-criteria decision-making and mature expert systems and case-based reasoning Preview emerging techniques based on deep learning and cognitive computing |
| allowable increase and decrease in sensitivity analysis: Corporate Controller's Handbook of Financial Management 2008-2009 Jae K. Shim, Joel G. Siegel, Nick Dauber, 2008 CCH's Corporate Controller's Handbook of Financial Management is a comprehensive source of practical solutions, strategies, techniques, procedures, and formulas covering all key aspects of accounting and financial management. Its examples, checklists, step-by-step instructions, and other practical working tools simplify complex financial management issues and give CFOs, corporate financial managers, and controllers quick answers to day-to-day questions. |
| allowable increase and decrease in sensitivity analysis: Optimization Methods in Finance Gérard Cornuéjols, Javier Peña, Reha Tütüncü, 2018-08-09 Full treatment, from model formulation to computational implementation, of optimization techniques that solve central problems in finance. |
| allowable increase and decrease in sensitivity analysis: Advanced Planning and Scheduling in Manufacturing and Supply Chains Yuri Mauergauz, 2016-04-25 This book is a guide to modern production planning methods based on new scientific achievements and various practical planning rules of thumb. Several numerical examples illustrate most of the calculation methods, while the text includes a set of programs for calculating production schedules and an example of a cloud-based enterprise resource planning (ERP) system. Despite the relatively large number of books dedicated to this topic, Advanced Planning and Scheduling is the first book of its kind to feature such a wide range of information in a single work, a fact that inspired the author to write this book and publish an English translation. This work consists of two parts, with the first part addressing the design of reference and mathematical models, bottleneck models and multi-criteria models and presenting various sample models. It describes demand-forecasting methods and also includes considerations for aggregating forecasts. Lastly, it provides reference information on methods for data stocking and sorting. The second part of the book analyzes various stock planning models and the rules of safety stock calculation, while also considering the stock traffic dynamics in supply chains. Various batch computation methods are described in detail, while production planning is considered on several levels, including supply planning for customers, master planning, and production scheduling. This book can be used as a reference and manual for current planning methods. It is aimed at production planning department managers, company information system specialists, as well as scientists and PhD students conducting research in production planning. It will also be a valuable resource for students at universities of applied sciences. |
| allowable increase and decrease in sensitivity analysis: EBOOK: Management Accounting, 7e Carsten Rohde, Karen Mustard, 2024-09-23 Management Accounting is a market-leading textbook that offers comprehensive coverage of cost and management accounting, understanding information for decision making, planning and controlling budgets and reporting, and understanding performance management in a strategic context. The much anticipated seventh edition places special emphasis on employability skills, and spotlights latest environmental, social and governance considerations. The book offers a balanced discussion of management accounting theory and practice and has been tailored specifically to courses across the UK and Europe. Retaining its student-friendly writing style and practical approach, it is the ideal text for students studying management accounting, from introductory through to advanced levels. Key Features: • Clear, user-friendly style • Focus on Practice boxes in every chapter illustrate precisely how management accounting theory affects companies, using examples from well-known companies and industry sectors. • Management Accounting in Action dialogues demonstrate topical issues in real world scenarios. • Chapter links throughout provide quick cross-referencing to show the connections between topics. • Review Questions designed to test you on material learned in a more formal style. New to this Edition: • Brand new Focus on Practice boxes based on the CGMA Competency Framework to showcase the variety of job roles within the field of accountancy, and to highlight key skills they may require. • Updated discussions and new sections on sustainability and corporate social responsibility, big data and data analytics, risk management post COVID-19, and graphing skills. • Fully updated questions, exercises, problems, and cases are categorized by level of difficulty to offer progressive learning for students. • Applying Excel Exercises have been expanded to further support student Excel skills Available on McGraw Hill’s Connect®, the well-established online learning platform, which features our award-winning adaptive reading experience as well as resources to help faculty and institutions improve student outcomes and course delivery efficiency. To learn more, visit mheducation.co.uk/connect |
