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Operations research

Operations Research (OR) in the USA,Canada, South Africa and Australia, andOperational Research in Europe, is an in-terdisciplinary branch of applied mathemat-ics and formal science that uses methodssuch as mathematical modeling , statistics ,and algorithms to arrive at optimal or nearoptimal solutions to complex problems. It istypically concerned with optimizing the max-ima (profit, assembly line performance, crop

yield, bandwidth, etc) or minima (loss, risk,etc.) of some objective function. Operations

research helps management achieve its goalsusing scientific methods.

Model of Operation research study, based onStafford Beer (1959). [1]

OverviewThe terms operations research and manage-ment science are often used synonymously.When a distinction is drawn, managementscience generally implies a closer relation-ship to the problems of business manage-ment . The field of operations research isclosely related to Industrial engineering . In-dustrial engineers typically consider Opera-tions Research (OR) techniques to be a major

part of their toolset.Some of the primary tools used by opera-tions researchers are statistics , optimization ,probability theory , queuing theory , game the-ory , graph theory , decision analysis , and sim-ulation . Because of the computational natureof these fields, OR also has ties to computerscience , and operations researchers usecustom-written and off-the-shelf software.

Operations research is distinguished by itsfrequent use to examine an entire manage-ment information system , rather than con-centrating only on specific elements (thoughthis is often done as well). An operations re-searcher faced with a new problem is

expected to determine which techniques aremost appropriate given the nature of the sys-tem, the goals for improvement, and con-straints on time and computing power. Forthis and other reasons, the human element of OR is vital. Like any other tools, OR tech-niques cannot solve problems by themselves.

HistorySome say that Charles Babbage (1791-1871)is the "father of operations research" because

his research into the cost of transportationand sorting of mail led to England’s universal"Penny Post " in 1840, and studies into the dy-namical behaviour of railway vehicles in de-fence of the GWR ’s broad gauge. [2] The mod-ern field of operations research arose duringWorld War II .

Modern operations research originated atthe Bawdsey Research Station in the UK in1937 and was the result of an initiative of thestation’s superintendent, A. P. Rowe . Roweconceived the idea as a means to analyse andimprove the working of the UK’s early warn-ing radar system, Chain Home (CH). Initially,he analyzed the operating of the radar equip-ment and its communication networks, ex-panding later to include the operating per-sonnel’s behaviour. This revealed unappreci-ated limitations of the CH network and al-lowed remedial action to be taken. [3]

Scientists in the United Kingdom includ-ing Patrick Blackett , Cecil Gordon, C. H.Waddington , Owen Wansbrough-Jones and

Frank Yates , and in the United States withGeorge Dantzig looked for ways to make bet-ter decisions in such areas as logistics andtraining schedules. After the war it began tobe applied to similar problems in industry .

World War IIBlackett’s team undertook a number of cru-cial analyses that aided the war effort. Bri-tain introduced the convoy system to reduceshipping losses, but while the principle of us-

ing warships to accompany merchant shipswas generally accepted, it was unclearwhether it was better for convoys to be small

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Patrick Blackett .

or large. Convoys travel at the speed of theslowest member, so small convoys can travelfaster. It was also argued that small convoyswould be harder for German U-boats to de-tect. On the other hand, large convoys coulddeploy more warships against an attacker.Blackett’s staff showed that the lossessuffered by convoys depended largely on thenumber of escort vessels present, rather thanon the overall size of the convoy. Their con-clusion, therefore, was that a few large con-

voys are more defensible than many small

ones. [3]In another piece of work, Blackett’s team

analysed a report of a survey carried out byRAF Bomber Command . For the survey,Bomber Command inspected all bombers re-turning from bombing raids over Germanyover a particular period. All damage inflictedby German air defenses was noted and therecommendation was given that armour beadded in the most heavily damaged areas.Their suggestion to remove some of the crewso that an aircraft loss would result in fewerpersonnel loss was rejected by RAF com-mand. Blackett’s team instead made the sur-prising and counter-intuitive

recommendation that the armour be placedin the areas which were completely un-touched by damage in the bombers which re-turned. They reasoned that the survey wasbiased, since it only included aircraft that re-turned to Britain. The untouched areas of re-turning aircraft were probably vital areas,which, if hit, would result in the loss of theaircraft.

