Front Matter

Front MatterSource: Operations Research, Vol. 14, No. 1 (Jan. - Feb., 1966), pp. i-xPublished by: INFORMSStable URL: http://www.jstor.org/stable/167971 .

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Copyright ? 1966 by the Operations Research Society of America. Published bi-monthly by the Operations Research Society of America at

Mount Royal & Guilford Avenues, Baltimore, Maryland, 21202. Entered as second-class matter at the Post Office at Baltimore, Maryland Subscription orders should be addressed to the Business Manager, NORVELL

E. MILLER, III, Mount Royal and Guilford Avenues, Baltimore, Maryland 21202.

Subscription Rate: $10.00 per volume; outside U. S. and Canada, $7.50 per volume. Single copies of the BULLETIN, $0.75 each. Back volumes are available only through Kraus Reprint Corporation, 16 E. 46th St., New York, N.Y. 10017.

Reprints of individual articles are not available; they should be requested from the authors.

FOR PERMISSION to quote or reproduce other than brief pas-

ages from OPERATIONS RESEARCH,

application should be made to the Editor.

Library of Congress Catalog Card NTumber 53-12816



OPERATIONS

The Journal of the Operations Research Society of America

January-February 1966 u VOLUME 14 NUMBER

1

I9 Pages 1-188

PUBLISHED BIMONrHLY 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. 401 N. Michigan Ave., Chicago, Ill. 60611

ASSOCIATE EDITORS WILLIAM W. COOPER, Carnegie Institute of Technology, Pittsburgh, Pennsylvania GEORGE B. DANTZIG, University of California, Richmond, California WALTER L. DEEMER, U. S. Arms Control & Disarmament Agency, 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 Wl, England JOSEPH 0. HARRISON, JR., Research Analysis Corporation, McLean, Virginia G. RONALD HERD, Kaman Aircraft Corporation, Bethesda, Maryland ROBERT HERMAN, General Motors Research Laboratories, Warren, Michigan WILLIAM J. HORVATH, University of Michigan, Ann Arbor, Michigan RONALD HOWARD, Massachusetts Institute of Technology, Cambridge, Massachusetts T. C. Hu, IBM Research Center, Yorktown Heights, N. Y. HUGH J. MISER, Travelers Research Center, Hartford, Connecticut MARCEL F. NEUTS, Purdue University, Lafayette, Indiana GEORGE E. NICHOLSON, University of North Carolina, Chapel Hill, North Carolina THORNTON PAGE, Wesleyan University, Middletown, Connecticut E. W. PAXSON, The Rand Corporation, Santa Monica, California PAUL RANDOLPH, Purdue University, Lafayette, Indiana ANDREW SCHULTZ, JR., Cornell University, Ithaca, New York GEORGE SHORTLEY, Booz * Allen Applied Research Inc., Bethesda, Maryland RYSZARD SYSKI, University of Maryland, College Park, Maryland LAJos TAKXCS, Columbia University, New York, New York R. M. THRALL, Editor, Management Science, Univ. of Mich., Ann Arbor, Mich. 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. M1aterial for the Analyst's Bookshelf should be submitted to HUGH J. M1ISER, Analyst's Bookshelf Editor, The Travelers Research Center, 250 Constitution Plaza, Hartford, Connecticut 06103. Announcements should be sent to the Editor of the BULLETIN, Van Court Hare, Jr., Analytical Associates, Inc., 420 Lexington Ave., New York, N. Y. 10017

MANAGING EDITOR AND ADVERTISING MANAGER

CHARLES P. CHADSEY Research Analysis Corporation

McLean, Virginia 22101

Copyright ? 1966 by the Operations Research Society of America. Published bimonthly by the Operations Research Society of America at Mount Royal

and Guilford Avenues, Baltimore, Maryland 21202. Second-class postage paid at the Post Office at Baltimore, Maryland 21202. Subscriptions and orders for back issues should be addressed to the Business Manager,

NORVELL E. MILLER, III, Mount Royal and Guilford Aves., Baltimore, Md. 21202. 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 artThles are not available from the SOCIETY.



OPERATIONS RESEARCH-

INCORPORATED

Supporting the Decision-Making Process with . . . * Operations and Systems Analysis * Engineering Analysis * R&D Program Evaluation and

Planning * Prediction of System Performance * Design and Imnplementation of

Management Information and Control Systems

ORI's record of accomplishment in support of the decision-making process goes back 1 i years. In that time, we have per- formed major contracts for more than 80 private organizations and military and civilian government agencies.