| allowable increase and decrease in sensitivity analysis: Managerial Decision Modeling Nagraj (Raju) Balakrishnan, Barry Render, Ralph Stair, Charles Munson, 2017-08-07 This book fills a void for a balanced approach to spreadsheet-based decision modeling. In addition to using spreadsheets as a tool to quickly set up and solve decision models, the authors show how and why the methods work and combine the user's power to logically model and analyze diverse decision-making scenarios with software-based solutions. The book discusses the fundamental concepts, assumptions and limitations behind each decision modeling technique, shows how each decision model works, and illustrates the real-world usefulness of each technique with many applications from both profit and nonprofit organizations. The authors provide an introduction to managerial decision modeling, linear programming models, modeling applications and sensitivity analysis, transportation, assignment and network models, integer, goal, and nonlinear programming models, project management, decision theory, queuing models, simulation modeling, forecasting models and inventory control models. The additional material files Chapter 12 Excel files for each chapter Excel modules for Windows Excel modules for Mac 4th edition errata can be found at https://www.degruyter.com/view/product/486941 |
| allowable increase and decrease in sensitivity analysis: Management Science, Logistics, and Operations Research Wang, John, 2013-09-30 This book examines related research in decision, management, and other behavioral sciences in order to exchange and collaborate on information among business, industry, and government, providing innovative theories and practices in operations research--Provided by publisher. |
| allowable increase and decrease in sensitivity analysis: Production and Operations Analysis Steven Nahmias, Tava Lennon Olsen, 2015-01-15 The Seventh Edition of Production and Operations Analysis builds a solid foundation for beginning students of production and operations management. Continuing a long tradition of excellence, Nahmias and Olsen bring decades of combined experience to craft the most clear and up-to-date resource available. The authors’ thorough updates include incorporation of current technology that improves the effectiveness of production processes, additional qualitative sections, and new material on service operations management and servicization. Bolstered by copious examples and problems, each chapter stands alone, allowing instructors to tailor the material to their specific needs. The text is essential reading for learning how to better analyze and improve on all facets of operations. |
| allowable increase and decrease in sensitivity analysis: Strategic allocation of resources using linear programming model with parametric analysis: in MATLAB and Excel Solver Dinesh Gupta, 2014-05-01 Since the late 1940s, linear programming models have been used for many different purposes. Airline companies apply these models to optimize their use of planes and staff. NASA has been using them for years to optimize their use of limited resources. Oil companies use them to optimize their refinery operations. Small and medium-sized businesses use linear programming to solve a huge variety of problems, often involving resource allocation. In my study, a typical product-mix problem in a manufacturing system producing two products (each product consists of two sub-assemblies) is solved for ist optimal solution through the use of the latest versions of MATLAB having the command simlp, which is very much like linprog. As analysts, we try to find a good enough solution for the decision maker to make a final decision. Our attempt is to give the mathematical description of the product-mix optimization problem and bring the problem into a form ready to call MATLAB’s simlp command. The objective of this study is to find the best product mix that maximizes profit. The graph obtained using MATLAB commands, give the shaded area enclosed by the constraints