Back Matter

Back MatterSource: Operations Research, Vol. 10, No. 4 (Jul. - Aug., 1962), pp. 590-xxviPublished by: INFORMSStable URL: http://www.jstor.org/stable/168069 .

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Announcements

EFFECTIVE August 6, 1962, material for the Analyst's Bookshelf and books for review should be sent to: DR. JOSEPH F. MCCLOSKEY, North American

Aviation, Inc., 1700 East Imperial Highway, El Segundo, California.

T HE Twenty-second National Meeting of the OPERATIONS RESEARCH SOCIETY

OF AMERICA will be held at the Sheraton Hotel in Philadelphia, Pennsylvania, November 7-9, 1962; ROBERT MIRSKY is the Meeting Chairman. The Trwenty- third National Meeting will be held at Sheraton-Cleveland Hotel, Cleveland, Ohio, May 27-28, 1963; E. LEONARD ARNOFF is the Meeting Chairman. The Twenty- fourth National Meeting will be held at the Olympic Hotel in Seattle, Washington in November, 1963; CORLIN 0. BEJuM, JR. is the Meeting Chairman.

JOINT sponsorship of the National Advanced-Technology Management Con- ference to be held September 3-7, 1962, Seattle, Washington is announced

by several organizations including ORSA. The conference is designed to create an atmosphere suitable for the exchange of ideas, both theoretical and practical, on the subject of Systems Management. Eminent program managers will give ex- positions on their ideas about the Philosophy, Concept, Theory and Practice of Advanced-Technology Program Management. General and Special Sessions Panels as well as Management Workshops of limited sizes will be held.

T HE Institute of Management Sciences is participating in a joint meeting with the American Statistical Association, Institute of Mathematical Statistics

and Biometrika to be held in Minneapolis, Minnesota on September 7-10, 1962. Afternoon sessions on September 7 and 9 will be devoted to invited papers on New Statistical Developments in Operations Research.

THE Deutsche Gesellschaft fur Unternehmensforschung (German Operations Research Society) invites the members of ORSA to attend their annual con-

ference in Bonn, October 17-19, 1962. There will be invited papers on "Sales Planning and Inventory Management." Contributed papers will deal with various specific problems giving an insight into the state of operations-research activities in Germany.

H EADQUARTERS, Air Force Logistics Command (EWACPA) Wright-Patterson Air Force Base (Dayton), Ohio announces a civil service opening for an

Operations Research Analyst in the Salary range: $9,000--$12,000.

HAROLD DAVIS has joined the U. S. Arms Control and Disarmament Agency. JOSEPH H. ENGEL has been appointed Director of the Operations Evaluation

Group. THOMAS A. GOLDMAN has joined the Economics Division of the Washing- ton research staff of the Operations Evaluation Group. COMMANDER WALTER E. MULLER has been transferred to the U. S. Navy Operational Test and Evaluation Force Staff in Norfolk as Project Analyst. R F. RINEHART has been appointed Director of Research of the Weapons Systems Evaluation Group of the Depart- ment of Defense.

590



*0

: The OPTIMrlUMl MIX...: * 0

For those analysts interested in pursuing a balanced

program of professional development-

Peat, Marwick, Caywood, Schiller & Co.'s current studies are divided almost equally between industrial and military Operations Research. Each member of our staff has the opportunity to parti- cipate in both areas.

Resumes will be welcomed from experienced personnel with advanced degrees in mathematics, physical sciences, engineering and economics.

Address resumes to:

PEAT, MARWICK, CAYWOOI), SCHILLER & CO.

203 North Wabash Avenue

Chicago 1, Illinois

An equal opportunity employer.

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o P E RAT I O N S For the Convenience of Society Memnbers and

A N A LYST Subscribers to Operations Research in Great Britain

Unique opportunities for professional The OPERATIONS RESEARCH SO- advancement continue to be created at CIETY OF AMERICA has made ar-

MELPAR, Inc. rangements with: Immediat openingfoMRS. M. KINNAIRD, Secretary Tmmediate opening for- .

