Front Matter

Front MatterSource: Operations Research, Vol. 11, No. 3 (May - Jun., 1963), pp. i-xiiPublished by: INFORMSStable URL: http://www.jstor.org/stable/168019 .

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OPERATIONS

The Journal of the Operations Research Society of America

May-June, 1963

VOLUME 11, NUMBER 3 -G

Pages 303-476

PUBLISHED BIMONTHLY BY THE

OPERATIONS RESEARCH SOCIETY OF AMERICA



OPERATIONS RESEARCH The Journal of the Operations Research Society of America

EDITOR THOMAS E. CAYWOOD

Peat, Marwick, Caywood, Schiller & Co. 203 N. Wabash Ave., Chicago 1, Ill.

ASSOCIATE EDITORS

RUSSELL L. ACKOFF, Case Institute of Technology, Cleveland, Ohio WILLIAM W. COOPER, Carnegie Institute of Technology, Pittsburgh, Pennsylvania GEORGE B. DANTZIG, The Rand Corporation, Santa Monica, California WALTER L. DEEMER, Operations Analysis Office, Hq., U.S.A.F., Washington, D. C. ROBERT DORFMAN, Harvard University, Cambridge, Massachusetts JOSEPH H. ENGEL, Operations Evaluation Group, Washington, D. C. CHARLES GOODEVE, British Iron & Steel Assn., London W1, England JOSEPH 0. HARRISON, JR., Research Analysis Corporation, Bethesda, Maryland G. RONALD HERD, Booz * Allen Applied Research, Inc., Bethesda, Maryland ROBERT HERMAN, General Motors Research Laboratories, Warren, Michigan WILLIAM J. HORVATH, University of Michigan, Ann Arbor, Michigan JOHN F. MAGEE, Arthur D. Little, Inc., Cambridge, Massachusetts JOSEPH F. MCCLOSKEY, North American Aviation, Inc., El Segundo, California THORNTON PAGE, Wesleyan University, Middletown, Connecticut E. W. PAXSON, The Rand Corporation, Santa Monica, California WILLIAM J. PLATT, Stanf9rd Research Institute, Menlo Park, California PAUL RANDOLPH, Purdue University, Lafayette, Indiana ANDREW SCHULTZ, JR., Cornell University, Ithaca, New York GEORGE SHORTLEY, Booz - Allen Applied Research, Inc., Bethesda, Maryland LAJos TAKkCS, Columbia University, New York, New York R. M. THRALL, Editor, Management Science, Ann Arbor, Michigan ROBERT S. WEINBERG, International Business Machines Corp., New York, N. Y. PETER B. WILSON, Canadian National Railways, Montreal, Quebec

MANUSCRIPTS of papers and Letters to the Editor should be submitted to the Editor or to one of the Associate Editors. Submission of a manuscript is considered to be a representation that it has been neither copyrighted nor published, that it is not being submitted for publication elsewhere, and that, if the work results from a military contract, it has been released for open publication. Material for the Analyst's Bookshelf should be submitted to JOSEPH F. Mc- CLOSKEY, Analyst's Bookshelf Editor, North American Aviation, Inc., 1700 East Imperial Highway, El Segundo, California. Announcements should be sent to the Editor.

MANAGING EDITOR AND ADVERTISING MANAGER

CHARLES P. CHADSEY Research Analysis Corporation

6935 Arlington Road, Bethesda 14, Maryland

Copyright ? 1963 by the Operations Research Society of America. Published bimonthly by the Operations Research Society of America at Mount

Royal and Guilford Avenues, Baltimore 2, Maryland. Second-class postage paid at the Post Office at Baltimore, Maryland. Subscriptions and orders for back issues should be addressed to the Business Manager,

NORVELL E. MimuERI HII, Mount Royal and Guilford Ayes., Baltimore 2, Md. Subscription Rate: $10.00 per volume (outside U. S. and Canada, $7.50 per volume).

Back volumes through 1959, $9.00. Single copies of back issues through 1959, $1.50; 1960, $2.00 per issue.

Reprints of individual articles are not available from the SOCIETY.



CAREER APPOINTMENTS

OPERATIONS EVALUATION _ GROUP

Tomorrow's Navy: "STEAMING AT 200 KNOTS"?

The pre-Columbia Indians had wheeled toys, but no wheeled load- carrying vehicles. Even with a man as prime mover they could have doubled or tripled the loads over their sometimes excellent roads. They failed to exploit their inventiveness.