As a result, ORI's broad based experience today runs the gamut from undersea, surface and ground warfare through air traffic control, missile systems and astronautics ... to the equally wide-ranging problem areas of industry.

Present areas of strong emphasis include cost effectiveness and resource allocation

studies in chemical and biological warfare, ASW, non-military oceanography, space systems such as Nimbus and Polaris, personnel-manpower systems, supersonic trans- port economics, reliability and perfornance analysis of meteorological and solar observa- tion satellites for NASA, and work with the Army Institute for Advanced Studies.

Corporate headquarters are in Silver Spring, Maryland (suburban Washington, D. C.). A second office is maintained in Santa Monica, California where an experienced staff is ready to undertake assignments of any magnitude for clients in the Western United States. ORI maintains field groups in residence at the Army War Col- lege and Ordnance Research Laboratory.

May we tell you more about ORI's capabilities, and outline our background in your specific problem areas? Please write: Dr. Emory Cook, President

Operations Research Incorporated, 1400 Spring Street, Silver Spring, Maryland (Suburb of Washington, D. C.). An equal opportunity employer.

i



DIRECTOR OF COMPUTING CENTRE

THE UNIVERSITY OF WESTERN ONTARIO

LONDON, ONTARIO, CANADA

The Computing Centre at the University of Western Ontario is to be established on July 1, 1966 as a separate unit within the Faculty of Graduate Studies. Its prime function will be to service and stimulate research interest on the campus. Close liaison will be maintained with the academic Department of Computer Science.

A Director is required to supervise the operation of the Centre (at present 20 persons, but rapid expansion is envisaged) and to provide leadership in promoting its use by University departments.

Present equipment consists of an I.B.M. 7040, 32K, 5 tapes and 1301 Disk.

Applicants should have had formal training in one of the following: electronics, physics, electrical engineering or mathematics.

Experience in computer operation is essential; preference will be given to applicants who have engaged in research.

Address all inquiries to: Dr. J. F. Hart, Head, Computer Science Department, University of Western Ontario, London, Ontario, Canada.

STANFORD RESEARCH I NSTITUTE has openings for OPERATIONS ANALYSTS & SENIORtOPERATIONS ANALYSTS who have exp. in planning and analyzing tactical air offensive missions or air defense operations. Activities involve data collection, weapons system capability analysis, development of analytic criteria, design of air and ballistic missile attacks, analysis of passive defense measures, air defense battle simulation, and analysis of air and ballistic missile defense postures. The scope of analyses includes weapons, IFF, and air space control systems assumed to be deployed in tactical operations worldwide. Background requirements for these positions are degrees in Engineering, Physics, Mathematics or Statistics, with preference given those possessing advanced degrees or graduate level courses. Individuals who have broad backgrounds in operations analysis in related fields are invited to apply, as are military personnel if they meet the experience and educational backgrounds. Industrial level salaries and benefits are provided. Resumes should be sent to: E. Richard Cantu STANFORD RESEARCH INSTITUTE

333 Ravenswood Menlo Park, California -an equal opportunity employer-



MANAGEM-ENT CONSULTANTS

OPERATIONS RESEARCH ANALYSTS

Expanding activities of an unusual organization designed to provide consulting services to a major corporation internally, as well as to outside clients on an international scale has resulted in a number of Senior-Level Positions.

PROGRAM MANAGER / SENIOR OPERATIONS ANALYST Minimum of Bachelor's degree in engineering, physics or mathematics and a Master's degree in Management, Operations Research or related disciplines required. Minimum of 5 years' experience in top level management consulting specializing in military and government organization and operations, simulation and gaming, information storage and re- trieval, advanced data processing and management information systems applications essential. Consultant must be mature and capable of dealing with clients on practical and immediate problems on a quick reaction basis. This management level position offers high growth potential for the right individual.

PROGRAM MANAGER / LOGISTICS ANALYST A number of positions exist for professional consultants with minimum of a Master's degree and 5 years' experience in the development and applications and advanced OR techniques for logistic analysis. Experience in inventory control, provisioning and sparing, configura- tion control, maintenance and repair analysis essential. Should possess an intimate knowledge of logistics operations on a world-wide scale. Some travel to Europe and the Far East will be required. Applicants should have published papers in logistics field. Multi-lingual capabilities desirable.