Operations Analyst-To conduct Operational Research Society operations and systems analysis Ltd. studies in connection with advanced 64 Cannon Street weapon systems, military tactics, organization and deployment of units, London EC. 4, England performance criteria for equipment and other related subjects. to accept payment of SOCIETY Write in confidence to- dues, and subscriptions to Opera- JOHN HAVERFIELD tions Research (in English Cur- Professional Employment Manager rency-X2.13.6).

MELPAR, Inc. In addition, MRS. KINNAIRD will A Subsidiary of Westinghouse Air Brake Co. answer or relay any questions

3321 Arlington Blvd. Falls Church, Va. concerning the SOCIETY, itS mem-

an equal opportunity employer bership, or publications.

~UNIVERSITY PRESS Applied Dynamic Programming The Rate and Direction

By Richard Bellman and Stuart Dreyjus of Inventive Activity:

Dynamic Programming has become Economic and Social Factors more and more widely known and The diversity of papers in this volume adopted as a valuable tool for the treat- reflects the new and intensive interest in ment of many challenging problems con- invention on the part of economists who fronting decision-making agencies in the have reawakened to the importance of economic, industrial, scientific, and invention in economic growth, industrial even political spheres of modern life. organization, defense economics, and Not only graduate students in mathe- management science. The topics covered matics and economics, but also engineers range from description and analysis of and research workers in "operations the way our political economy allocates analysis" will find interest in the book its inventive effort, to studies of the de- as it takes them into the computational cision-making process in specific in- aspects of applying the techniques of dustrial laboratories. Published for The Dynamic Programming. A RAND Corp- National Bureau of Economic Research. oration Research Study. 400 pages. $8.50 680 pages. Tables, charts. $12.50

Order from your bookstore, or

PRINCETON UNIVERSITY PRESS, Princeton, New Jersey

xvi



. ... X.. . ..........;. . . . . .. . . .. .. .. .. . ..... g0. . .. .g.

TECH NEWS~~~~~~~~~~~~~~~~~~.....

