Operational research, also known as operations research, is an interdisciplinary branch of applied mathematics Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions and formal science A formal science is a branch of knowledge that is concerned with formal systems, for instance, logic, mathematics, systems theory and the theoretical aspects of computer science, information theory, decision theory, statistics, and linguistics that uses advanced analytical methods such as mathematical modeling A mathematical model uses mathematical language to describe a system. The process of developing a mathematical model is termed mathematical modelling . Mathematical models are used not only in the natural sciences (such as physics, biology, earth science, meteorology) and engineering disciplines, but also in the social sciences (such as economics,, statistical analysis Statistics is the formal science of making effective use of numerical data relating to groups of individuals or experiments. It deals with all aspects of this, including not only the collection, analysis and interpretation of such data, but also the planning of the collection of data, in terms of the design of surveys and experiments, and mathematical optimization In mathematics and computer science, optimization, or mathematical programming, refers to choosing the best element from some set of available alternatives to arrive at optimal or near-optimal solutions to complex decision-making problems. It is often concerned with determining the maximum In mathematics, maxima and minima, known collectively as extrema , are the largest value (maximum) or smallest value (minimum), that a function takes in a point either within a given neighbourhood (local extremum) or on the function domain in its entirety (global extremum). More generally, the maxima and minima of a set (as defined in in set (of profit, performance, or yield) or minimum (of loss, risk, or cost) of some real-world objective. Originating in military efforts before World War II, its techniques have grown to concern problems in a variety of industries.[1]

Contents

Overview

Operational research encompasses a wide range of problem-solving techniques and methods applied in the pursuit of improved decision-making and efficiency.[2] Some of the tools used by operational researchers are statistics Statistics is the formal science of making effective use of numerical data relating to groups of individuals or experiments. It deals with all aspects of this, including not only the collection, analysis and interpretation of such data, but also the planning of the collection of data, in terms of the design of surveys and experiments, optimization In mathematics and computer science, optimization, or mathematical programming, refers to choosing the best element from some set of available alternatives, probability theory Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single occurrences or evolve over time in an apparently random, queuing theory Queueing theory is the mathematical study of waiting lines . The theory enables mathematical analysis of several related processes, including arriving at the (back of the) queue, waiting in the queue (essentially a storage process), and being served by the server(s) at the front of the queue. The theory permits the derivation and calculation of, game theory Game theory is a branch of applied mathematics that is used in the social sciences, most notably in economics, as well as in biology , engineering, political science, international relations, computer science, and philosophy. Game theory attempts to mathematically capture behavior in strategic situations, in which an individual's success in making, graph theory In mathematics and computer science, graph theory is the study of graphs: mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of vertices. A graph may be undirected, meaning, decision analysis Decision Analysis is the discipline comprising the philosophy, theory, methodology, and professional practice necessary to address important decisions in a formal manner. Decision analysis includes many procedures, methods, and tools for identifying, clearly representing, and formally assessing the important aspects of a decision situation, for, mathematical modeling A mathematical model uses mathematical language to describe a system. The process of developing a mathematical model is termed mathematical modelling . Mathematical models are used not only in the natural sciences (such as physics, biology, earth science, meteorology) and engineering disciplines, but also in the social sciences (such as economics, and simulation Simulation is used in many contexts, including the modeling of natural systems or human systems in order to gain insight into their functioning. Other contexts include simulation of technology for performance optimization, safety engineering, testing, training and education. Simulation can be used to show the eventual real effects of alternative. Because of the computational nature of these fields, OR also has strong ties to computer science Computer science or computing science is the study of the theoretical foundations of information and computation, and of practical techniques for their implementation and application in computer systems. It is frequently described as the systematic study of algorithmic processes that create, describe, and transform information. Computer science. Operational researchers faced with a new problem must determine which of these techniques are most appropriate given the nature of the system, the goals for improvement, and constraints on time and computing power.