SR. ECONOMIST / OPERATIONS ANALYST Minimum of a Master's degree with technical training in microeconomics, mathematics, the physical sciences and operations research required. Minimum of 5 years' experience in cost effectiveness and economic analysis including experience in market and product planning is desirable. Should have extensive experience in simulation, regional planning, community action programs, urban renewal activities and thorough familiarity with government organization and operation. Experience should be related to man/machine systems such as command control and intelligence operations.

All of the above positions are Senior Level with salaries open. Extensive fringe benefits offered. All professional staff operate on a fairly independent basis with a wide latitude for both professional and salaried growth. Advanced educational work is encouraged with liberal tuition refund plan.

Please Forward Resume In Complete Confidence To

P H 1 LCO A SUBSIDIARY OF 7 7

TECHREP DIVISION P. 0. BOX 10 * DEPARTMENT 811-AR e FT. WASHINGTON, PA. 19034

An Equal Opportunity Employer

iii



Operations CHALLENGING OPPORTUNI- Anal sts ~~TIES IN RESEARCH AND DEVEL- Analysts OPMENT

Our System Engineering Dept. Several responsible posi-

is expanding its professional staff tions in operations research is expanding its professional staff

and systems analysis related in the areas of operations to new advanced under-

analysis and cost effectiveness OPERATIONS water weapon systems. Op- analysis and cost effectiveness RESEARCH portunities to develop and

studies. Current projectsinldapy ne tchqus stud les. Current projects include Participation in weapon the analysis of weapon systems WEAPON cost/effectiveness, optimiza-

n asSYSTEM tion of parameters, and and advanced space systems ANALYSIS kill probability studies.

and limited war studies. These appointments offer POSITIONS Faculty appointments. Op- offer ~~~~~~~~~~portunity to participate in exceptional opportunities. OFFER the organization of a grad-

uate curriculum in Opera-

You are invited to submzit your tions Research. Excellent working and living condi- resume, including salary requirements, tions. in confidence to: MR. N. R. HARRELL, MAIL STOP #26 ORDNANCE RESEARCH

LABORATORY

BROWN THE PENNSYLVANIA STATE ENGINEERING COMPANY, INC. UNIVERSITY 300 Sparkman Drive, N.W. P. 0. Box 30 Huntsville, Alabama 35805 State College, Pennsylvania 16801

"An Equal Opportunity Employer" Send Resume to Personnel Director

IN OPERATIONS RESEARCH ... QUANTITATIVE METHODS: A Survey and Guide for Managers

By BILLY E. GOETZ, Massachusetts Institute of Technology. 541 pages, $12.50 (Text Edition also available). This sound introduction to the mathematical approach to managerial decision is noteworthy both for its refreshing writing style and its coverage. In order to give the reader "the feel" of the subject matter, Professor Goetz has retained much of the mathematics but has thoroughly explained all the mathematics used.

FORTRAN IV PROGRAMMING

By ROBERT S. LEDLEY, National Biochemical Research Foundation. 240 pages, $4.95 (cloth), $3.75 (soft cover). Teaches FORTRAN programming, start- ing at an elementary level, describing the nature of programming and flow charting, etc., and offering a complete treatment of FORTRAN language. In order to fully motivate and orient the student, the "why and wherefore" of au- tomatic programming language concepts are considered.

INTRODUCTION TO THE THEORY OF SWITCHING CIRCUITS

By E. J. McCLUSKEY, Princeton University. McGraw-Hill Series in Electrical and Electronics Engineering. 318 pages, $12.50. This important study provides broad coverage of the fundamental concepts of switching circuit theory, present- ing the theory in a manner which illustrates its applicability to a wide range of devices and physical realizations.

Send for your examination copies today

& McGRAW-HILL BOOK COMPANY * 330 West 42nd Street / New York, N.Y. 10036



Applied Mathematicians Operations Analysts ' Applied Physicists

CAREER APPOINTMENTS

vision

Vision-at Booz*Allen Applied Research-is the union of insight and farsightedness in the service of military, governmental and industrial clients. The clarity of this vision has been evident in our organization's reputation for competence, our increasing responsibilities ... and our continuing need for additional new talent.

Your career growth at Booz'Allen Applied Research will be as rapid as your talents permit. Because our breadth of interests en- compasses astronautics, communications, computer technology, mathematics and statistics, meteorology, operations research, reliability, and a dozen more, each professional staff member is able to participate in a wide range of interdisciplinary assignments. If you wish to share an outstanding record of diversified achievement and can bring us appropriate abilities and experience, we would like to hear from you. Please write Mr. Robert J. Flint, Director of Professional Appointments.