For Scientists, Mathematicians

Operations Evaluation Group

~~~~~~~~~~~.............. . ;;......... .. . ;.... g..... . X..

One of our analysts has returned from field aassignment with the fleet and told us a significant improvement re- { , suited when one of his recommendations was put into { , practice during fleet maneuvers. OEG's field activities, _X_4. assigned on a rotational basis, represent unique travel opportunities for scientists and mathematicians. There A are QEG men with the fleet in the Mediterranean, the Ad / t Far East, Hawaii, Key West, Norfolk, and San Diego, and .\_ i field representatives in Newport, R. L and London, ^}

OEG's technical management has been transferred tto the Franklin Institute. We will operate as a part of the\ new Center of Naval Analyses, in a role that promises (i)) to be broader than our former one. Having just celebrated its 20th anniversary of work for the U. S. Navy, QEG looks forward to an even more productive future.

"For 20 years, the Navy has consistently been the first of the services to foresee the opportunities for operations research and the requirements on its part to assure its success"-Dr. Jacinto Steinhardt, QEG director, at the OEG Vicennial conference.

OEG provides scientific analysis in diverse problem areas of Naval operations, including nuclear warfare, air, submarine, and anti-submarine warfare, logistics, and strategic planning. QEG's present expansion has created a need for scientists, mathematicians, economists, and engineers with advanced degrees to fill career positions whose potential is as outstanding as their challenge. Imaginative, enterprising scientists thrive on the complex problem-solving they do at OEG . . . assignments that often involve important contributions to our national purpose. The positions are well paid and carry comprehensive peripheral benefits. Please send your resume to Dr. Frank Bothwell, Chief Scientist, Center of Naval Analyses.

e. .... ..... S. ....j W

OEG CENTER OF NAVAL ANALYSES

Arlington Towers, Arlington 9, Virginia An equal opportunity employer

..., .... . ........ .... ..

... ..

. . ......

... ..ll ..



BOOKS

ANNOUNCING SOMETHING NEW...

OPERATIONS RESEARCH I MANAGEMENT SCIENCE International Literature Digest Service

This is a new monthly service, both for management and the techni- cian, offering a single source of world-wide coverage of the literature * Digests more than 400 American and foreign periodicals * Includes subject, title, authors, journal, purpose, summary, re-

sults * Covers new contributions made in transactions of meetings both

here and abroad * Uses the services of more than 100 reviewers * Presents lengthy resumes, giving original data, graphs, etc., so

that reference to the original material is not often necessary These are only a few of the advantages you'll get with your sub- scription to OR/MS($75 the year). Send today for the complete brochure which includes sample pages.

INTERSCIENCE PUBLISHERS 440 PARK AVENUE SOUTH, NEW YORK 16, N.Y. A DIVISION OF JOHN WILEY & SONS, INC.

.51

STANFORD RESEARCHNTUT

Has Openings in Challenging Professional Positions for

Operations Analysts

To conduct analyses of en~es ,offe~s qfliquixvii

0- weapons systemsatalIvIsfqufedjwsun 0- air defense systems Io mobilization problems aikotdeoibbhyn Io civil defense problems preci prtin'rsa~i~ Io industrial operations research

data processing applicationsalyhaegnffrg xelt

Write to ... onenc n rd zrine PROFESSIONAL EMPLOYMENT MANAGER idaetuyoptniesad

STAN FORD RESEARCH INSTITUTE ~~f~irtas~ain c vW MENLO PARK, CALIFORNIA bnteae

An equal opportunity employer

xviii



F

TVOPERATIONS RESEARCH

ANALYST

Celanese Corporation of America is continuing to in-

tensify its utilization of mathematically-based scientific

disciplines for its engineering, manufacturing, product

distribution and management decision-information

activities. The current opening will complete a small bult

select group of professional specialists formed for this

eff ort.

The man sought should be capable of and vitally

interested in the application of his know-how to opera-

tions ranging from the Mexican Border to Canada in-

volving chemicals, fibers, plastics and polymers. Knowl-

edge or advanced degree in mathematics or statistics is desirable. A high level of individual initiative and action

also will characterize the successful applicant.

He will work as an internal consultant between top

management and the line and staff employees responsible

for sales forecasts, production schedules, process opera-

tion and control, inventory and quality control, and the

transportation of product to customer. These and re-

lated activities are complex and often require the use of

high-speed computers. They demand the highest order

of ability in problem definition and solution.

The position, based in Charlotte, North Carolina,

provides an opportunity to make substantial contributions in a growing operation conducive to personal

achievement and reward. If you by virtue of interests,

goals, education and experience feel that you belong in

this challenging young enterprise, please send complete