One of (tie several missions of the Navy's Operations Evaluation Group is to insure that new concepts do not remain in the toy stage if they can be used profitably to carry a load. For instance, fast hovercraft are just emerging from the status of a toy. They are small and expen- sive. But they may prove moderately seaworthy, and they are quite fast. They can surely be built bigger and perhaps as fast as 200 knots.

So ... OEG is asking ... * To what Naval missions could very fast hovercraft contribute?

With what effectiveness? * How much are they likely to cost? * How reliable are they likely to be?

Now one of the two components of the Center for Naval Analyses of the Franklin Institute, the Operations Evaluation Group (OEG) is the oldest continuing operations research group in this country.

Its tasks range from assisting in the determination of a Navy R&D program to meet long-range requirements to on-the-spot assistance to Naval commanders at sea. Twenty years of experience ... coupled with the broader range of problems assigned to the new Center for Naval Analyses (CNA) ... makes OEG an interesting environment for research.

If you are a physical scientist, Dr. J. H. Engel, Director mathematician or economist and Operations Evaluation Group interested in a professional car- Center for Naval Analyses eer with OEG, write: Arlington 9, Virginia

An equal opportunity employer



AT THE WASHINGTON

AT CORG E~li RESEARCH CENTER Now located at Ft. Belvoir, VTir- Located in Georgetown, WRC ginia (adjacent to Washington). _ is presently working in satellite

CORG has several appointments m a

directed to Ella |11 111 | l coIn uterie war games semi- b

available for operations research- cutomuater L.Jed wa r games,

oriented scientists with back automeated limelds wrgae grounds in the physical, bchav t Foral and system sciences. Staff appointments are available

Assignments are in war gaming O for senior analysts interested in tactical and logistical systems, these fields. . . A senior techni- simulation models, weapons sys- cal/management position is also

tems, and computer applicatio ~available at WRC for a scientist to direct the OR Division.

Inquiries for CORG should be directed to Inquiries for WRC should be

directed to Mr. Martin N. Chase, Director ' rJmsL eknDrco Combat Operations M.JmsL eknDrco Research Group Washington Research Center

Bo 1161 1 l

Fort Belvoir, 1 a. 3600 M St., N, W. Fort Belvoir, Va. ~~~~~~~~Washington, D. C.