Work in operational research and management science may be characterized as one of three categories:[3]

The major subdisciplines in modern operational research, as identified by the journal Operations Research [4], are:

History

As a formal discipline, operational research originated in the efforts of military planners during World War II Albania · Australia · Austria · Azerbaijan · Belarus · Belgium · Brazil · Bulgaria · Burma · Cambodia · Canada · Ceylon (Sri Lanka) · Channel Islands · China · Czechoslovakia · Denmark · Dutch East Indies · Egypt · Estonia · Finland · France · Germany · Gibraltar · Greece · Greenland · Hong Kong · Hungary · Iceland ·. In the decades after the war, the techniques began to be applied more widely to problems in business, industry and society. Since that time, operational research has expanded into a field widely used in industries ranging from petrochemicals to airlines, finance, logistics, and government, moving to a focus on the development of mathematical models that can be used to analyze and optimize complex systems, and has become an area of active academic and industrial research. [1]

Historical origins

In the World War II era, operational research was defined as "a scientific method of providing executive departments with a quantitative basis for decisions regarding the operations under their control."[5] Other names for it included operational analysis (UK Ministry of Defence from 1962)[6] and quantitative management.[7]

Prior to the formal start of the field, early work in operational research was carried out by individuals such as Charles Babbage Charles Babbage, FRS was an English mathematician, philosopher, inventor, and mechanical engineer who originated the concept of a programmable computer. Parts of his uncompleted mechanisms are on display in the London Science Museum. In 1991, a perfectly functioning difference engine was constructed from Babbage's original plans. Built to. His research into the cost of transportation and sorting of mail led to England's universal "Penny Post" in 1840, and studies into the dynamical behaviour of railway vehicles in defence of the GWR The Great Western Railway was a British railway company that linked London with the south west and west of England and most of Wales. It was founded in 1833, received its enabling Act of Parliament in 1835, and ran its first trains in 1838. It was engineered by Isambard Kingdom Brunel who chose a broad gauge of 7 ft 0+1⁄4 in (2,140 mm), but from's broad gauge.[8] Percy Bridgman brought operational research to bear on problems in physics in the 1920's and would later attempt to extend these to the social sciences. [9] The modern field of operational research arose during World War II Albania · Australia · Austria · Azerbaijan · Belarus · Belgium · Brazil · Bulgaria · Burma · Cambodia · Canada · Ceylon (Sri Lanka) · Channel Islands · China · Czechoslovakia · Denmark · Dutch East Indies · Egypt · Estonia · Finland · France · Germany · Gibraltar · Greece · Greenland · Hong Kong · Hungary · Iceland ·.

Modern operational research originated at the Bawdsey Research Station in the UK in 1937 and was the result of an initiative of the station's superintendent, A. P. Rowe. Rowe conceived the idea as a means to analyse and improve the working of the UK's early warning radar system, Chain Home Chain Home was the codename for the ring of coastal Early Warning radar stations built by the British before and during World War II. The system otherwise known as AMES Type 1 consisted of radar fixed on top of a radio tower mast, called a 'station' to provide long-range detection of aircraft. This system had shortcomings in not being able to (CH). Initially, he analyzed the operating of the radar equipment and its communication networks, expanding later to include the operating personnel's behaviour. This revealed unappreciated limitations of the CH network and allowed remedial action to be taken. [10]