resume, including salary requirements, in confidence,

to Mr. Glen Smyth.

I ~co 11 CORPORATION OF AMERICA

An equal opportunity employer

522 Fifth Avenue, New York 36, New York

Xix



Have You Completed the Questionnaire of the Mathematics and Statistics Sec- tion of the National Register of Scien- tific and Technical Personnel?

On behalf of the Operations Research Society of America and various mathematical organizations the American Mathematical Society is assembling and maintaining a register of mathematicians, statisticians, and mathematical scientists. The mathematics register is a section of the National Register of Scientific and Technical Personnel, which is an official responsibility of the National Science Foundation. The main objective of the Register is to provide up-to-date information on the scientific manpower resources of the United States. It is also increasingly valuable to our profession as a source of statistical information. At the request of the National Science Foundation, the American Mathematical Society has mailed the 1962 reporting forms to its section in the National Register. We are counting again on the splendid cooperation accorded to the previous cycle of the Register by most of the mathematicians and mathematical scientists. If you received a National Register questionnaire from the Ameri- can Mathematical Society, won't you please fill it in now and send it to the Headquarters Offices of the Society at 190 Hope Street, Providence 6, Rhode Island. If you have never received a questionnaire and feel that you are qualified for inclusion in the Register, please send a note to that effect to the above address.

Merrill M. Flood, Past President Operations Research Society of America

xx



HERBERT HALBRECHT ASSOCIATES, INC. Management Counsel * Executive Recruitment

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

CHICAGO 0 LOS ANGELES 0 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 professional 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.

xxi



Operations Research

The growing Operations Research Program at NCR has provided lasting opportunities for graduate level personnel in areas of work spanning the complete corporate program. These operations include:

* Long range planning for all phases of corporate activity * Guide lines for future products research * Operational specifications for computer based systems

of the future.

Persons with a Ph.D. in any appropriate field or equivalent education are invited to explore the outstanding opportunity this presents. Versatility and ability to handle complex non-orthodox problems is desirable. Graduate training in operations research, physics, engineering, mathematics, or economics is preferred. Experience in the analytical techniques of abstract model development is necessary. To pursue the matter of your future further, write now including a complete description of your preparation to date. All qualified applicants will be considered regardless of race, creed, color, or national origin. Direct replies to:

T. F. Wade, Technical Placement The National Cash Register Company South Main & K Streets, Dayton 9, Ohio

NCR PROVIDES TOTAL SYSTEMS -FROM ORIGINAL ENTRY TO FINAL REPORT- THROUGH ACCOUNTING MACHINES, CASH REGISTERS OR ADDING MACHINES, AND DATA PROCESSING

The National Cash Register Co. * 1,039 offices in 121 countries * 78 years of helping business save money

NCR

xxii



OPERATIONS ANALYSTS * MATHEMATICIANS * WEAPONS COST ANALYSTS

Join Republic in Giving a New Direction to 'AM"

Aerospace Technology thru

weapon system analysis

Intensifying research and development in several vital areas including advanced space, missile and aircraft weapon systems present skilled analysts at Republic with unparalleled diversity of technical challenges. The Weapon System Analysis Group evaluates, compares and establishes requirements for next-generation weapons in all flight regimes.

To implement these studies the most sophisticated and integrated research complex in the East is available ... Republic's Paul Moore Research and Develop- ment Center. Other resources include a centralized Computer Division with IBM 7090 and ancillary 1401 computers as well as a 70,000 volume technical library.

Mathematicians and analysts with all levels of experience who wish to contribute to the new direction Republic is imparting to aerospace technology should write in confidence to:

Mr. George R. Hickman Technical Employment Manager, Dept. 30 G

REPUBLIC AVIATION CORPORATION

FARMINGDALE, LONG ISLAND, NEW YORK An Equal Opportunity Employer

Xxiii



TECHNOLOGICAL PLANNING WEAPONS SYSTEMS ANALYSIS

Expansion Of Our Monterey Laboratory Offers Exceptional Opportunities For Experienced Analysts To Lead And Con-

tribute To 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 integration of major sub-systems into overall weapon systems.

POSITIONS AT ALL LEVELS are available for professionals with specific experience in long-range planning or weapons systems analysis, along with a back- ground in physics, mathematics, statistics or engineering.

