Applications of Operations Research and Management Science for Military Decision Making

1. Front Matter

   Pages i-xix

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2. Mathematical Modeling, Management Science, and Operations Research for Military Decision-Making

   • William P. Fox, Robert Burks

   Pages 1-15

3. Statistics and Probability in Military Decision-Making

   • William P. Fox, Robert Burks

   Pages 17-99

4. Modeling by Fitting Data

   • William P. Fox, Robert Burks

   Pages 101-135

5. Mathematical Programming: Linear, Integer, and Nonlinear Optimization in Military Decision-Making

   • William P. Fox, Robert Burks

   Pages 137-191

6. Introduction to Multi-attribute Military Decision-Making

   • William P. Fox, Robert Burks

   Pages 193-249

7. Game Theory

   • William P. Fox, Robert Burks

   Pages 251-329

8. Modeling Change with Dynamical Systems Models

   • William P. Fox, Robert Burks

   Pages 331-393

9. MONTE CARLO Simulation and AGENT-BASED Modeling (ABM) in Military Decision-Making

   • William P. Fox, Robert Burks

   Pages 395-453

10. Logistics Network Modeling

    • William P. Fox, Robert Burks

    Pages 455-483

11. Back Matter

    Pages 485-487

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Based on many years of applied research, modeling and educating future decision makers, the authors have selected the critical set of mathematical modeling skills for decision analysis to include in this book. The book focuses on the model formulation and modeling building skills, as well as the technology to support decision analysis. The authors cover many of the main techniques that have been incorporated into their three-course sequence in mathematical modeling for decision making in the Department of Defense Analysis at the Naval Postgraduate School.

The primary objective of this book is illustrative in nature. It begins with an introduction to mathematical modeling and a process for formally thinking about difficult problems, illustrating many scenarios and illustrative examples. The book incorporates the necessary mathematical foundations for solving these problems with military applications and related military processes to reinforce the applied nature of themathematical modeling process.

• Military Decision Making
• Mathematical Modeling
• Model Fitting
• Optimization
• Decision Analysis
• Multi-Attribute Decision Making
• Game Theory Models
• Monte Carlo Simulation
• Agent Based Models
• Dynamical Systems Models
• Differential Equations
• Discrete Modeling

• Department of Mathematics, College of William and Mary, Williamsburg, USA

  William P. Fox

• Department of Defense Analysis, Naval Postgraduate School, Monterey, USA

  Robert Burks

William P. Fox is currently a professor in the department of mathematics at the College of William and Mary and is also Professor Emeritus in the Department of Defense Analysis at the Naval Postgraduate School in Monterey, CA. He earned his Ph.D. in Industrial Engineering/Operations Research at Clemson University, and his M.S. in Operations Research and Systems Analysis at the Naval Postgraduate School. He is responsible for coordination of a three-course sequence in Mathematical Modeling for Decision Making. His research interests include mathematical education; STEM education; quantitative decision theory; multi-attribute decision making and sensitivity analysis; and applications of game theory. He is the author of many textbooks and journal articles.

Robert Burks is an Associate Professor and Director, Wargaming Activity Hub in the Department of Defense Analysis, Naval Postgraduate School, Monterey, CA. He earned his Ph.D. in Operations Research at the Air Force Institute of Technology and his M.S. in Operations Research at the Florida Institute of Technology. He currently teaches courses in Modeling for Military Decision Making, Irregular Warfare Modeling, and Wargaming. His research interests include Agent-Based Modeling, Information Operations modeling, Wargaming, and Combat Modeling.

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