This book provides sample exercises, techniques, and solutions to employ mathematical modeling to solve problems in Operations Research and Business Analytics. Each chapter begins with a scenario and includes exercises built on realistic problems faced by managers and others working in operations research, business analytics, and other fields employing applied mathematics. A set of assumptions is presented, and then a model is formulated. A solution is offered, followed by examples of how that model can be used to address related issues.Key elements of this book include the most common problems the authors have encountered over research and while consulting the fields including inventory theory, facilities' location, linear and integer programming, assignment, transportation and shipping, critical path, dynamic programming, queuing models, simulation models, reliability of system, multi-attribute decision-making, and game theory.In the hands of an experienced professional, mathematical modeling can be a powerful tool. This book presents situations and models to help both professionals and students learn to employ these techniques to improve outcomes and to make addressing real business problems easier. The book is essential for all managers and others who would use mathematics to improve their problem-solving techniques.No previous exposure to mathematical modeling is required. The book can then be used for a first course on modeling, or by those with more experience who want to refresh their memories when they find themselves facing real-world problems. The problems chosen are presented to represent those faced by practitioners.The authors have been teaching mathematical modeling to students and professionals for nearly 40 years. This book is presented to offer their experience and techniques to instructors, students, and professionals.
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This book provides sample exercises, techniques, and solutions to employ mathematical modeling to solve problems in Operations Research and Business Analytics. als.
1. Chapter 1. Inventory Problem1.1 Introduction1.2 Inventory Problems1.3 Inventory and Economic Order Quantity (EOQ)1.3.1 Inventory Analysis with EOQ formula driven approach1.3.2 Time Invariant Asphalt EOQ model1.4 Facility Location with an Oil Rig Location Problem1.5 Computer Cabling Location of Central Computer1.6 Exercises1.7 References2. Chapter 2 Product Mix: Linear Programming Problems2.1 Linear Programing Problem Introduction2.2 Simple Manufacturing Example2.3 Financial Planning2.4 Blending Formulation Example2.5 Production Planning Problem2.6 Shipping Problem2.7 Product Mix2.8 Supply Chain Operations (Gasoline Distribution)2.9 Product Mix with LINDO2.10 Exercises2.11 References and Additional Readings3. Chapter 3 Transportation and Shipping Problems3.1 Transportation and Shipping Revisited3.2 Transportation and Shipping Warehouse Problem3.2.1 Modification to the Warehouse Problem3.3 Transportation Network3.4 Exercises3.5 References and Additional Readings4. Chapter 4 Assignment Models4.1 Training Centers and Offices4.1.1 Assignment Problem4.2 Exercises4.3 References and Additional Readings5. Chapter 5 Mathematical Programming Methods5.1 Data Envelopment Analysis (DEA)5.2 Manufacturing Problem with DEA5.3 Shortest Path Problems5.3.1 Network analysis5.3.2 . Kruskal’s Method for Network Analysis Problem5.3.3 Prim’s Algorithm5.3.4 Dijkstra’s Algorithm5.4 Maximum Flow Problem5.4.1 Example 5.1. Max Flow through a given network5.5 Critical Path in Project Plan Network5.5.1 Example 5.2. CPM5.6 Minimum Cost Flow Problem5.6.1 Example 5.3. Min cost flow through a network5.7 General Integer Linear Programs5.7.1 Example 5.4. Manufacturing Equipment5.7.2 Example 5.5. Integer LP Programs by EXCEL5.8 Mixed Integer Programming Application: "Either-Or" Constraints5.8.1 Conditional Relations Among Constraints5.8.2 A Case of Discrete Finite Valued Variable5.8.3 0 - 1 Integer Linear Programs5.9 Illustrious Example5.9.1 Example 5.7. Consider the following Knapsack Problem5.9.2 Example 5.8. Traveling Salesperson Problem5.9.3 Example 5.9. Capital Budgeting Applications5.9.4 Example 5.10. Marketing Application5.9.5 Example 5.11. The Cutting Stock Problem5.10 An Engineering Application: Mixing Substances5.11 Exercises5.12 References and Additional Readings6. Chapter 6 Resource Allocation Models using Dynamic Programming6.1 Introduction: Basic Concepts and Theory6.2 Characteristics of Dynamic Programming6.2.1 Working Backwards6.2.2 Example 6.1 A Knapsack Problem.6.3 Modeling and Applications of Discrete Dynamic Programming6.3.1 Oil Well Investment DP Application6.4 Exercises6.5 References and Suggested Readings7. Chapter 7 Queuing Models7.1 Introduction to Queuing Theory7.1.1 Simple Fast Food Service Queue Example 7.17.2 The Multi-server Problems7.3 Exercises7.4 References and Suggested Readings8. Chapter 8 Simulation Models8.1 Missile Attack8.2 Gasoline-Inventory simulation8.3 Queuing model8.4 R Applied simulation8.5 Exercises8.6 References and Additional Readings9. Chapter 9 System Reliability Modeling9.1 Introduction to Reliability Modeling9.2 Modeling Component Reliability9.2.1 Battery Problem – Reliability Example 9.19.2.2 Battery Problem Revisited – Reliability Example 9.29.3 Modeling series and parallel components9.3.1 Modeling Series Systems9.3.2 Radio Components – Example 9.39.3.3 Modeling Parallel Systems (Two Components)9.3.4 Parallel Bridges – Example 9.49.4 Modeling Active Redundant Systems9.4.1 Manufacturing – Example 9.59.5 Modeling Standby Redundant Systems9.5.1 Battery Problems Revisited for Stand-by – Example 9.69.5.2 Stake Out Problem Revisited – Example 9.79.6 Models of Large Scale Systems9.7 Exercises9.8 References and Suggested Readings10. Chapter 10 Modeling Decision Making with Multi-Attribute Decision Modeling with Technology10.1 Introduction10.2 Delphi Method10.2.1 Pairwise Comparison by Saaty (AHP)10.2.2 Entropy Method10.3 Simple Additive Weights (SAW) Method10.4 Technique of Order Preference by Similarly to the Ideal Solution (TOPSIS)10.5 Modeling of Ranking Units using Data Envelopment Analysis (DEA) with Linear Programming10.6 Technology for Multi-Attribute Decision Making (MADM)10.6.1 Technology and Simple Additive Weights10.7 Exercises10.8 References and Suggested Readings.11. Chapter 11 Regression Techniques11.1 Introduction to Regression Techniques11.1.1 Correlation, covariance, and its misconceptions11.1.2 Correlation: A Measure of LINEAR relationship11.1.3 Calculating the Correlation11.1.4 Correlation for Global Warming Data Example 11.111.1.5 Testing the Significance of a Correlation with hypothesis testing11.2 Model Fitting and Least Squares11.2.1 Global Warming Example 11.111.3 The Different Curve Fitting Criterion11.3.1 A Least-Squares Fit Explosive Data Example 11.211.4 Diagnostics and Interpretations11.4.1 Fruit Flies Over Time – Example 11.411.4.2 Revisit Explosive Problem – Example 11.511.4.3 Revisit the Cubic Model – Example 11.611.5 Diagnostics and Inferential Statistics11.5.1 The Spring Mass System Using R11.5.2 Simple Linear Regression Model with complete explanation summary in R11.6 Polynomial Regression in R11.6.1 Recovery Level Versus Time – Example 11.811.6.2 Wheat Production Revisited11.7 Exercises11.8 References and Suggested Readings12. Chapter 12 Marketing Strategies and Competition Using Game Theory.12.1 Total Conflict Games12.1.1 Market Shares12.1.2 Hitter-Pitcher Dual – A Conflict Game Example12.1.3 The Expanded Hitter-Pitcher Dual12.2 The Partial Conflict Game Analysis without Communication12.3 Methods to Obtain the Equalizing Strategies12.3.1 Linear Programming with Two Players and Two Strategies Each12.4 Nash Arbitration Method12.4.1 R and the Nash Arbitration Method12.5 Exercises12.6 References and Additional Readings13. Index
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Produktdetaljer