BOOZ * ALLEN APPLIED RESEARCH Inc. 135 South LaSalle Street, Chicago, Illinois 60603

New York * Washington * Cleveland * Chicago * Los Angeles An equal opportunity employer

V



ENGINEERS * PHYSICISTS * MATHEMATICIANS

N AVAL PROBLEM

SOL VING

The Applied Physics Laboratory, The Johns Hopkins University now offers both senior and associate staff appointments in naval operations analysis covering broadly defined areas of submarine, surface, and air operations. . . present andfuture.

Primary requirements include (1) interest in solving complex problems of conflict that go far beyond the limitations of Game Theory, and (2) ability to abstract operational models from the complexity of real or proposed systems. Back-ground in physics, engineering or mathematics is most applicable; knowledge of operations research techniques and modern computer usage in combat simulation is useful but not mandatory.

The APL location in suburban Washington affords a choice of city, suburban or country living and offers many benefits including complete service and recreationalfacilities and superior public and private schools. Programs leading to advanced degrees from The Johns Hopkins University may be pursued at APL. In addition, staff members may continue their education at six other area universities with APL financial support.

Direct your inquiry to: Mr. W. S. Kirby, Professional Staffing

The Applied Physics Laboratory The Johns Hopkins University

8681 Georgia Avenue, Silver Spring, Maryland (Suburb of Washington, D. C.) An equal opportunity employer

vi



Exceptional Opportunities for

OPERATIONS RESEARCHERS

EXPERIENCED IN BUSINESS AND INDUSTRY

These opportunities are for practitioners who respond to the challenge in Operations Research consulting. We seek men who are able to convert sound theory to sound practice, at all stages from the first contact with a client through the final on-stream use of an operating system.

Our engagements call for men with skill, ingenuity and versatility, working in many businesses and industries with other highly qualified professionals from our own and other disciplines. On these engagements there is stress on independent responsibility.

High performance standards call for commensurate rewards. The steady expansion of our Operations Research capability is evidence that the rewards are here-in job satisfaction- in intellectual stimulus-in other important intangibles-and in more conventional ways.

We invite you to get in touch with us for fuller information. We'd prefer to hear from you now-but are always on the lookout for the right men, Write to the personal attention of:

Dr. E. Leonard Arnoff Principal and Director of Operations Research Ernst & Ernst Cleveland, Ohio 44115

vii



New Openings in Applied OPERATIONS Operations Research

RESEARCH Matson Research Corp. is adding a se- lected number of Senior Operations Re- search Scientists to its permanent staff for

Professional careeropportunityim man- immediate assignment to major projects. agement consulting, offering services to Responsibilities include participation as Senior Project Leader from conception business and industry in the United through completion of assignments for na- States and abroad. Must have advanced tional/international corporations and non- military government agencies in this coun- degree with major in Operations Re- try and abroad.

search. and experience in commercial Positions require an advanced degree and a minimum of five years' experience in ap- applications of Linear Programming, plied management research. Econometrics, Inventory and Simulation Models. For distribution and management information backgrounds particularly desired. confidential review of your background, San Francisco location and an expanding send complete resume. professional company make this a unique

professional opportunity.

Dr. Ernest Koenigsberg, LESTER B. KNIGHT Vice President-Technical Director

Matson Research Corporation & ASSOCIATES, INC. 215 Market Street, San Francisco,

549 W. Randolph St., Chicago, IIt. 60606 California 94105

An Equal Opportunity Employer

Anatol Rapoport Albert M. Chammah

Prisoner's Dilemma This book explores the nature of conflict in the deceptively simple game from which the book takes its title. If two players cooperate, they both win; if they don't, they both lose. But they can cooperate only if each trusts the other, and the game is so structured that there is no rational basis for trusting. Moving beyond game theory, Prisoner's Dilemma builds a bridge between scientific psychology (based on hard data and reproducible experiments) and the psychology of complex inner motivations which create conflict and human strife. 272 pages $7.50

The University of Michigan Press Ann Arbor



PROFESSIONAL OPPORTUNITIES

Spindletop's steady growth has created sciences, and behavioral sciences. Since a continuing need for operations operations began in mid-1962, over 50 research scientists at many levels of industrial firms and government agen- training and experience. Present open- cies have been added to our growing ings are for M.S. (or equivalent) to client list. Here, in an environment con- Ph.D. in mathematics, statistics, and ductive to professional development, a quantitative sciences to perform cost variety of talents and specialties is effectiveness, alternate approach, feasi- melded into interdisciplinary teams as- bility, and optimum performance stud- signed to solve specific problems. If you ies for military and civilian clients, are the kind of man who seeks satisfac- ies 000. military and civilian clients. tion exploring beyond his specialty, $8,000-18,000. who welcomes the challenge of inter- Spindletop is an independent, not-for- disciplinary research, and who profit corporation providing contract expresses himself well both verbally research services in the areas of systems and on paper, please contact Mr. Hal sciences, techno-economics, physical D. Saffell, Personnel Manager.