Map of Kammhuber Line

When Germany organised its air defencesinto the Kammhuber Line , it was realisedthat if the RAF bombers were to fly in abomber stream they could overwhelm the

night fighters who flew in individual cells dir-ected to their targets by ground controllers.It was then a matter of calculating the statist-ical loss from collisions against the statisticalloss from night fighters to calculate howclose the bombers should fly to minimise RAFlosses. [4]

The "exchange rate" ratio of output to in-put was a characteristic feature of operationsresearch. By comparing the number of flyinghours put in by Allied aircraft to the numberof U-boat sightings in a given area, it waspossible to redistribute aircraft to more pro-ductive patrol areas. Comparison of ex-change rates established "effectiveness

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ratios" useful in planning. The ratio of 60mines laid per ship sunk was common to sev-eral campaigns: German mines in Britishports, British mines on German routes, andUnited States mines in Japanese routes. [5]

Operations research doubled the successrate of aerial attacks on submarines by re-commending a shallower detonation settingon the depth charges being dropped by air-craft. The depth charges had previously beenset to detonate at the depth where the shock of the explosion would be most efficientlytransferred through the water, but submar-ines were unable to reach that depth in thelimited time available after being spotted bythe aircraft. Shallower detonation depth set-tings reduced the distance of the detonationfrom the submarine: a close detonation with

lower shock transmission efficiency was moredestructive than a more distant detonationwith better transmission. [5]

Operations research doubled the on-targetbomb rate of B-29s bombing Japan from theMarianas Islands by increasing the trainingratio from 4 to 10 percent of flying hours; re-

vealed that wolf-packs of three United Statessubmarines were the most effective numberto enable all members of the pack to engagetargets discovered on their individual patrol

stations; revealed that glossy enamel paintwas more effective camouflage for nightfighters than traditional dull camouflagepaint finish, and the smooth paint finish in-creased airspeed by reducing skin friction. [5]

On land, the operational research sectionsof the Army Operational Research Group(AORG) of the Ministry of Supply werelanded in Normandy in 1944, and they fol-lowed British forces in the advance acrossEurope. They analysed, among other topics,the effectiveness of artillery, aerial bombing,and anti-tank shooting.

After World War II After World War II, military operational re-search in the United Kingdom became knownas "operational analysis" (OA) within the UK Ministry of Defence , where OR stands for"Operational Requirement". With expandedtechniques and growing awareness, militaryOR or OA was no longer limited to only oper-ations, but was extended to encompass

equipment procurement, training, logisticsand infrastructure.

Vietnam

The influence of systems analysis on the Vietnam war is debated by scholars. VanCreveld, in ’Command at War’ argues thatthe influence has been exaggerated, but onthe other hand, it ’did help create the inform-ation pathologies’ in the war and ’made nosmall contribution to its outcome’ [6]

Scope of operationsresearchExamples of applications in which operationsresearch is currently used include:• critical path analysis or project planning :

identifying those processes in a complexproject which affect the overall duration of the project

• designing the layout of a factory forefficient flow of materials• constructing a telecommunications

network at low cost while stillguaranteeing QoS (quality of service) orQoE (Quality of Experience) if particularconnections become very busy or getdamaged

• road traffic management and ’one way’street allocations i.e. allocation problems.

• determining the routes of school buses (orcity buses) so that as few buses areneeded as possible

• designing the layout of a computer chip toreduce manufacturing time (thereforereducing cost)

• managing the flow of raw materials andproducts in a supply chain based onuncertain demand for the finishedproducts

• efficient messaging and customerresponse tactics

• robotizing or automating human-driven

operations processes• globalizing operations processes in orderto take advantage of cheaper materials,labor, land or other productivity inputs

• managing freight transportation anddelivery systems (Examples: LTLShipping , intermodal freight transport )

• scheduling :• personnel staffing• manufacturing steps• project tasks• network data traffic: these are known

as queueing models or queueingsystems.

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• sports events and their televisioncoverage

• blending of raw materials in oil refineries• determining optimal prices, in many retail

and B2B settings, within the disciplines of pricing science

Operations research is also used extensivelyin government where evidence-based policyis used.

Societies and journalsThe International Federation of OperationalResearch Societies [7] is an umbrella organiz-ation for operations research societies world-wide. Significant among these are:• Institute for Operations Research and the

Management Sciences (INFORMS) [8]

• The Operational Research Society. [9]• EURO is the association of European

Operational Research Societies. [10]

• CORS is the Canadian OperationalResearch Society. [11]

• ASOR is the Australian Society forOperations Research. [12]

• MORS is the Military Operations ResearchSociety [13] : based in the United Statessince 1966 with the objective of enhancingthe quality and usefulness of militaryoperations research analysis in support of defense decisions. (MORS) [14]

• ORSNZ is the Operations ResearchSociety of New Zealand. [15]

• ORSP is the Operations Research Societyof the Philippines [16]

• ORSI the Operational Research Society of India, [17] and

• ORSSA the Operations Research Societyof South Africa. [18]

Other important Operations Research organ-izations are:

• Simulation Interoperability StandardsOrganization (SISO) [19]

• Interservice/Industry Training, Simulationand Education Conference (I/ITSEC) [20]

In 2004 INFORMS began an initiative to mar-ket the OR profession better, including awebsite entitled The Science of Better [21]

which provides an introduction to OR and ex-amples of successful applications of OR to in-dustrial problems.