WE ARE LOCATED on the beautiful Monterey Peninsula-one of the most desirable living and working areas in the West. 100 miles south of San Francisco, Monterey enj oys a temperate, smog-free climate year around.

For further information, please submit professional resume in confidence to:

Mr. W. E. Daly

LFE ELECTRONICS A DIVISION OF LABORATORY FOR ELECTRONICS, INC.

MONTEREY LABORATORY 305 WEBSTER STREET MONTEREY, CALIFORNIA

An Equal Opportunity Employer

xxiv



AT 0 I 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.) 0 AN EQUAL OPPORTUNITY EMPLOYER

Xxv



An Independent Research Organization in a Stimulating University Environment

OPERATIONS ANALYSTS Excellent opportunities in operations research are now available at the Research Triangle Institute, an independent nonprofit research organization

located on its own campus in North Carolina's Research Triangle Park.

Imaginative, resourceful analysts are needed at all levels for expand- ing programs in civil and military defense and industrial operations research.

Rapid advancement is possible for experienced operations analysts and also for qualified recent graduates in mathematics, statistics, physical sciences, engineer-

ing, and economics.

A stimulating environment for professional and cultural development is provided by close association with the Triangle universities: Duke, North Carolina, and North Carolina State. Nearby mountains and beaches enhance pleasant

living conditions.

For further information, please write to:

Dr. Edgar A. Parsons Head, Operations Research Division

RESEARCH TRIANGLE INSTITUTE

AN EQUAL OPPORTUNITY EMPLOYER

Post Office Box 490 Durham, North Carolina

Xxvi



- PUBLICATIONS in

OPERATIONS RESEARCH

Sponsored by the Operations Research Society of America David B. Hertz, Editor for Publications in Operations Research

We are pleased to announce the publication in September i962. of Nos. 1 6 and 7 in our ORSA series:

6-Wagner. STATISTICAL MANAGEMENT OF INVENTORY SYSTEMS

The first book to emphasize and explore the basic difficulties in carrying out OR policies. Gives a step-by-step procedure for evaluating control plans and provides the tools for analyzing control devices. Stress is placed on personnel control as well as physical procedures. Approx. 232 pages. Prob. $8. 9;.

,-Mills: PRICE, OUTPUT, AND INVENTORY POLICY A Study in the Economics of the Firm and Industry. Formu- lates, analyzes, estimates, and tests models of firms' decision making. Features an integration of theory and empirical studies from economics, OR, and management science. Approx. 304 pages. Prob. $7.7S.

* The first 5 books in the series are also available: i I-Morse: QUEUES, INVENTORIES, AND MAINTENANCE. 202 pages. E

$6.50. 2-Peck-Hazelwood: FINITE QUEUING TABLES. 2IO pages. $8.;o.

I 3-McKean: EFFICIENCY IN GOVERNMENT THROUGH SYSTEMS ANALYSIS. 336 pages. $8.oo.

4-OR Group-Case Institute: A COMPREHENSIVE BIBLIOGRAPHY ON OPERATIONS RESEARCH. i88 pages. $6.50. 5-Ackoff (Editor): PROGRESS IN OPERATIONS RESEARCH, Volume I. 505 pages. PI$50.

I I

N.B. These volumes are available to members of the Society at a discount of 25 %. To secure this discount, members should send checks, made out to John Wiley & Sons, Inc., to the Business Manager of the Society.

I I

Published by

JOHN WILEY & SONS, Inc. 440 Park Avenue South, New York 16, N.Y.

I_ _ __ _ _ __ _ _ __ _ _I__ __ _ _



Contents

OPERATIONS RESEARCH

Volume 10 July-August 1962 Number 4

MERRILL M. FLOOD-New Operations Research Potentials .......... 423

NEW METHODS IN MATHEMATICAL PROGRAMMING, edited by Philip Wolfe................................................... 437

PHILIP WOLFE-Some Simplex-Like Nonlinear Programming Pro- cedures ...................................................... 438

K. B. HALEY-The Solid Transportation Problem ...... ............... 448

A. MADANSKY-Methods of Solution of Linear Programs Under Uncer- tainty ...................................................... 463

MARCEL COURTILLOT-On Varying All the Parameters in a Linear-Pro- gramming Problem and Sequential Solution of a Linear-Programming Problem ...................................................... 471

WILLIAM S. JEWELL-Optimal Flow through Networks with Gains ...... 476

EDWARD B. BERMAN-A Model for the Monte Carlo Determination of Optimal Stock Distribution in a Spatial Inventory System ...... 500

F. E. A. BRIGGS-A Dual Labelling Method for the Hitchcock Problem . . 507 ARTHUR F. VEINOTT, JR. AND HARVEY M. WAGNER-Optimal Capac-

ity Scheduling-I . 518 ARTHUR F. VEINOTT, JR. AND HARVEY M. WAGNER-Optimal Capacity

Scheduling-II. 533 PAUL WEIDLINGER-The Lethal Radius of a Salvo .. . 547

N. U. PRABHU-Elementary Methods for Some Waiting Time Prob- lems . 559

LETTERS TO THE EDITOR.... . 567

PAUL J. BURKE-Priority Traffic with At Most One Queuing Class .... 567

HERBERT K. WEISS-The Fiske Model of Warfare .................. 569

THE ANALYST'S BOOKSHELF .7................... 572

BOOKS.......................................................... 572

PERIODICALS ............ 585

ANNOUNCEMENTS................................................... 590

Composed and Printed by Waverly Press, Inc. Baltimore 2, Maryland



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