The breadth of information about operations research and the overwhelming size of previous sources on the subject make it a difficult topic for non-specialists to grasp. Fortunately, Introduction to the Mathematics of Operations Research with Mathematica, Second Edition delivers a concise analysis that benefits professionals in operations research and related fields in statistics, management, applied mathematics, and finance.
The second edition retains the character of the earlier version, while incorporating developments in the sphere of operations research, technology, and mathematics pedagogy. Covering the topics crucial to applied mathematics, it examines graph theory, linear programming, stochastic processes, and dynamic programming. This self-contained text includes an accompanying electronic version and a package of useful commands. The electronic version is in the form of Mathematica notebooks, enabling you to devise, edit, and execute/reexecute commands, increasing your level of comprehension and problem-solving.
Mathematica sharpens the impact of this book by allowing you to conveniently carry out graph algorithms, experiment with large powers of adjacency matrices in order to check the path counting theorem and Markov chains, construct feasible regions of linear programming problems, and use the "dictionary" method to solve these problems. You can also create simulators for Markov chains, Poisson processes, and Brownian motions in Mathematica, increasing your understanding of the defining conditions of these processes. Among many other benefits, Mathematica also promotes recursive solutions for problems related to first passage times and absorption probabilities.
The OR department included faculty that would be hugely influential to the development of the field, including Kenneth Arrow, Harvey Wagner, Alan Manne, Arthur Veinott, and the father of linear programming, George Dantzig. Stanford Operations Research would later merge, first with the department of Engineering and Economic Systems (EES), and later with the departments of Industrial Engineering (IE) and Engineering Management (EM) to become Stanford Management Science & Engineering (MS&E).
Profs. Hillier and Lieberman published the preeminent introductory textbook for operations research for five editions, and Prof. Hillier would continue their work through many more editions. This book, which has been translated into more than 15 languages, has educated more than a million students globally.
I was supposed to go elsewhere for college. My dad was the dean of the faculty at Grays Harbor College, which is a community college where I grew up in Aberdeen, Washington. My two older brothers had started off there. It would have been a good college and an opportunity to join my dad, take courses from him, be on his debate squad, and so forth. I would start off there and then transfer to the University of Washington. My family was not affluent. It would be less expensive, and it was all very promising.
But then, my high school chemistry teacher happened to mention to the class that a particularly generous scholarship was being offered by Stanford. I was immediately interested. So I applied, and I got a really good scholarship that covered full tuition and a third of my room and board. That of course still left two-thirds of my room and board, and that was going to be pretty expensive. I was going to turn it down, but then our pastor mentioned that the American Baptist Foundation was giving college scholarships too. Somebody came down from Seattle and interviewed me, and they offered me a scholarship to cover another good fraction of the room and board. And so with the two scholarships together, I went to Stanford in 1954.
The biggest influence on my educational path at Stanford and my overall career in operations research was my undergraduate freshman advisor. Out of all of the Stanford faculty members who could have been assigned to me, I got a new assistant professor named Gerald Lieberman. He took me under his wing.
Jerry told me that I needed to set my goals higher and grab the opportunity to get a PhD while specializing in operations research. It sounded exciting, and I gradually came to accept that this was something I was capable of doing. He became my graduate advisor and later my dissertation advisor.
Jerry also arranged within the department that as a graduate student, I would teach a couple of courses, one of which was Introduction to Operations Research. This was the same course I had taken from Jerry in my junior year. I was a little nervous because there was a faculty member auditing the course. But I loved the opportunity to dig deeper into the various areas of operations research, and I made a special effort to develop this course as best I could.
Naturally, it was Jerry who convinced me to join the faculty, even though it was frowned upon to immediately join the faculty at the same school where you had just done both your undergraduate and graduate work. At this point, there were other interesting operations research programs beyond Stanford, and I interviewed and received offers from various universities. At the end of an interviewing trip, I called my wife to say that I had decided to accept a position at Carnegie Mellon.
Over the next three days while the airport was snowed in, Jerry kept telling me that I should stay at Stanford because this program was going to be special. He convinced me, and I joined the faculty in the Department of Industrial Engineering in September 1961. The next year, I also became part of the new Interdepartmental Program in Operations Research. Five years later, we became the Department of Operations Research, a small but high-powered department. George Dantzig, probably the most important pioneer in operations research, joined the department, and we started to attract the top students. Jerry was right. It was a special place and opportunity.
Back when I was developing the Introduction to Operations Research course as a graduate student, I learned the ins and outs of all the major operations research techniques. Jerry then came to me and said that the field needed an introduction to operations research textbook, and he invited me to be his co-author on such a book. It was a wonderful opportunity.
Over the summer of 1963, I spent long hours making very good progress on what would become the first edition. Along with Jerry, I kept working on it more gradually during the course of my regular duties for the next three years, and we both tried it out with students.
It was published in 1967, and it was a huge success. The field was waiting for this path-breaking textbook. Then things really took off as the years went by. In addition to dominating the domestic market, the book went worldwide with more than 15 translations.
As more years passed, a new opportunity arose. Our textbook was primarily aimed at STEM students, so it used quite a bit of mathematics. However, business schools had started offering a course, typically called Introduction to Management Science, that introduced operations research at an elementary level with a minimum of mathematics. Our publisher felt that we could adapt our original textbook using spreadsheets, and we finally agreed to do it.
During the mid-1990s, I was facing a real dilemma about how to proceed without Jerry. I owed so much to him, so I wanted to keep our work going to honor him. Also, our textbook was so important to the field that I felt an obligation to keep developing new editions. But how was I going to write this new book, and still keep up with new editions of the OR textbook by myself? I decided that the only way I could accomplish this would be to take an early retirement from my faculty responsibilities, become a professor emeritus, and focus on the books full-time. I made this big move in 1996.
The field has continually evolved, but this has really been noticeable in the last couple of decades or so. Before then, operations research was a hot topic, but in the early 2000s, people started talking about and publishing books about analytics and related topics such as data science, data analytics, machine learning, and AI.
I had the privilege of leading an MS&E fundraising campaign in 2005 to establish the Dantzig-Lieberman Operations Research Fellowships in the department. The response was overwhelming. This endowment fund has awarded 29 fellowships since it started, which is a fitting tribute to the eminent George Dantzig and to Jerry Lieberman, who was both an academic giant and a real prince of a man.
In spite of becoming an emeritus, I have never retired. My goal is to retire when I reach the age of 90 in a few years. I hope to enjoy the pleasures of retirement as much as I have enjoyed the satisfaction of contributing to my beloved field of operations research.
Hamdy Taha, emeritus professor of industrial engineering, has published the 50th anniversary edition of Operations Research: An Introduction. Since its inception in 1971 and now in its 11th edition, the textbook has been widely adopted by academic institutions in the U.S. and around the world.
The book introduces and teaches operations research basics, focusing on the algorithmic and practical implementation of operations research techniques. The goal is to optimize the decision-making process in a multitude of operational environments, particularly industry and business.
Taha was a Senior Fulbright Scholar to Carlos III University in Madrid, Spain. He received the Alumni Award for Excellence in Research and the Nadine Baum Faculty Teaching Award, both from the U of A, and numerous other research and teaching awards from the College of Engineering.
Fluent in three languages, Taha has also held academic positions at Universidad de las Amricas in Mexico and Cairo University in Egypt. In 2003, he was inducted into the Arkansas Academy of Industrial Engineering as an honorary member. His son, Tarek, is a graduate of the U of A Department of Industrial Engineering and former president of the Arkansas Academy of Industrial Engineering.
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