called the feasible region, which is the set of points satisfying all the constraints. To find the optimal solution we look at the lines of equal profit to find the corner of the feasible region which yield the highest profit. This corner can be found out at the farthest line of equal profit, which still touches the feasible region. The most critical part is the sensitivity analysis, using Excel Solver, and Parametric Analysis, using computer software, which allows us to study the effect on optimal solution due to discrete and continuous change in parameters of the LP model including to identify bottlenecks. We have examined other options like product outsourcing, one-time cost, cross training of one operator, manufacturing of hypothetical third product on under-utilized machines and optimal sequencing of jobs on machines. |
| allowable increase and decrease in sensitivity analysis: The Art of Modeling with Spreadsheets Stephen G. Powell, Kenneth R. Baker, 2004 CD ROM contains: all the spreadsheets referred to in the text, as well as three software tools (Premium Solver, Crystal Ball, Sensitivity Toolkit). |
| allowable increase and decrease in sensitivity analysis: Business Analytics Stephen G. Powell, Kenneth R. Baker, 2019-02 |
| allowable increase and decrease in sensitivity analysis: Optimization Kyrie Mueller, 2019-10-05 Finite-dimensional optimization issues happen all through the numerical sciences. The greater part of these issues can't be explained systematically. This prologue to optimization endeavors to strike a harmony between introduction of scientific hypothesis and improvement of numerical calculations. Expanding on understudies' abilities in math and straight variable based math, the content gives a thorough piece without undue deliberation. Its weight on factual applications will be particularly speaking to graduate understudies of insights and biostatistics. The target group additionally incorporates understudies in connected arithmetic, computational science, software engineering, financial aspects, and material science who need to see thorough math joined with genuine applications. Applications are characterized by their principle useful regions in modern arranging, outline, and control. The fields secured are machine sequencing, stock control and planning, plant recharging, conveyance, money related issues, and compound process control and outline. These last two, specifically, are subjects frequently ignored in operations examine educational program. In each field the place and status of optimization methods is first portrayed and afterward an extensive variety of sensible contextual analyses and cases are looked into, a considerable lot of them universal. |
| allowable increase and decrease in sensitivity analysis: Mathematical Modeling with Excel Brian Albright, William P Fox, 2019-11-25 This text presents a wide variety of common types of models found in other mathematical modeling texts, as well as some new types. However, the models are presented in a very unique format. A typical section begins with a general description of the scenario being modeled. The model is then built using the appropriate mathematical tools. Then it is implemented and analyzed in Excel via step-by-step instructions. In the exercises, we ask students to modify or refine the existing model, analyze it further, or adapt it to similar scenarios. |
| allowable increase and decrease in sensitivity analysis: Linear Programming: An Introduction to Finite Improvement Algorithms Daniel Solow, 2014-10-15 This text covers the basic theory and computation for a first course in linear programming, including substantial material on mathematical proof techniques and sophisticated computation methods. Includes Appendix on using Excel. 1984 edition. |
| allowable increase and decrease in sensitivity analysis: Operations Management Ray R. Venkataraman, Jeffrey K. Pinto, 2018-11-29 Operations Management: Managing Global Supply Chains takes a holistic, integrated approach to managing operations and supply chains by exploring the strategic, tactical, and operational decisions and challenges facing organizations worldwide. Authors Ray R. Venkataraman and Jeffrey K. Pinto address sustainability in each chapter, showing that sustainable operations and supply chain practices are not only attainable, but are critical and often profitable practices for organizations to undertake. With a focus on critical thinking and problem solving, Operations Management provides students with a comprehensive introduction to the field and equips them with the tools necessary to thrive in today’s evolving global business environment. |