Journals

INFORMS publishes twelve scholarly journ-als about operations research, including thetop two journals in their class, according to2005 Journal Citation Reports .[22] They are:

• Decision Analysis• Information Systems Research• INFORMS Journal on Computing• INFORMS Transactions on Education (an

open access journal)• Interfaces: An International Journal of the

Institute for Operations Research and the Management Science s

• Management Science: A Journal of the Institute for Operations Research and the Management Sciences

• Manufacturing & Service Operations Management

• Marketing Science• Mathematics of Operations Research• Operations Research: A Journal of the

Institute for Operations Research and the Management Sciences

• Organization Science• Transportation Science .Other journals• European Journal of Operational Research

(EJOR) : Founded in 1975 and is presentlyby far the largest operational research

journal in the world, with its around 9,000pages of published papers per year. In2004, its total number of citations was thesecond largest amongst OperationalResearch and Management Science

journals;• INFOR Journal : published and sponsoredby the Canadian Operational ResearchSociety;

• Journal of Defense Modeling andSimulation (JDMS): Applications,

Methodology, Technology : a quarterly journal devoted to advancing the scienceof modeling and simulation as it relates tothe military and defense. [23]

• Journal of the Operational ResearchSociety (JORS) : an official journal of TheOR Society; [24]

• Journal of Simulation (JOS) : an official journal of The OR Society; [25]

• Military Operations Research (MOR) :published by the Military OperationsResearch Society ;

• Opsearch : official journal of theOperational Research Society of India;

• OR Insight : a quarterly journal of The OR Society; [26]

• TOP : the official journal of the Spanish

Society of Statistics and OperationsResearch. [27]

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See alsoOperationresearchtopics• Assignment

problem• Decision

Analysis• Dynamic

programming• Linear

programming• Inventory

theory• Optimal

Maintenance• Optimization

• Real optionsanalysis

• Scheduling• Stochastic

processes• Systems

analysis• Systems

thinking

Operationresearchers• Operations

researchercategory

• Russell L. Ackoff

• AnthonyStaffordBeer

• AlfredBlumstein

• C. WestChurchman

• GeorgeDantzig

• RichardKarp

• Frederick W.Lanchester

• Thomas L.Magnanti

• Alvin E.Roth

Related fields• Database

normalization• Industrial

Engineering• Industrial

organization• Management

science• Managerial

economics• Military

simulation• Modeling &

Simulation• Search Based

SoftwareEngineering

• Simulation• System

Dynamics• System

Safety• Systems

theory• Wargaming

Further reading• C. West Churchman, Russell L. Ackoff &

E. L. Arnoff, Introduction to Operations Research , New York: J. Wiley and Sons,1957

• Joseph G. Ecker & Michael Kupferschmid, Introduction to Operations Research ,Krieger Publishing Co.

• Frederick S. Hillier & Gerald J.Lieberman, Introduction to Operations

Research , McGraw-Hill: Boston MA; 8th.(International) Edition, 2005

• Maurice W. Kirby, Operational Researchin War and Peace , Imperial College Press,London, 2003

• Michael Pidd, Tools for Thinking: Modelling in Management Science , J.Wiley & Sons Ltd., Chichester; 2nd.Edition, 2003

• Hamdy A. Taha, Operations Research: An Introduction , Prentice Hall; 8th. Edition,2006

• Wayne Winston, Operations Research: Applications and Algorithms , DuxburyPress; 4th. Edition, 2003

References[1] Stafford Beer (1959). Cybernetic and

Management . English Universities Press.[2] M.S. Sodhi, "What about the ’O’ in O.R.?"

OR/MS Today, December, 2007, p. 12,http://www.lionhrtpub.com/orms/orms-12-07/frqed.html

[3] "Numbers are Essential": Victory in theNorth Atlantic Reconsidered, March-May1943

[4] [1][5] ^ Milkman, Raymond H. (May 1968).

Operations Research in World War II.

United States Naval Institute Proceedings.

[6] Van Creveld, Command at War, p 241[7] IFORS[8] INFORMS[9] The OR Society[10] EURO[11] CORS[12] ASOR [13] MORS[14] [2][15] ORSNZ[16] ORSP[17] ORSI[18] ORSSA [19] SISO[20] I/ITSEC[21] The Science of Better[22] INFORMS Journals[23] JDMS[24] The OR Society ;[25] The OR Society ;[26] The OR Society ;

[27] TOP

External links• INFORMS OR/MS Resource Collection : a

comprehensive set of OR links.• International Federation of Operational

Research Societies

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Categories : Applied mathematics , Formal sciences , Operations research , Mathematical optim-ization , Management , Mathematical science occupations , Fields of application of statistics

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