Scientists in the United Kingdom including Patrick Blackett Patrick Maynard Stuart Blackett, Baron Blackett OM CH FRS was an English experimental physicist known for his work on cloud chambers, cosmic rays, and paleomagnetism. He also made a major contribution in World War II advising on military strategy and developing Operational Research. His left-wing views saw an outlet in third world development and later Lord Blackett OM PRS, Cecil Gordon, C. H. Waddington, Owen Wansbrough-Jones Sir Owen Haddon Wansbrough-Jones KBE, CB , was a leading academic chemist and soldier whose career included serving as Chief Scientist to the British Ministry of Supply, Frank Yates Frank Yates was one of the pioneers of 20th century statistics. He was born in Manchester, Jacob Bronowski Jacob Bronowski was a British mathematician and biologist of Polish-Jewish origin. He is best remembered as the presenter and writer of the 1973 BBC television documentary series, The Ascent of Man and Freeman Dyson Freeman John Dyson FRS is a British-born American theoretical physicist and mathematician, famous for his work in quantum field theory, solid-state physics, and nuclear engineering. Dyson is a member of the Board of Sponsors of The Bulletin of the Atomic Scientists. Dyson has lived in Princeton, New Jersey for over fifty years, and in the United States with George Dantzig George Bernard Dantzig was an American mathematician, and the Professor Emeritus of Transportation Sciences and Professor of Operations Research and of Computer Science at Stanford looked for ways to make better decisions in such areas as logistics Logistics is the management of the flow of goods, information and other resources between the point of origin and the point of consumption in order to meet the requirements of consumers . Logistics involves the integration of information, transportation, inventory, warehousing, material handling, and packaging, and occasionally security. Logistics and training schedules. After the war it began to be applied to similar problems in industry.

Second World War

Patrick Blackett Patrick Maynard Stuart Blackett, Baron Blackett OM CH FRS was an English experimental physicist known for his work on cloud chambers, cosmic rays, and paleomagnetism. He also made a major contribution in World War II advising on military strategy and developing Operational Research. His left-wing views saw an outlet in third world development and

During the Second World War close to 1,000 men and women in Britain were engaged in operational research. About 200 operational research scientists worked for the British Army The British Army is the land armed forces branch of Her Majesty's Armed Forces in the United Kingdom. It came into being with the unification of the Kingdoms of England and Scotland into the Kingdom of Great Britain in 1707. The new British Army incorporated Regiments that had already existed in England and Scotland and was administered by the War.[11]

Patrick Blackett worked for several different organizations during the war. Early in the war while working for the Royal Aircraft Establishment Coordinates: 51°16′46″N 0°47′17″W / 51.279475°N 0.787926°W The Royal Aircraft Establishment England, was a British research establishment latterly under the UK Ministry of Defence (MOD) (RAE) he set up a team known as the "Circus" which helped to reduce the number of anti-aircraft artillery Anti-aircraft warfare, or air defence, is any method of engaging hostile military aircraft in defence of ground objectives, ground or naval forces or denial of passage through a specific airspace region, area or anti-aircraft combat zone. It is also used in denying entry into national air space to unauthorized aircraft rounds needed to shoot down an enemy aircraft from an average of over 20,000 at the start of the Battle of Britain The Battle of Britain is the name given to the air campaign waged by the German Air Force (Luftwaffe) against the United Kingdom during the summer and autumn of 1940. The objective of the campaign was to gain air superiority over the Royal Air Force (RAF), especially Fighter Command. The name derives from a famous speech delivered by Prime to 4,000 in 1941.[12]

In 1941 Blackett moved from the RAE to the Navy, first to the Royal Navy's Coastal Command, in 1941 and then early in 1942 to the Admiralty The Admiralty was formerly the authority in the Kingdom of England, and later in the United Kingdom, responsible for the command of the Royal Navy. Originally exercised by a single person, the office of Lord High Admiral was from the 18th Century onward almost invariably put "in commission", and was exercised by the Lords Commissioners.[13] Blackett's team at Coastal Command's Operational Research Section (CC-ORS) included two future Nobel prize The Nobel Prizes are annual international awards bestowed by Scandinavian committees in recognition of cultural and scientific advances. They were established in 1895 by the Swedish chemist Alfred Nobel, the inventor of dynamite. The prizes in Physics, Chemistry, Physiology or Medicine, Literature, and Peace were first awarded in 1901. The winners and many other people who went on to be preeminent in their fields.[14] They undertook a number of crucial analyses that aided the war effort. Britain introduced the convoy Naval convoys have been used for hundreds of years, and examples of merchant ships/cars traveling under naval protection have been traced back to the 12th Century. The use of organized naval convoys dates from when ships began to be separated into specialist classes and national navies were established system to reduce shipping losses, but while the principle of using warships to accompany merchant ships was generally accepted, it was unclear whether it was better for convoys to be small or large. Convoys travel at the speed of the slowest member, so small convoys can travel faster. It was also argued that small convoys would be harder for German U-boats U-boat is the anglicized version of the German word U-Boot , itself an abbreviation of Unterseeboot (undersea boat), and refers to military submarines operated by Germany, particularly in World War I and World War II. Although in theory U-boats could have been useful fleet weapons against enemy naval warships, in practice they were most to detect. On the other hand, large convoys could deploy more warships against an attacker. Blackett's staff showed that the losses suffered by convoys depended largely on the number of escort vessels present, rather than on the overall size of the convoy. Their conclusion, therefore, was that a few large convoys are more defensible than many small ones.[15]

