Teaching Trends
OR's Top 25
Twenty-five books that shaped how operations research is taught and practiced
By Saul I. Gass
I try not to live dangerously. I do not run red lights or ride roller coasters. So why would I risk being pummeled with stones and shot with arrows by trying to select the 25 books (out of the thousands) that were most influential to the development of operations research? Two reasons come to mind: (1) Like the proverbial mountain, the challenge was there to be climbed, and (2) I was on my way to such a selection by developing, for the 50th anniversary of the founding of ORSA, a timeline of important OR events that included the publication of seminal books. Thus, when Peter Horner, the editor of ORMS Today, asked me for such a list for this educational issue, I could not say no.
In making the list, I decided to progress down the timeline until I hit 25. The list covers the first three decades of OR-related books published in the United States. I expect that many of you will not agree with the totality of my list, but I cannot imagine that your list and my list would have an empty intersection. Each of us has our favorites: the ones that got us through the exams, the ones that helped us develop the model or complete the project, the ones that turned us on to OR or queueing or linear programming. We view the world from where we stand. I trust that my view is a clear one, and it will at least cause you to nod yes or shake your head no (but not violently!). The OR profession owes much to these 25 authors and editors: insights, research, writing skills and devotion to their craft.
1. 1947: "Theory of Games and Economic Behavior," by J. von Neumann, O. Morgenstern; Princeton University Press, 641 pages.
The seminal book that sets forth the modern axiomatic notion of utility, the basic concepts of games of strategy, and their application to economic and social theory. It is here that we first learn about utility and gambles, zero- and non-zero sum games, mixed strategies, and two- and n-person games. The book was originally published in 1944, but the revised 1947 edition is considered the standard reference (it includes, as an appendix, the authors' first statement of an axiomatic derivation of numerical utility theory).
2. 1950: "An Introduction to Probability Theory and Its Applications, Vol. I," by W. Feller; John Wiley & Sons, 419 pages.
The basic reference and text that helped introduce early OR researchers (and many students) to probabilistic concepts with applications to Markov chains, renewal theory, random walks and stochastic processes. The long awaited Volume II was published in 1966.
3. 1951: "Methods of Operations Research," by P. M. Morse, G. E. Kimball; MIT Press and John Wiley & Sons, 158 pages.
Originally a 1946 Department of the Navy classified report, this book introduced the basic concepts of OR to U.S. industrial, business and nonmilitary governmental executives, as well as to the academic research community. Its first sentence gave us the famous definition of OR: "Operations Research is a scientific method of providing executive departments with a quantitative basis for decisions regarding the operations under their control."
4. 1951: "Activity Analysis of Production and Allocation," by T. C. Koopmans (ed.); John Wiley & Sons, 404 pages.
This is the proceedings of the June 20-24, 1949 Cowles Commission for Research in Economics conference held at the University of Chicago (also known as the 0th Mathematical Programming Symposium). It is noted for being the first general publication on linear programming and contains Dantzig's papers on the linear programming model, the general and transportation simplex method, linear programming and game theory, plus related papers by Arrow, Brown, Dorfman, Gale, Geisler, Koopmans, Kuhn, Morgenstern, Samuelson, Simon, Tucker and Wood.
5. 1952: "Introduction to the Theory of Games," by J. McKinsey; McGraw-Hill Book Company, 371 pages.
The first text that presented the concepts of game theory as developed by von Neumann and Morgenstern, including a discussion of linear programming and its relationship to two-person zero-sum games.
6. 1953: "An Introduction to Linear Programming," by A. Charnes, W. W. Cooper, A. Henderson; John Wiley & Sons, 74 pages.
This book was the first to give an extended discussion of the economic interpretation of linear programming (using the famous nut-mix problem), coupled with the basic mathematical theory and explanation of the simplex method and duality. It also discusses the perturbation of a linear-programming problem that resolves the issue of degeneracy.