ISBN
9781032717555
Publisert
2024-08-30
Utgiver
Vendor
Chapman & Hall/CRC
Vekt
453 gr
Høyde
234 mm
Bredde
156 mm
Aldersnivå
U, P, 05, 06
Språk
Product language
Engelsk
Format
Product format
Innbundet
Antall sider
254

Biographical note

Dr. William P. Fox is currently a visiting professor of Computational Operations Research at the College of William and Mary. He is an emeritus professor in the Department of Defense Analysis at the Naval Postgraduate School and teaches a three-course sequence in mathematical modeling for decision making. He received his Ph.D. in Industrial Engineering from Clemson University. He has taught at the United States Military Academy for twelve years until retiring and at Francis Marion University where he was the chair of mathematics for eight years. He has many publications and scholarly activities including twenty plus books and one hundred and fifty journal articles.

Colonel (R) Robert E. Burks, Jr., Ph.D. is an Associate Professor in the Defense Analysis Department of the Naval Postgraduate School (NPS) and the Director of the NPS’ Wargaming Center. He holds a Ph.D. in Operations Research from the Air Force Institute of Technology. He is a retired logistics Army Colonel with more than thirty years of military experience in leadership, advanced analytics, decision modeling, and logistics operations who served as an Army Operations Research analyst at the Naval Postgraduate School, TRADOC Analysis Center, United States Military Academy, and the United States Army Recruiting Command.

Other books by William P. Fox and Robert E. Burks: Advanced Mathematical Modeling with Technology, 2021, CRC Press.

Other books by William P. Fox from CRC Press:

Probability and Statistics for Engineering and the Sciences with Modeling using R (w/Rodney X. Sturdivant, 2023, CRC Press
Mathematical Modeling in the Age of the Pandemic, 2021, CRC Press.
Advanced Problem Solving Using Maple: Applied Mathematics, Operations Research, Business Analytics, and Decision Analysis (w/William Bauldry), 2020, CRC Press.
Mathematical Modeling with Excel (w/Brian Albright), 2020, CRC Press.
Nonlinear Optimization: Models and Applications, 2020, CRC Press.
Advanced Problem Solving with Maple: A First Course (w/William Bauldry), 2019. CRC Press.
Mathematical Modeling for Business Analytics, 2018, CRC Press.