While performing an analysis of the methods used by RAF Coastal Command to hunt and destroy submarines, one of the analysts asked what colour the aircraft were. As most of them were from Bomber Command they were painted black for nighttime operations. At the suggestion of CC-ORS a test was run to see if that was the best colour to camouflage the aircraft for daytime operations in the grey North Atlantic skies. Tests showed that aircraft painted white were on average not spotted until they were 20% closer than those painted black. This change indicated that 30% more submarines would be attacked and sunk for the same number of sightings.[16]

Other work by the CC-ORS indicated that on average if the depth at which aerial delivered depth charges (DCs) was changed from 100 feet to 25 feet, the kill ratios would go up. The reason was that if a U-boat saw an aircraft only shortly before it arrived over the target then at 100 feet the charges would do no damage (because the U-boat wouldn't have time to descend to that depth), and if it saw the aircraft a long way from the target it had time to alter course under water so the chances of it being within the 20 feet kill zone of the charges was small. It was more efficient to attack those submarines close to the surface when these targets' locations were better known than to attempt their destruction at greater depths when their positions could only be guessed. Before the change of settings from 100 feet to 25 feet, 1% of submerged U-boats were sunk and 14% damaged. After the change, 7% were sunk and 11% damaged. (If submarines were caught on the surface, even if attacked shortly after submerging, the numbers rose to 11% sunk and 15% damaged). Blackett observed "there can be few cases where such a great operational gain had been obtained by such a small and simple change of tactics".[17]

Bomber Command's Operational Research Section (BC-ORS), analysed a report of a survey carried out by RAF Bomber Command.[citation needed] For the survey, Bomber Command inspected all bombers returning from bombing raids over Germany over a particular period. All damage inflicted by German air defenses was noted and the recommendation was given that armour be added in the most heavily damaged areas. Their suggestion to remove some of the crew so that an aircraft loss would result in fewer personnel loss was rejected by RAF command. Blackett's team instead made the surprising and counter-intuitive recommendation that the armour be placed in the areas which were completely untouched by damage in the bombers which returned. They reasoned that the survey was biased, since it only included aircraft that returned to Britain. The untouched areas of returning aircraft were probably vital areas, which, if hit, would result in the loss of the aircraft.[citation needed]

Map of Kammhuber Line

When Germany organised its air defences into the Kammhuber Line, it was realised that if the RAF bombers were to fly in a bomber stream they could overwhelm the night fighters who flew in individual cells directed to their targets by ground controllers. It was then a matter of calculating the statistical loss from collisions against the statistical loss from night fighters to calculate how close the bombers should fly to minimise RAF losses.[18]

The "exchange rate" ratio of output to input was a characteristic feature of operational research. By comparing the number of flying hours put in by Allied aircraft to the number of U-boat sightings in a given area, it was possible to redistribute aircraft to more productive patrol areas. Comparison of exchange rates established "effectiveness ratios" useful in planning. The ratio of 60 mines laid per ship sunk was common to several campaigns: German mines in British ports, British mines on German routes, and United States mines in Japanese routes.[19]

