By Captain Wayne P. Hughes, Jr. USN (Retired)

22 November, 1999


Methods of Operations Research, by Philip M. Morse and George E. Kimball, 1951, MORS reprinting 1998, 158 pages, $25.00


Search and Screening, by Bernard O. Koopman, revised edition, 1980, MORS reprinting 1999, 368 pages, $24.00


Naval Operations Analysis, by Daniel H. Wagner, W. Charles Mylander, and Thomas J. Sanders, 3rd edition, Naval Institute Press, 421 pages, $22.95


Three out of four of what are widely regarded as the greatest works in the early literature of U. S. Navy operations analysis have been recently reprinted, two having gone through substantial revisions.1 Methods of Operations Research came out as OEG Report in 1946 and was declassified and published by MIT Press in 1951. Search and Screening, originally OEG Report 56, was updated by Bernie Koopman in 1980 shortly before he died. The MORS publications committee, with permission, decided to reissue them as a service to the military OR community. The much-improved third edition of Naval Operations Analysis is just released by the Naval Institute Press. All three books are priced to the reader’s advantage.

   Morse and Kimball's Methods of Operations Research is a cornerstone of our profession. Its examples are taken from navy analysis in World War II, but the book is pertinent for a wide readership. I did not know this during my half-dozen tours in OA billets on active duty. Not until I came to teach at NPS did I discover the breadth and depth and continuing wisdom of what is usually just called "Morse and Kimball." Chapter 1 lays out the tenets of our profession in a fashion that has never been exceeded. A fresh reading today will contrast contemporary MOR emphasis on model building and attempts at realistic combat simulation compared with the more pragmatic aim espoused by M&K to help improve an operation by close observation of it followed by an artful mathematical characterization of its salient properties. The book's careful definition of OR, with quantitative methods as the distinguishing characteristic, is also robust for non-military application and is the one most often quoted in the literature.

   Chapter 8 is the companion and complement of Chapter 1. It discusses the early analysts' experience with organizational problems (how to deal with a commander and his staff) and processes (how to adapt to the location and type of problem).

   "Realism" is a term hardly used by M&K. They stress that real wartime data is inaccurate data. They believe in optimization techniques and illustrate with World War II applications, including an example using game theory. But they accompany the solutions with words of caution about hedging against the factors that the optimization cannot handle. Rather than optimization, they emphasize "hemibel thinking," which says to look for operational performance that is below the theoretically possible by at least a factor of three, because then big improvements can be achieved with or without optimality.

   Perhaps Chapter 3 is the best and best known. It introduces measures of effectiveness and liberally illustrates them with wartime applications. The highly nuanced MOPs, MOEs, and MOFEs developed much later in two MORS workshops are a kind of inverted indicator of M&K's genius. The MORS product is a modestly useful extension compared with the M&K original. For instance, in chapter 3 may be found the often-cited example of an early electronic warfare duel between ASW aircraft and U-boats transiting the Bay of Biscay. The duel is incidental to M&K's main purpose, which is to show how "operational sweep rate" reduces a bewildering variety of data to a useful, single-valued MOE.

   The short, sweet Bay of Biscay section is one of many that inspired extensions and elaborations of the methods in Methods of Operations Research. For example, Brian McCue's new classic, U-Boats in the Bay of Biscay, is a direct descendent that is more than a reappraisal enriched with data and computer power not available to M&K.  McCue's book also contains an extension of a rudimentary campaign analysis by M&K that used differential equations to determine whether long range bombers were best applied against U-boats by attacking the Biscay ports' submarine pens, the construction yards in the Baltic, or U-boats directly in the Atlantic sea lanes.

   M&K's development of Lanchester’s linear law in its duel form is the only one I have seen (Lanchester related the linear law only to duels, never to area fire). The exploration of the probabilistic form of the square law a few pages later is another of their many developments that has been expanded by others later. Here and throughout the book the mathematical notation is old fashioned, yet practical, clear, and parsimonious compared to modern conventions.

   And I have hardly begun to describe the content of Methods of Operations Research. The coverage in a mere 145 pages is amazing. Many of its methods have been extended and enriched, but I doubt that any two analysts today could assemble the breadth of practical material covered by Philip Morse and George Kimball.

   The young mathematician, B. O. Koopman, was recognized by Phil Morse for his ability to use mathematics to represent the phenomena of search and detection--what today we call models. Before the end of the war Morse assigned Koopman to assemble the many pieces of search theory that had been developed and applied. The product was the original edition of Search and Screening. Like Methods of Operations Research, the book's methods have enjoyed many extensions by notables such as Alan Washburn, Larry Stone, and a whole stable of operations analysts who got their start under Dan Wagner. Lateral range curves, sweep widths, the inverse cube law, forestalling (the reduction in sweep width caused by a target with its own sensor), the random search formula, limiting lines of approach, the density of targets by relative bearing, the original optimum search formulation (locally random, globally efficient search), barrier search and expanding search formulas--all are here. As Koopman said in the 1980 edition, his original report had no references because there were none to cite.

   Today the mathematics of ASW screening is almost lost science. With the return to prominence of diesel submarines, Koopman's Chapter 9 and chapter 10 are a good place to relearn the core concepts of surface screen placement and aerial search plans. The concluding section of chapter 9, entitled "The New Factors and the New Screens," is highly applicable for search and screen configurations against both diesel and nuclear submarines in the 21st Century.