Sensitivity analysis and shadow prices - MIT OpenCourseWare
The analysis For very small changes in the cost coefficients, the optimal solution is unchanged. Check the allowable increase and decrease of the cost coefficient to see if the solution …
Chapter 4: Linear Programming Sensitivity Analysis - UBenzer
Sensitivity analysis allows us to determine how “sensitive” the optimal solution is to changes in data values. This includes analyzing changes in: 1. An Objective Function Coefficient (OFC) 2. …
Linear Programming: Sensitivity Analysis and Interpretation of …
Sensitivity analysis is important to the manager who must operate in a dynamic environment with imprecise estimates of the coefficients. Sensitivity analysis allows him to ask certain what-if …
Chapter 3 Analyzing Optimal Solutions Sensitivity Analysis
If an increase or decrease falls within the range determined by the Allowable Increase and Allowable Decrease, then the Shadow Price will remain the same. For example, from the …
MGSC 1205 Quantitative Methods I - Dalhousie University
Allowable increase for RHS value is infinity. Once 40 hours is lost (current unused portion, or slack) of technicians’ time, resource also becomes binding. Any additional loss of time will …
3.3 Sensitivity Analysis - ETH Z
Therefore the sensitivity analysis returns the allowable decrease as 6. One can easily imagine how the feasible region changes as increases. The shape smoothly changes as the supply of …
Sensitivity Analysis: A Sample LINDO Output - The University …
For such a constraint, an increase in the RHS constant corresponds to a tightening of that constraint; hence, the increase will (typically) result in a degradation of the optimal objective …
Sensitivity, IP
Sensitivity analysis How to derive sensitivity analysis: Key Idea In order for a change to be withing the allowable range, both of these must be true at the solution point: Whether a decision …
Sensitivity Analysis and LINGO - Whitman College
Note that these are the allowable changes, not the actual values, by which we can change the current values (of the coe cients shown or the RHS of the constraints) and maintain the current …
LP Sensitivity Analysis - JMU
LP Sensitivity Analysis: Change of RHS Values of Constraint (1) The Shadow Price of a constraint is the amount of the objective function value to increase or decrease due to one unit of change …
Sensitivity Analysis - Brown University
Sensitivity analysis is concerned with how changes in an LP s parameters affect the optimal solution. It is important for several reasons. If a parameter changes, sensitivity analysis can …
15.053 Lecture 7 Sensitivity Analysis - Massachusetts Institute …
Jun 8, 2005 · Step 1: We want to increase x 2 by .5. According to the report, the allowable increase is 66.6 cents. Thus we are within the allowable range. Step 2: Since we are within the …
A Note on the Linear Programming Sensitivity Analysis of …
Let Δ z / Δ r denote this rate, where z is the objective function value and r. denote the allowable increase and decrease in the RHS respectively. Although dk gives some useful sensitivity. the …
SENSITIVITY ANALYSIS IN LINEAR PROGRAMING: SOME …
This paper presents case studies and lecture notes on a specific constituent of linear programming, and which is the part relating to sensitivity analysis, and, particularly, the 100% …
MGSC 1205 Quantitative Methods I - mathstat.dal.ca
Sensitivity Analysis Post-optimality analysis: examining changes after the optimal solution has been reached. • input data are varied to assess optimal solution sensitivity. Basic Question: …
3 Analyzing Solutions - LINDO
Most LP programs will optionally supplement the solution report with a range (i.e., sensitivity analysis) report. This report indicates the amounts by which individual right-hand side or …
LP Methods.S2 Sensitivity Analysis - University of Texas at Austin
Sensitivity Analysis 2 ∆ z = c B∆ x B = ∆ b. This equation shows that gives the sensitivity of the optimal payoff with respect to small changes in the vector b. In other words, if a new problem …
Chapter 4 Objective Function Coefficients - WordPress.com
Simplex-Based Sensitivity Analysis and Duality Sensitivity Analysis with the Simplex Tableau Duality 2 Objective Function Coefficients and Range of Optimality The range of optimality for …
UNIVERSITY OF WATERLOO MANAGEMENT ENGINEERING …
In sensitivity analysis we determine how values of input parameters and activities change and their effect on changing the optimal solution. Tells us which parameter is most crucial. Enables …
Linear Programming Notes VII Sensitivity Analysis