Operational research doubled the on-target bomb rate of B-29s bombing Japan from the Marianas Islands by increasing the training ratio from 4 to 10 percent of flying hours; revealed that wolf-packs of three United States submarines were the most effective number to enable all members of the pack to engage targets discovered on their individual patrol stations; revealed that glossy enamel paint was more effective camouflage for night fighters than traditional dull camouflage paint finish, and the smooth paint finish increased airspeed by reducing skin friction.[19]

On land, the operational research sections of the Army Operational Research Group (AORG) of the Ministry of Supply (MoS) were landed in Normandy in 1944, and they followed British forces in the advance across Europe. They analysed, among other topics, the effectiveness of artillery, aerial bombing, and anti-tank shooting.

After World War II

This section requires expansion.

With expanded techniques and growing awareness of the field at the close of the war, operational research was no longer limited to only operational, but was extended to encompass equipment procurement, training, logistics and infrastructure.

Academic Denis Bouyssou describes the historical development of operational research from the 1940s to the 1970s as follows. "The historical development of Operational Research (OR) is traditionally seen as the succession of several phases: the 'heroic times' of the Second World War, the 'Golden Age' between the fifties and the sixties during which major theoretical achievements were accompanied by a widespread diffusion of OR techniques in private and public organisations, a 'crisis' followed by a 'decline' starting with the late sixties, a phase during which OR groups in firms progressively disappeared while academia became less and less concerned with the applicability of the techniques developed".[20]

Individuals such as Stafford Beer and George Dantzig pioneered early academic efforts in operational research.

Problems addressed with operational research

Operational research is also used extensively in government where evidence-based policy is used.

Management science

In 1967 Stafford Beer characterized the field of management science as "the business use of operations research".[21] However, in modern times the term management science may also be used to refer to the separate fields of organizational studies or corporate strategy. Like operational research itself, management science (MS), is an interdisciplinary branch of applied mathematics devoted to optimal decision planning, with strong links with economics, business, engineering, and other sciences. It uses various scientific research-based principles, strategies, and analytical methods including mathematical modeling, statistics and numerical algorithms to improve an organization's ability to enact rational and meaningful management decisions by arriving at optimal or near optimal solutions to complex decision problems. In short, management sciences help businesses to achieve their goals using the scientific methods of operational research.

The management scientist's mandate is to use rational, systematic, science-based techniques to inform and improve decisions of all kinds. Of course, the techniques of management science are not restricted to business applications but may be applied to military, medical, public administration, charitable groups, political groups or community groups.

Management science is concerned with developing and applying models and concepts that may prove useful in helping to illuminate management issues and solve managerial problems, as well as designing and developing new and better models of organizational excellence. [22]

The application of these models within the corporate sector became known as Management science.[23]

Techniques

Some of the fields that are considered within Management Science include:

Applications of management science

Applications of management science are abundant in industry as airlines, manufacturing companies, service organizations, military branches, and in government. The range of problems and issues to which management science has contributed insights and solutions is vast. It includes:.[22]

Management science is also concerned with so-called ”soft-operational analysis”, which concerns methods for strategic planning, strategic decision support, and Problem Structuring Methods (PSM). In dealing with these sorts of challenges mathematical modeling and simulation are not appropriate or will not suffice. Therefore, during the past 30 years, a number of non-quantified modelling methods have been developed. These include:

Societies and journals

Societies

The International Federation of Operational Research Societies (IFORS)[24] is an umbrella organization for operational research societies worldwide, representing approximately 50 national societies including those in the US,[25] UK,[26] France,[27] Germany, Canada,[28] Australia,[29] New Zealand,[30] Philippines,[31] India,[32], Japan and South Africa,[33]. The constituent members of IFORS form regional groups, such as that in Europe,[34]. Other important operational research organizations are Simulation Interoperability Standards Organization (SISO)[35] and Interservice/Industry Training, Simulation and Education Conference (I/ITSEC)[36]

In 2004 the US-based organization INFORMS began an initiative to market the OR profession better, including a website entitled The Science of Better[37] which provides an introduction to OR and examples of successful applications of OR to industrial problems. This initiative has been adopted by the Operational Research Society in the UK, including a website entitled Learn about OR,[38].