   Technical appendices comprise 180 of Search and Screening's 358 pages. Since the eyeball is going to be a primary means to detect ships and aircraft having stealth properties, Appendix E, Visual Detection, is a handy reference and has a bibliography of seventy entries (through 1975).

   The full development of the inverse cube law, derived in its original form for visual detection, is covered in Chapter 3. After the war Koopman followed, and sometimes led, experiments designed to measure radar and sonar detection as a function of lateral range. He concluded that the inverse cube law is often a sufficient approximation for all three types of sensors. This is extremely useful to know, because Koopman proved that when the “law” applies then the equivalent sweep width for n identical searchers is the individual sweep width times the square root of the number of searchers. As Brian McCue shows, this core proof can be adapted for dissimilar sweep widths of dissimilar search systems (still under the inverse cube law assumption). In his admirable 1981 book, Search and Detection, Alan Washburn wrote with tongue lightly touching cheek, “The fact that . . . these expressions can be evaluated in closed form is a circumstance so remarkable as to cause one to suspect divine interference. The inverse cube law is therefore possibly holy, and in any case deserves consideration . . .in circumstances where the precise assumptions lying behind it are not directly verifiable.”

   To the extent that we are serious about “information operations,” Koopman belongs on every military analyst's shelf. This is particularly true for army analysts, who need a keener appreciation of search theory's power. Every military operation, whether major war, small scale conflict, or military activity without any shooting, starts with information acquisition, and continues with information augmentation until it is over. As Koopman himself observed in an entirely new chapter 1 for his 1980 edition, non-military operations such as the search for mineral deposits, criminals, disease and contamination, and electronic signals, all can benefit from search theory. Search and Screening is the bible--well, the old testament at least--of quantitative techniques for information acquisition and denial. I speculate that an imaginative problem-solver well grounded in Koopman could apply some of his methods for detection and denial in cyberspace.

   When the first edition of Naval Operations Analysis was published in 1968 I was asked by the Naval Institute Press to review it. My appraisal was positive but I remarked that the book's methods were rather elementary. The reaction at the Naval Academy was "Wow, our students think the text is too challenging." At the time, two semesters of operations analysis were taken by all Academy students, so the reaction is not surprising. The second edition published in 1977 was a mite simpler in spots, but was useful as a senior undergraduate text.

   The new third edition of Naval Operations Analysis retains the clarity of the second edition, but it would be a stretch to say the book is elementary from stem to stern. Currently only mathematics majors, and too few students at that, take operations analysis at the Naval Academy, so they should have no problem dealing with the material. Nevertheless the book is entirely up to date and covers comprehensively all of the core concepts of the sea-going side of our profession.

   It is remarkable that the previous editions have nothing on the analysis of weapon performance. One reason was assuredly because the first edition was prepared by recent graduates of the Naval Postgraduate School, my classmates. With one minor exception dealing with the proper distribution of a torpedo salvo, the NPS curriculum in 1962-64 had nothing on weapon performance. The extensive work in chapter 6 of Morse and Kimball, "Gunnery and Bombardment Problems" was unknown to us. A second, more speculative reason may be that in peacetime at sea we dealt constantly with sensor and communications effectiveness, but we had no combat data for weapons. Be that as it may, in the third edition LCDR Steve Rowland has written a fine new chapter called Target Coverage based on material by Washburn, Morse and Kimball, and Eckler and Burr.

   The third edition is such a thoroughgoing overhaul of the second that it is virtually a new book. The introductory chapter is sharpened and enriched by Dan Wagner. There is new or much enhanced material on sonar and radar detection by Frank Andrews and David Anderson. A new chapter on Computer Assisted Search by Wagner brings search methodologies up to date. (I was especially pleased to see included the methodology for the USS Scorpion search originally described by Tony Richardson and Larry Stone.) The chapters on Mine Warfare by Al Washburn and Reliability [theory] by Jim Esary, both of NPS, are strong replacements for two weak chapters in the second edition. The chapter on Fleet Air Warfare contains the best of the second edition and adds new material by co-author Sanders, LCDR Richard Phares, and APL's estimable Dick Hunt. At the end of each chapter may be found problem sets (with answers) and an historical review of the literature accompanied by a comprehensive bibliography.

   There is yet more new or reworked subject matter, but the above is enough to indicate that the new Naval Operations Analysis was produced with loving care. So many cooks stirred the broth that Wagner, Mylander, and Sanders deserve high praise for a fare that tastes like the product of a single chef. I know for a fact that the review process (twenty-four reviewers) was so extensive and uncompromising that to the authors at times it seemed endless. The figures were done by co-author Sanders; they are a strength of the book because the artist knew his material.

   Naval Operations Analysis was Dan Wagner's swan song. The book is a fitting capstone to his distinguished career, as well as a tribute from its many other authors.


1 The fourth is OEG Report 51, Antisubmarine Operations in World War II, by C. M. Sternhell and A. M. Thorndike. Following a history of ASW operations in the Atlantic, the second half of the book, from page 89 to page 179, is a collection of analyses conducted and accompanying data.

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last update: 05 January 2000