METHODS OF OPERATIONS RESEARCH PHILIP M. MORSE IKOFRShOU OK Im SHS MASSAC in M, rrs ivsrrii LI OF ri, c iiNOLO FOHMKHLl IMH1 TOR OK m.-K Hril WE PONS SlHlM-M A H AFION SHIM 1 OKKICK OK rilK SKCHhrVKk OK DKKKNSh GEORGE E. KIV1HAIJ IKOKI-SSOK OF III MlSlU OLlMHI IMVMiSlI FOKMI HI 1 1. IM l i D1UKCTOK orhii noNs IA IA rioN CHOI I MTK1 hTAri-Ji NAN FIRST EDITION REVISED Publinhod jointly by THE TECHNOLOGY PRESS OF MASSACHUSETTS INSTITUTE OF TECHNOLOGY and JOHN WILEY SONS, INC. - NEW YORK CHAPMAN HALL, LTD. - LONDON Chapters I and VIII copyrighted 1951 by The Technology Press Chapters II through VII appear herein through the courtesy of the Office of Scientific Research and De velopment and the United States Navy SECOND PRINTING JULY, 1 95 1 PREFACE IN A sfcNSE, this book should have no authors names or else several pages of names Parts of the book were written by various persons during and at the end of World War II. What the undersigned have done is to collect the material, rewrite some in the light of later kno ledge, expand some to make it more generally intelligible, add chapters on organization and general procedures, and cement the mosaic into hat is hoped to be a fairly logical structure Since the undersigned were members of the Operations Research Gtuup, U. S, Navy, it is perhaps not surprising that the examples given are draun chiefly from the work of this group, though an effort has been made to include examples from the work of other groups Many persons have helped by discussions and editorial criticism, including members of other operations jf ear I roujis in this country and in Kngland To mention a few ould slight many others, so none l l c named. During the war the scope, methods, and triumphs of operations research ere not appreciated by most scientists or by most military men because no information was freely available If e are not to lose this valuable experience and background, some of it must be made available to the scientists and engineer as well ax to the artried services This is particularly important if the methods of operations research have important peacetime applications as it is believed they do. The first publication of this woik as in classified form, just after World War II. To further the purposes mentioned in the preceding paragraph, hem ever, the 1 volume has now been declassified, after suitable modification of a feu examples. The first and last chapters have been entirely rewritten, to bring the discussion up to date, in particular with respect to nonmihtury applications There has been growing interest in the application of the techniques of operations research in industry and other nonmihtary operations. This is evidenced by the formation of a committee on operations research of the U. S. National Research Council and of an Operations Research dub in London, and by the institution of classes in operations research in several American Universities. It is hoped that the present, unclassified edition of MKTHODB OF OPERATIONS HUBKARCH vill be equally of interest and of use to industrial, merchandising, and nonmihtary govern mental executives as the earlier, classified edition seems to have been in military circles. PHILIP M. MOIIHK GEORGK K KIM BALL Wa hington, D. C., April 1950 CONTENTS CHAPTER PAGE 1 Introduction . .... 1 2 Probability . . . . . . . .... 11 3 The Use of Measures of Effectiveness . . 38 4 Strategical Kinematics . . .. ... .61 5 Tactical Analysis . . . . 81 6 Gunnery and Bombardment Problems . . . 110 7 Operational Experiments Auth Equipment and Tactics . . . 129 8 Organizational and Procedural Problems . . 137 Tables . . . .146 Bibliography . . . 154 Index . . . . ...

This volume, available for the first time in paperback, is a standard work on the physical aspects of acoustics. Starting from first principles, the authors have successfully produced a unified and thorough treatment of the subjects of generation, propagation, absorption, reflection, and scattering of compressional waves in fluids, progressing to such topics as moving sound sources, turbulence, and wave-induced vibration of structures. Material is included on viscous and thermal effects, on the acoustics of moving media, on plasma acoustics, on nonlinear effects, and on the interaction between light and sound. Problems, with answers in many cases, are given at the end of each chapter. They contain extensions to further applications, thus enhancing the reference value of the book. Many of the examples worked out in the text and in the problem solutions were not previously published. Anyone familiar with calculus and vector analysis should be able to understand the mathematical techniques used here.

