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.
Table of Contents:
Preface, Chapter 1 Inventory Problem 1.1 INTRODUCTION 1.2 INVENTORY PROBLEMS 1.3 INVENTORY AND ECONOMIC ORDER QUANTITY (EOQ) 1.4 FACILITY LOCATION WITH AN OIL RIG LOCATION PROBLEM 1.5 COMPUTER CABLING LOCATION OF CENTRAL COMPUTER 1.6 EXERCISES Chapter 2 Product Mix: Linear Programming Problems 2.1 LINEAR PROGRAMMING PROBLEM INTRODUCTION 2.1.1 Formulations 2.2 SIMPLE MANUFACTURING EXAMPLE 2.3 FINANCIAL PLANNING 2.4 BLENDING FORMULATION EXAMPLE 2.5 PRODUCTION PLANNING PROBLEM 2.6 SHIPPING PROBLEM 2.7 PRODUCT MIX 2.8 SUPPLY CHAIN OPERATIONS (GASOLINE DISTRIBUTION) 2.9 PRODUCT MIX WITH LINDO 2.10 EXERCISES Chapter 3 Transportation and Shipping Problems 3.1 TRANSPORTATION AND SHIPPING WAREHOUSE PROBLEM 3.2 TRANSPORTATION NETWORK 3.3 EXERCISES Chapter 4 Assignment Models 4.1 TRAINING CENTERS AND OFFICES 4.2 EXERCISES Chapter 5 Mathematical Programming Methods 5.1 DATA ENVELOPMENT ANALYSIS (DEA) 5.2 MANUFACTURING PROBLEM WITH DEA 5.3 SHORTEST PATH PROBLEMS 5.4 MAXIMUM FLOW PROBLEM 5.5 CRITICAL PATH IN PROJECT PLAN NETWORK 5.6 MINIMUM COST FLOW PROBLEM 5.7 GENERAL INTEGER LINEAR PROGRAMS 5.8 MIXED INTEGER PROGRAMMING APPLICATION: “EITHER-OR” CONSTRAINTS 5.9 ILLUSTRIOUS EXAMPLES 5.10 AN ENGINEERING APPLICATION: MIXING SUBSTANCES 5.11 EXERCISES Chapter 6 Resource Allocation Models Using Dynamic Programming 6.1 INTRODUCTION: BASIC CONCEPTS AND THEORY 6.2 CHARACTERISTICS OF DYNAMIC PROGRAMMING 6.3 MODELING AND APPLICATIONS OF DISCRETE DYNAMIC PROGRAMMING 6.4 EXERCISES Chapter 7 Queuing Models 7.1 INTRODUCTION TO QUEUING THEORY 7.2 THE MULTI-SERVER PROBLEMS 7.3 EXERCISES Chapter 8 Simulation Models 8.1 MISSILE ATTACK 8.2 GASOLINE-INVENTORY SIMULATION 8.3 QUEUING MODEL 8.4 R APPLIED SIMULATION 8.5 EXERCISES 8.6 RECRUITING SIMULATION MODEL 8.7 SIMPLE QUEUING PROBLEM Chapter 9 System Reliability Modeling 9.1 INTRODUCTION TO RELIABILITY MODELING 9.2 MODELING COMPONENT RELIABILITY 9.3 MODELING SERIES AND PARALLEL COMPONENTS 9.4 MODELING ACTIVE REDUNDANT SYSTEMS 9.5 MODELING STANDBY REDUNDANT SYSTEMS 9.6 MODELS OF LARGE-SCALE SYSTEMS 9.7 EXERCISES Chapter 10 Modeling Decision-Making with Multi-Attribute Decision Modeling with Technology 10.1 INTRODUCTION 10.3 SIMPLE ADDITIVE WEIGHTS (SAW) METHOD 10.4 TECHNIQUE OF ORDER PREFERENCE BY SIMILARITY TO THE IDEAL SOLUTION (TOPSIS) 10.5 MODELING OF RANKING UNITS USING DATA ENVELOPMENT ANALYSIS (DEA) WITH LINEAR PROGRAMMING 10.6 ILLUSTRATIVE EXAMPLES 10.7 TECHNOLOGY FOR MULTI-ATTRIBUTE DECISION-MAKING (MADM) 10.8 EXERCISES Chapter 11 Regression Techniques 11.1 INTRODUCTION TO REGRESSION TECHNIQUES 11.2 MODEL FITTING AND LEAST SQUARES 11.3 THE DIFFERENT CURVE-FITTING CRITERION 11.4 DIAGNOSTICS AND INTERPRETATIONS 11.5 DIAGNOSTICS AND INFERENTIAL STATISTICS 11.6 POLYNOMIAL REGRESSION IN R 11.7 EXERCISES Chapter 12 Marketing Strategies and Competition Using Game Theory 12.1 TOTAL CONFLICT GAMES 12.2 THE PARTIAL CONFLICT GAME ANALYSIS WITHOUT COMMUNICATION 12.4 NASH ARBITRATION METHOD 12.5 EXERCISES, INDEX.
About the Author :
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.