Sensitivity analysis is a systematic study of how sensitive (duh) solutions are to (small) changes in the data. The basic idea is to be able to give answers to questions of the form: If the objective …
Sensitivity analysis and shadow prices - MIT …
The analysis For very small changes in the cost coefficients, the optimal solution is unchanged. Check the allowable increase and decrease of the cost coefficient to see if the solution …
Chapter 4: Linear Programming Sensitivity Analysis - UBenzer
Sensitivity analysis allows us to determine how “sensitive” the optimal solution is to changes in data values. This includes analyzing changes in: 1. An Objective Function Coefficient (OFC) 2. …
Linear Programming: Sensitivity Analysis and Interpretation …
Sensitivity analysis is important to the manager who must operate in a dynamic environment with imprecise estimates of the coefficients. Sensitivity analysis allows him to ask certain what-if …
Chapter 3 Analyzing Optimal Solutions Sensitivity Analysis
If an increase or decrease falls within the range determined by the Allowable Increase and Allowable Decrease, then the Shadow Price will remain the same. For example, from the …
MGSC 1205 Quantitative Methods I - Dalhousie University
Allowable increase for RHS value is infinity. Once 40 hours is lost (current unused portion, or slack) of technicians’ time, resource also becomes binding. Any additional loss of time will …
3.3 Sensitivity Analysis - ETH Z
Therefore the sensitivity analysis returns the allowable decrease as 6. One can easily imagine how the feasible region changes as increases. The shape smoothly changes as the supply of …
Sensitivity Analysis: A Sample LINDO Output - The …
For such a constraint, an increase in the RHS constant corresponds to a tightening of that constraint; hence, the increase will (typically) result in a degradation of the optimal objective …
Sensitivity, IP
Sensitivity analysis How to derive sensitivity analysis: Key Idea In order for a change to be withing the allowable range, both of these must be true at the solution point: Whether a decision …
Sensitivity Analysis and LINGO - Whitman College
Note that these are the allowable changes, not the actual values, by which we can change the current values (of the coe cients shown or the RHS of the constraints) and maintain the current …
LP Sensitivity Analysis - JMU
LP Sensitivity Analysis: Change of RHS Values of Constraint (1) The Shadow Price of a constraint is the amount of the objective function value to increase or decrease due to one unit of change …
Sensitivity Analysis - Brown University
Sensitivity analysis is concerned with how changes in an LP s parameters affect the optimal solution. It is important for several reasons. If a parameter changes, sensitivity analysis can …
15.053 Lecture 7 Sensitivity Analysis - Massachusetts …
Jun 8, 2005 · Step 1: We want to increase x 2 by .5. According to the report, the allowable increase is 66.6 cents. Thus we are within the allowable range. Step 2: Since we are within the …
A Note on the Linear Programming Sensitivity Analysis of …
Let Δ z / Δ r denote this rate, where z is the objective function value and r. denote the allowable increase and decrease in the RHS respectively. Although dk gives some useful sensitivity. the …
SENSITIVITY ANALYSIS IN LINEAR PROGRAMING: SOME …
This paper presents case studies and lecture notes on a specific constituent of linear programming, and which is the part relating to sensitivity analysis, and, particularly, the 100% …
MGSC 1205 Quantitative Methods I - mathstat.dal.ca
Sensitivity Analysis Post-optimality analysis: examining changes after the optimal solution has been reached. • input data are varied to assess optimal solution sensitivity. Basic Question: …
3 Analyzing Solutions - LINDO
Most LP programs will optionally supplement the solution report with a range (i.e., sensitivity analysis) report. This report indicates the amounts by which individual right-hand side or …
LP Methods.S2 Sensitivity Analysis - University of Texas at …
Sensitivity Analysis 2 ∆ z = c B∆ x B = ∆ b. This equation shows that gives the sensitivity of the optimal payoff with respect to small changes in the vector b. In other words, if a new problem …
Chapter 4 Objective Function Coefficients - WordPress.com
Simplex-Based Sensitivity Analysis and Duality Sensitivity Analysis with the Simplex Tableau Duality 2 Objective Function Coefficients and Range of Optimality The range of optimality for …
UNIVERSITY OF WATERLOO MANAGEMENT ENGINEERING …
In sensitivity analysis we determine how values of input parameters and activities change and their effect on changing the optimal solution. Tells us which parameter is most crucial. Enables …