7. 1953: "The Theory of Inventory Management," by T. Whitin; Princeton University Press, 245 pages.
An early compendium of basic inventory control methods, theory of the firm and military applications. The second edition (1957) was expanded (347 pages) to include material published after 1953 by Whitin and co-authors that appeared in Management Science, Journal of the Operations Research Society, and Naval Research Logistics Quarterly, plus an article by Whitin and H. Wagner on "Dynamic Problems in the Theory of the Firm."
8. 1954: "Operations Research for Management," by J. McCloskey, F. Trefethen (eds.); The Johns Hopkins Press, 409 pages.
The first publication that covers the history of OR and the relationship between management and the operations researcher (authors include Goodeve, Henderson, Johnson); the methods of OR including statistics, information theory, linear programming, queueing theory, suboptimization, symbolic logic, computers, game theory (authors include Ackoff, Blackwell, Cushen, Harrison, Hitch, Morse); and case histories including the famous studies of "Utilization of Negro Manpower in the Army" (Hausrath) and "Operations Research in Agriculture" (Thornthwaite).
9. 1957: "Dynamic Programming," by R. Bellman; Princeton University Press, 434 pages.
This book, by the originator of dynamic programming, discusses this important approach to resolving multi-stage decision problems and presents the famous principle of optimality: an optimal policy (set of decisions) has the property that, whatever the initial state and initial decision are, the remaining decisions must constitute an optimal policy with regard to the state resulting from the first decision.
10. 1957: "Games and Decisions: Introduction and Critical Survey," by R. D. Luce, H. Raiffa; John Wiley & Sons, 309 pages.
The first book that integrates in a rather non-mathematical manner von-Neumann and Morgenstern's utility and game theories. It made these concepts accessible to practitioners and researchers, and helped set the future course of decision-making under uncertainty.
11. 1957: "Introduction to Operations Research," by C. Churchman, E. Arnoff, R. Ackoff; John Wiley & Sons, 645 pages.
This is the first integrated text in OR written by three OR pioneers who were then associated with the Case Institute of Technology. Although written for the "prospective" consumer and "potential" practitioner, and without exercises, it served as a basic text for many years.
12. 1958: "Linear Programming: Methods and Applications," by S. I. Gass; McGraw-Hill Book Co., 223 pages.
This was the first book on linear programming that was written as text. It grew out of an introductory course in linear programming given at the Graduate School, U.S. Department of Agriculture, Washington, D.C. The first and subsequent editions were translated into Russian, Spanish, Polish, Czechoslovakian, Japanese and Greek, and were the first such books in the respective countries.
13. 1958: "Linear Programming and Economic Analysis," by R. Dorfman, P. A. Samuelson, R. Solow; McGraw-Hill Book Co., 525 pages.
The first book that emphasizes the econometric basis of linear programming and its application to a wide range of econometric topics. It introduced the power of linear programming and its application to business and industry to the economic profession. Samuelson and Solow have received the Nobel Prize in Economics.
14. 1958: "Queues, Inventory and Maintenance," by P. M. Morse; John Wiley & Sons, 202 pages.
Written by a prime mover of OR in the United States, this expository book brings together for the first time key theoretical and applied aspects of queueing theory. It was the first book published in the ORSA Publications in Operations Research Series.
15. 1959: "Mathematical Methods of Operations Research," by T. L. Saaty; McGraw-Hill Book Co., 421 pages.
The first graduate-level text that integrated the basic mathematical aspects of OR. It includes chapters on optimization, linear and quadratic programming, game theory, probability, statistics and queueing, with applications and problems.
16. 1960: "Finite Markov Chains," by J. G. Kemeny, J. Laurie Snell; Van Nostrand Company, Inc., 210 pages.
The first English language presentation of finite Markov chains. Designed as an undergraduate text, it describes applications to random walks, Leontief input-output model and occupational mobility.
17. 1961: "Industrial Dynamics," by J. Forrester; MIT Press, 464 pages.