Contributing Authors Include George P. Wadsworth, Bernard O. Koopman, Herbert P. Galliher And Others.

Contributing Authors Include George P. Wadsworth, Bernard O. Koopman, Herbert P. Galliher And Others.

METHODS OF OPERATIONS RESEARCH PHILIP M. MORSE IKOFRShOU OK Im SHS MASSAC in M, rrs ivsrrii LI OF ri, c iiNOLO FOHMKHLl IMH1 TOR OK m.-K Hril WE PONS SlHlM-M A H AFION SHIM 1 OKKICK OK rilK SKCHhrVKk OK DKKKNSh GEORGE E. KIV1HAIJ IKOKI-SSOK OF III MlSlU OLlMHI IMVMiSlI FOKMI HI 1 1. IM l i D1UKCTOK orhii noNs IA IA rioN CHOI I MTK1 hTAri-Ji NAN FIRST EDITION REVISED Publinhod jointly by THE TECHNOLOGY PRESS OF MASSACHUSETTS INSTITUTE OF TECHNOLOGY and JOHN WILEY SONS, INC. - NEW YORK CHAPMAN HALL, LTD. - LONDON Chapters I and VIII copyrighted 1951 by The Technology Press Chapters II through VII appear herein through the courtesy of the Office of Scientific Research and De velopment and the United States Navy SECOND PRINTING JULY, 1 95 1 PREFACE IN A sfcNSE, this book should have no authors names or else several pages of names Parts of the book were written by various persons during and at the end of World War II. What the undersigned have done is to collect the material, rewrite some in the light of later kno ledge, expand some to make it more generally intelligible, add chapters on organization and general procedures, and cement the mosaic into hat is hoped to be a fairly logical structure Since the undersigned were members of the Operations Research Gtuup, U. S, Navy, it is perhaps not surprising that the examples given are draun chiefly from the work of this group, though an effort has been made to include examples from the work of other groups Many persons have helped by discussions and editorial criticism, including members of other operations jf ear I roujis in this country and in Kngland To mention a few ould slight many others, so none l l c named. During the war the scope, methods, and triumphs of operations research ere not appreciated by most scientists or by most military men because no information was freely available If e are not to lose this valuable experience and background, some of it must be made available to the scientists and engineer as well ax to the artried services This is particularly important if the methods of operations research have important peacetime applications as it is believed they do. The first publication of this woik as in classified form, just after World War II. To further the purposes mentioned in the preceding paragraph, hem ever, the 1 volume has now been declassified, after suitable modification of a feu examples. The first and last chapters have been entirely rewritten, to bring the discussion up to date, in particular with respect to nonmihtury applications There has been growing interest in the application of the techniques of operations research in industry and other nonmihtary operations. This is evidenced by the formation of a committee on operations research of the U. S. National Research Council and of an Operations Research dub in London, and by the institution of classes in operations research in several American Universities. It is hoped that the present, unclassified edition of MKTHODB OF OPERATIONS HUBKARCH vill be equally of interest and of use to industrial, merchandising, and nonmihtary govern mental executives as the earlier, classified edition seems to have been in military circles. PHILIP M. MOIIHK GEORGK K KIM BALL Wa hington, D. C., April 1950 CONTENTS CHAPTER PAGE 1 Introduction . .... 1 2 Probability . . . . . . . .... 11 3 The Use of Measures of Effectiveness . . 38 4 Strategical Kinematics . . .. ... .61 5 Tactical Analysis . . . . 81 6 Gunnery and Bombardment Problems . . . 110 7 Operational Experiments Auth Equipment and Tactics . . . 129 8 Organizational and Procedural Problems . . 137 Tables . . . .146 Bibliography . . . 154 Index . . . . ...

Operations research originated during World War II with the military's need for a scientific method of providing executive departments with a quantitative decision-making basis. This volume-co-written by the father of operations research and one of his closest associates-originally appeared in classified form but was later made available to scientists, engineers, and other nonmilitary professionals. The authors discuss probability and the use of measures of effectiveness. They explore strategical kinematics, tactical analysis, gunnery and bombardment problems, operational experiments with equipment and tactics, and organizational and procedural problems. This new edition features an introduction by Saul I. Gass. 51 figures. 31 tables.