TECHNICAL OPERATIONS Research tehOPs An Equal Opportunity Employer



~~~~~~~~~~~~~ -

This could be a one sentence description of TECH/OPS work at CORG (Combat Operations Research Group). Actually, it's pretty accurate. Our assignment at CORG is to provide detailed answers to fundamental questions about the Army of the Future . . How will the Army fight . . . How will the Army equip . . . How will the Army organize? In. carrying out its prime responsi- bility of designing the Army of the future, the U. S. Army Combat Developments Command re- lies on CORG to provide technical studies, data, and information. TECH/OPS' analysts at CORG conduct studies in the areas of logistics, communications, weapons systems and tactics which serve as a basis for USACDC actions.

TECH/OPS work at CORG is typical of the Company's work in the System Sciences . .. Omega, 473L, COMSAT, TRAG, VALOR to name a few other programs -programs which have a direct influence on military and government planners and decision makers. If you would like to work in an environment where your individual contributions count, we would like to hear from you. Our present staffing requirements are described on the facing page.

TECHNICAL OPERATIONS Research An Equal Opportunity Employer

_~~~~~~~~~~~~~~~~~~I



3 significant texts CIRCUITS, MATRICES, AND physics. It is designed for students who have LINEAR VECTOR SPACES completed the equivalent of one semester of advanced calculus. The physical applications, ex- By LAWRENCE P. HUELSMAN, plained in some detail, are kept on a fairly ele- University of Arizona. McGraw-Hill mentary level. In this extensive revision, the ex- position has been revised throughout. Additional Electronic and Electrical Engineering material has been introduced on differential Series. 300 pages, $10.75. equations and boundary conditions, on uniform

Senior graduate leveltetforelctra . convergence, complex-valued functions, Fourier Senior graduate level text for electrical engineers, integrals, convergence of Legendre's series, The first circuits text to include material on uniqueness of solutions, and other topics. Addi- linear vector spaces. In general, the purpose of tional attention has been given to the mathe- this book is to help the student develop new matical analysis. tools and techniques in network analysis after he has had a basic foundation in the area. The MATRIX VECTOR ANALYSIS scope of this book is such that it applies to all linear lumped circuits, both passive and active, By RICHARD L. EISENMAN, U.S. reciprocal and non-reciprocal. Air Force Academy. Available in July,

FOURIER SERIES AND 1963. A concise text and reference book for under- BOUNDARY VALUE graduate courses. It blends matrix algebra with

PROBLEMS, traditional vector analysis: matrix ideas are ap- Second Edition plied to vector methods, and vector ideas are applied to matrix methods. Physical ideas are By RUEL V. CHURCHILL, Univer- used freely to illustrate and motivate mathe- sity of Michigan. 256 pages, $6.75. matical concepts, but the continuity of development is mathematical rather than physical. The An introductory treatment of Fourier series and author's aim is to dispose of artificial barriers their applications to boundary value problems in between vectors and matrices, and more gen- partial differential equations of engineering and erally between pure and applied mathematics

send for your on-approval copies now

McGRAW-HILL BOOK COMPANY 330 W. 42nd St. New York 36, N.Y.

The expanding Operations A Research program at Melpar, Inc.

has created challenging professional positions for

OPERATIONS RESEARCH AN ALYSTS

To perform model construction for special military operations and the quantitative analysis of detection, early warning, and communications networks. Will assist in analyzing performance and characteristics of instrumentation emerging from research and development programs. Strong background in mathematics, data processing, and experience in meteorology desirable.

For further details, write in strictest confidence to: John A. Haverfield, Manager-Professional Placement

MELPAR v INC A SUBSIDIARY OF WESTINGHOUSE AIR BRAKE COMPANY

3386 Arlington Boulevard, Falls Church, Virginia (a suburb of Washington, D. C.)

an equate opportunity employer

iv



DOU~GL

A NEW OPPORTUNITY

Douglas Aircraft is pleased to announce professional openings in a newly formed Advanced Developments Plans and Systems Analysis Section. The Douglas Aircraft Division is strengthening its leadership in the field of transportation, covering the complete spectrum from surface transportation to space vehicles.

A unique opportunity exists to utilize experience in both military and commercial operations and, most important, to enrich your professional experience by doing creative work in both management science and operations research.

Opportunities exist for work in the following fields:

* Advance Product Planning * Competitive Strategies * Commercial Transportation System Evaluation * Military Weapon Systems Effectiveness * Total System Costing * Operations Analysis Project Leadership

Please send resume to: L. P. Kilgore, Supervisor, Personnel Dept. 621-L3 Douglas Aircraft Division 3855 Lakewood Blvd. Long Beach, Calif.

An equal opportunity employer

V



HERBERT HALBRECHT ASSOCIATES, INC. Management Counsel * Executive Recruitment