The seminal book by the originator of system dynamics, a computer-based simulation approach that applies a differential equation model with feedback loops to the study of policy analysis and design of complex systems. The technique has been extended by Forrester to "Urban Dynamics" (1969) for analyzing urban growth and decay, and "World Dynamics" (1971) for analyzing environmental and population issues.
18. 1962: "Flows in Networks," by L. Ford, Jr., D. Fulkerson; Princeton University Press, 194 pages.
The first unified treatment of the subject, this book helped to establish network analysis and related results in graph and combinatorics as OR areas of research and application. It includes a detailed discussion of the "out-of-kilter" method for solving minimal cost network problems.
19. 1963: "Linear Programming and Extensions," by G. Dantzig; Princeton University Press, 621 pages.
This book, by the "father" of linear programming and the inventor of the simplex method, has served generations of OR analysts and students as a source and text for both theory and applications. It includes most of Dantzig's theoretical and applied developments in linear programming and its extensions up to that time.
20. 1962: "Smoothing, Forecasting and Prediction of Discrete Time Series," by R. Brown; Prentice Hall, 468 pages.
Exponential smoothing, developed by Brown in 1944, along with related smoothing and forecasting techniques, is given a full discussion in this first such text. A precursor book was Brown's "Statistical Forecasting for Inventory Control" (1959).
21. 1965: "Management Models and Industrial Applications of Linear Programming," by A. Charnes, W.W. Cooper; John Wiley & Sons, Volume I, 467 pages, Volume II, 859 pages.
Written as a text by two pioneers in OR and linear programming, this book is a collection of their theoretical research and applied developments. It continues to serve as a source book for OR researchers and graduate students.
22. 1967: "The Theory of Scheduling," by R. W. Conway, W. L. Maxwell, L. Miller; Addison-Wesley, 294 pages.
This is the first book that provided a complete and systematic treatment of the theoretical aspects of scheduling. Based on a graduate OR course and written as a text, it brought the full range of techniques (algebraic, stochastic, simulation) for resolving job shop and other scheduling problems to the attention of the OR research, practitioner and academic communities.
23. 1967: "Introduction to Operations Research," by F. Hillier, G. Lieberman, Holden-Day, Inc., 639 pages.
A widely used introductory OR text. Aimed at junior and senior undergraduates and first-year graduate students, it was used both by business and engineering schools. Now in its seventh edition (2001, McGraw-Hill Book Co.), it has 1,214 pages and a CD-ROM, and is as popular as ever.
24. 1968: "Nonlinear Programming: Sequential Unconstrained Minimization Techniques," by A. V. Fiacco, G. P. McCormick; John Wiley & Sons.
Recipient of the 1968 ORSA Lanchester Prize for the best English language publication in OR, this book provided a unified theory (SUMT) on methods and computational procedures for transforming and solving a constrained minimization problem by a sequence of unconstrained minimizations of an appropriate auxiliary function. SUMT has also been shown to provide a basis for more recent work on interior point methods for solving linear programming problems.
25. 1969: "Principles of Operations Research," by H. Wagner; Prentice-Hall, Inc., 1,039 pages.
Written as an undergraduate and graduate text for students in business, economics, engineering, liberal arts and public administration, this book set a new standard for such texts in terms of its inclusiveness and clarity of writing. It received the ORSA 1969 Lanchester Prize and the AIIE Book Award.
Saul Gass retired from the University of Maryland last year as the Dean's Lifetime Achievement Professor at the Robert H. Smith School of Business, University of Maryland. Gass' career in operations research dates back to 1952 — the same year the Operations Research Society of America was founded — and includes long stints on both the practice and academic sides of the profession. A past president of ORSA, Gass has received numerous awards from INFORMS over the years, including the Kimball Medal for service to the society and the profession and the INFORMS Expository Writing Award. When asked about a sequel to his Top 25 Most Influential OR Books to cover the years 1970 through the present, Gass says, "Stay tuned."
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