h an equal opportunity employer

SPINDLETOP RESEARCH Ironworks Road, Lexington, Kentucky 40505

Operations Research Analysis Boeing has sold more jetliners than all analysis, market research, inventory con- other aircraft makers in the free world trol and production planning, new prod- combined, and now has a commercial uct development and long-range planning. backlog of over $2 billion. The next gen- Requirements for these positions in- eration of jets is now on the drawing clude an advanced degree in operations boards and in the wind tunnels, provid- research or in mathematics, statistics or ing opportunities in operations research physical sciences with a knowledge of analysis which involve the study of a operations research. Additional experi- wide range of business, industrial and ence in computer programming and eco- military problems. nomic analysis is desirable. Responsibilities include consulting with Salaries are competitively commensurate all levels of management in matters in- with your experience and educational volving problem formulation through to background. Travel and moving allow- implementation. ances are paid to newly hired personnel. Engineering and Military Studies - Assign- Boeing is an equal opportunity employer. ments involve developing synthesized Send your resume, today, to Mr. Thomas models to evaluate relative importance Sheppard, Commercial Airplane Division, of military systems in their operational The Boeing Company, P. 0. Box 707-BGV, environment at various levels of effec- Renton, Washington 98055. tiveness and economic value. Business and Industrial Studies - Respon- - J sibilities include financial and economic COMMERCIAL AIRPLANE DIVISION

ix



Operations Research Society of America

19 65- 19-66

OFFICERS OF THE SOCIETY

GEORGE SHORTLEY, President Booz, Allen Applied Research Inc. 4733 Bethesda Avenue Bethesda, Maryland 20014

JOSEPH H. ENGEL, Secretary Center for Naval Analyses 1401 Wilson Boulevard Arlington, Virginia 22209

JOHN F. MAGRBB, Vice-President Arthur D. Little, Inc. 35 Acorn Park Cambridge, Massachusetts 02140

THOMAS E. OBERBECK, Treasurer Office of Research Analyses (RRRR) Holloman AFB New Mexico 88330

COUNCIL OF THE SOCIETY

1964-66 Past President. ALEX M. MOOD, Office of Education, Washington, D. C. 20202 1965-67 Past President, GEORGE E. KIMBALL, Arthur D. Little, Inc., 35 Acorn Park,

Cambridge, Massachusetts 02140 1963-66 W. EDWARD CUSHEN

Institute for Applied Tech- nology

National Bureau of Standards Washington, D. C. 20234

1964-67 MURRAY GEISLER The Rand Corporation 1700 Main Street Santa Monica, California 90401

1965-68 RALPH E. GOMORY Thomas J. Watson Research

Center P. O. Box 218 Yorktown Heights, N. Y. 10598

LESLIE C. EDIE: The Port of New York Authority 111 Eighth Avenue New York, New York 10011

DAVID B. HERTZ McKinsey & Co., Inc. 270 Park Avenue New York, New York 10017

HERBERT K. WEIss Data Systems Division Litton Industries 8000 Woodley Van Nuiys, California

CHAIRMEN OF STANDING COMMITTEES

Membership Committee NEWTON A. ABLAHAT

General Electric Company 777 14th Street, N.W. Washington, D. C. 20005

Publications Committee RUSSELL L. ACEOFF

Management Science Center University of Pennsylvania Philadelphia, Pennsylvania 19104

Education Committee CHARLES D. FLAGLE

The Johns Hopkins University Baltimore, Maryland 21218

Nominating Committee PAUL L. KINGSTON

IBM Corporation Romax Building 731 James Street Syracuse, New York 13203

CHAIRMEN OF OTHER COMMITTEES

Lanchester Prize Committee WALTER L. DEEMER

Sections Committee WILLIAM J. NEMEREVER

Meetings Committee DAVID A. KATCHER

Representative to IFORS HUGH J. MISER

Representative to the NRC ROBERT F. RINEHART

Representatives to the AAAS W. EDWARD CUSHEN ELLIS A. JOHNSON



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