332 SOUTH MICHIGAN AVENUE CHICAGO 4, ILL. HARRISON 7-2876

CHICAGO * LOS ANGELES * NEW YORK

Specialists in recruitment and

placement at all levels . . ..

nationally . . . in the fields of

OPERATIONS RESEARCH

THE MANAGEMENT SCIENCES

ELECTRONIC DATA PROCESSING

MATHEMATICAL SCIENCES

SCIENTIFIC MANAGEMENT

We welcome the opportunity of reviewing the resume of any pro-

f essional who is serious in his intent to make a change. All inquiries

are treated confidentially.

We will send to all respondents a list of specific employment opportunities we are currently seeking to fill throughout the United States. Also, we will furnish to him a position appraisal form which he will find helpful in objectively evaluating the various employment opportunities that are referred to him.

All of the firms with which we work pay our charges and in no case does any applicant have any financial obligation to Halbrecht Associates, Incorporated.

vi



Exceptional Opportunities for

OPERATIONS RESEARCHERS

-and for others too: Operations Research oriented physical and behavioral scientists, mathematicians, statisticians, actuarial statisticians, and engineers, for instance.

Because we are a firm that is still expanding after a half century of unbroken growth, we recognize and respect talent, and have openings for seniors, intermediates, and juniors, in all the firm's districts.

Our constant need is for people who are problem- minded-with a flair for thoroughly effective solutions and their implementation, by suitable means, whether conventional or unconventional. This means premiums on versatility, independent thinking, ability to carry re- sponsibility, and ability to grow in stature.

We offer the opportunity to deal professionally with management problems in many firms and industries -at the decision-making and payoff evaluation level. We offer the challenge this implies, and the opportunity to use your full present skills and to develop new skills. We offer an excellent professional environment, among fellow professionals, where you are considered and treated as an individual.

We'd prefer to hear from you now-but are always on the lookout for the right man. Write to the personal attention of:

Dr. E. Leonard Arnoff Director of Operations Research Ernst & Ernst Cleveland 14, Ohio

Vii



For the Convenience of Society Members and Subscribers to Operations Research in Great Britain

The OPERATIONS RESEARCH SO-

CIETY OF AMERICA has made ar- rangements with:

MRS. M. KINNAIRD, Secretary Operational Research Society Ltd. 64 Cannon Street London E.C. 4, England

to accept payment of SOCIETY

dues, and subscriptions to Opera- tions Research (in English Cur- rency-?2.13.6).

In addition, MRS. KINNAIRD will answer or relay any questions concerning the SOCIETY, its membership, or publications.

Ws e ~~~~~~~~~~~~~~~~~~:

san francisco

The first steamship company with a top-management level operations research staff invites applications from experienced scientists, mathematicians and engineers for project leader responsibilities in solving a broad range of transportation problems. Top salary and benefits. Ideal living environment. Submit detailed resume and salary requirements to:-

Personnel Relations Dept MATSON NAVIGATION CO.

215 Market Street, San Francisco 5, Calif.

An Equal Opportunities Employer

4;~~~~~~~~~~~~A

OPERATIONS RESEARCH

APPLIED MATHEMATICS

STATISTICS, RELIABILITY

Opportunities at intermediate and senior levels in the Washington Office of an expanding scientific firm, with a challenging research program involving experimental design, mathematical models, and war gaming. Experience in practical applications required

Apply to

George Shortley, Director, BOOZ-ALLEN APPLIED RESEARCH, INC.

4815 Rugby Avenue Bethesda 14, Maryland

We are an equal opportunity employer.

OPPORTUNITIES IN

OPERATIONS RESEARCH

A need exists for men interested in the application of operations research techniques to a wide variety of industrial problems. This need reflects expanding opportunities for experienced statisticians and mathematicians.

Apply to

John H. Roseboom, Director, BOOZ-ALLEN APPLIED RESEARCH, INC.

135 South La Salle Street Chicago 3, Illinois

We are an equal opportunity employer.

viii



THE CALIFORNIA ANALYSIS CENTER, INC.

presents

AN INTENSIVE 5-DAY COURSE ON

SI MULATION MODELING AND PROGRAMMING by means of the

SI MSCRIPT SIMULATION PROGRAMMING LANGUAGE

SIMULATION is widely used in such fields as manufacturing, logistics, eco-

nomics, transportation and military operations. Unfortunately, simulation program. ming with conventional techniques is extremely time consuming.

SIMSCRIPT is especially designed to facilitate the writing of simulation programs. For the operations research and management science analyst, the SIMSCRIPT language serves as a convenient notation for formulating simulation models. For the programmer, it reduces programming time severalfold as com- pared to simulations written in FORTRAN. It also permits relatively easy program modification and expansion. If the analyst and programmer are not the same

person, SIMSCRIPT greatly simplifies the problem of communication. SIMSCRIPT translators are available for the 709/7090 computer systems and

are being developed for other computers.

THE C.A.C.I. COURSE is designed to give the student a sound working knowledge of SIMSCRIPT programming. All details of the use of the system will be presented in lectures and in supervised exercise sessions.

TEXT, SIMSCRIPT: A Simulation Programming Language, H. Markowitz, B. Haus- ner and H. Karr, A RAND Corporation Research Study, Prentice-Hall, Inc.

INSTRUCTORS, Harry M. Markowitz and Herbert W. Karr. Before joining C.A.C.I. Harry Markowitz was associated with the RAND Corporation, The General Electric Company and the Cowles Foundation for Research in Economics. Herb Karr was formerly with the RAND Corporation, The General Electric Company and the Planning Research Corporation. Both are well known for publications in various fields.

GENERAL INFORMATION Alternate Dates-New York June 17-21, Chicago June 24-28, Washington, D.C. July 8-12, San Francisco August 5-9. Fee-$250 including text and materials. To enroll (or for further information concerning C.A.C.I. services) write California Analysis Center, Inc. 9465 Wilshire Blvd. Suite 420-F Beverly Hills, California.

ix



TECHNOLOGICAL PLANNING WEAPONS SYSTEMS ANALYSIS

LFE'S Monterey Laboratory is Engaged in Programs Involving.

Analysis of broad military missions and organizations to determine the operational requirements of supporting hardware systems of the future. System performance and cost effectiveness studies of the integra- tion of major subsystems into overall weapon systems.

TYPICAL PROJECTS INCLUDE:

* PERFORMANCE OPTIMIZATION TECHNIQUES...

For communications systems, air and sea transportation systems, logistics systems, and advanced ASW systems, i.e. dash, hydrofoils etc.

* PLANNING STUDIES...

To define the character of, and electronic system requirement for tactical military operations of the future.

* SYSTEM RELIABILITY REQUIREMENTS ...

* SYSTEM CONCEPTS AND EVALUATIONS...

For artillery fire control, paradrop supply and aerial radiological monitoring.

* SIMULATION AND GAMING ...

Of satellite systems, military air and ground operations.

We invite your inquiry for further information on our capabilities in the above areas or related systems and operations analysis.

Please write:

DIRECTOR

LFE ELECTRONICS A DIVISION OF LABORATORY FOR ELECTRONICS, INC,

305 WEBSTER STREET MONTEREY, CALIFORNIA

x



A The accent is on thought ... on providing an excellent scientific environment for work and exchange

of ideas (as befits an organization controlled and directed by scientists).

The result: productive effort. ORI has doubled its business volume every year since 1956 and the expansion goes on unabated. Consequently, we have unusual opportunities for engineers and scientists interested in analyzing operational and executive decision problems in astronautics, missile systems, undersea and surface warfare, and industrial transportation systems.

You will deal with top level technical and management personnel . . . you will work on critical national problems ... your financial rewards will reflect the importance of your work and are worthy of your attention.

Write: Harvey Kushner, Director, Physical Systems Division

OPERATIONS RESEARCH INCORPORATED 8605 CAMERON STREET, SILVER SPRING, MARYLAND (RESIDENTIAL SUBURB OF WASHINGTON, D.C.) * AN EQUAL OPPORTUNITY EMPLOYER A

xi



Operations Research Society of America 1962-1963

OFFICERS OF THE SOCIETY

HUGH J. MISER President ALEXANDER M. MOOD, Vice-President The MITRE Corporation C-E-I-R, Inc. Box 208 9171 Wilshire Boulevard Bedford, Mass. Beverly Hills, California

GORDON D. SHELLARD, Secretary JOHN E. WALSH, Treasurer New York Life Insurance Co. System Development Corporation 51 Madison Avenue 2500 Colorado Avenue New York 10, N. Y. Santa Monica, California

COUNCIL OF THE SOCIETY 1961-63 Past President, MARTIN L. ERNST, Arthur D. Little, Inc., 35 Acorn Park,

Cambridge 40, Massachusetts 1962-64 Past President, MERRILL M. FLOOD, Mental Health Research Institute, Uni-

versity of Michigan, Ann Arbor, Michigan

1960-63 GEORGE E. KIMBALL GEORGE SHORTLEY Arthur D. Little, Inc. Booz-Allen Applied Research Inc., 35 Acorn Park 4815 Rugby Avenue Cambridge 40, Massachusetts Bethesda 14, Maryland

1961-64 C. WEST CHURCHMAN EDWIN W. PAXSON School of Business Admin. The Rand Corporation University of California 1700 Main Street Berkeley 4, California Santa Monica, California

1962-65 ROGER R. CRANE ANDREW W. MARSHALL Touche, Ross, Bailey & Smart The Rand Corporation 80 Pine Street 1700 Main Street New York 5, New York Santa Monica, California

CHAIRMEN OF STANDING COMMITTEES Membership Committee Education Committee

LESLIE (. EDIE GIFFORD H. SYMONDS Port of New York Authority Case Institute of Technology 111 Eighth Avenue University Circle New York 11, N. Y. Cleveland 6, Ohio

Publications Committee Nominating Committee ROBERT E. MACHOL PAUL D. BIRKHAHN

Conductron Corporation The Atlantic Refining Company 343 S. Main Street 260 South Broad Street Ann Arbor, Michigan Philadelphia 1, Pennsylvania

CHAIRMEN OF OTHER COMMITTEES Lanchester Prize Committee Representative to IFORS

MARTIN L. ERNST MARTIN L. ERNST

National Problems Committee Representative to the NRC WILLIAM PLATT GEORGE SHORTLEY

Sections Committee Representatives to the AAAS Louis P. CLARK GLEN D. CAMP

ROBERT DORFMAN

Meetings Committee PAUL STILLSON Stillson Assoc.

8445 Tobias Rd. Panorama City, Calif.



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