Journals

INFORMS publishes twelve scholarly journals about operations research, including the top two journals in their class, according to 2005 Journal Citation Reports.[39] They are:

Other journals

See also

Operation research topics
Operation researchers
Related fields

Notes

This article includes a list of references, related reading or external links, but its sources remain unclear because it lacks inline citations. Please improve this article by introducing more precise citations where appropriate. (June 2009)
  1. ^ a b http://www.hsor.org/what_is_or.cfm
  2. ^ http://www.bls.gov/oco/ocos044.htm
  3. ^ What is Management Science Research? University of Cambridge 2008. Retrieved 5 June 2008.
  4. ^ http://www3.informs.org/site/OperationsResearch/index.php?c=10&kat=Forthcoming+Papers
  5. ^ "Operational Research in the British Army 1939–1945, October 1947, Report C67/3/4/48, UK National Archives file WO291/1301 Quoted on the dust-jacket of: Morse, Philip M, and Kimball, George E, Methods of Operations Research, 1st Edition Revised, pub MIT Press & J Wiley, 5th printing, 1954.
  6. ^ UK National Archives Catalogue for WO291 lists a War Office organisation called Army Operational Research Group (AORG) that existed from 1946 to 1962. "In January 1962 the name was changed to Army Operational Research Establishment (AORE). Following the creation of a unified Ministry of Defence, a tri-service operational research organisation was established: the Defence Operational Research Establishment (DOAE) which was formed in 1965, and it absorbed the Army Operational Research Establishment based at West Byfleet."
  7. ^ http://brochure.unisa.ac.za/myunisa/data/subjects/Quantitative%20Management.pdf
  8. ^ 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
  9. ^ P. W. Bridgman, The Logic of Modern Physics, The MacMillan Company, New York, 19207
  10. ^ http://www.britannica.com/EBchecked/topic/682073/operations-research/68171/History#ref22348
  11. ^ Kirby, p. 117
  12. ^ Kirby, pp. 91–94
  13. ^ Kirby, p. 96,109
  14. ^ Kirby, p. 96
  15. ^ "Numbers are Essential": Victory in the North Atlantic Reconsidered, March–May 1943
  16. ^ Kirby, p. 101
  17. ^ (Kirby, pp. 102,103)
  18. ^ [1]
  19. ^ a b Milkman, Raymond H. (May 1968). Operations Research in World War II. United States Naval Institute Proceedings.
  20. ^ Bouyssou, Denis, Questioning the history of operational in order to prepare its future http://hal.ccsd.cnrs.fr/docs/00/02/86/41/PDF/cahierLamsade196.pdf
  21. ^ Stafford Beer (1967) Management Science: The Business Use of Operations Research
  22. ^ a b What is Management Science? Lancaster University, 2008. Retrieved 5 June 2008.
  23. ^ What is Management Science? The University of Tennessee, 2006. Retrieved 5 June 2008.
  24. ^ IFORS
  25. ^ INFORMS
  26. ^ The OR Society
  27. ^ http://www.roadef.org/content/index.htm
  28. ^ CORS
  29. ^ ASOR
  30. ^ ORSNZ
  31. ^ ORSP
  32. ^ ORSI
  33. ^ ORSSA
  34. ^ EURO
  35. ^ SISO
  36. ^ I/ITSEC
  37. ^ The Science of Better
  38. ^ Learn about OR
  39. ^ INFORMS Journals
  40. ^ Decision Analysis
  41. ^ INFORMS Transactions on Education
  42. ^ JDMS
  43. ^ a b c The OR Society;
  44. ^ Mathematical Methods of Operations Research website
  45. ^ TOP

References

Further reading

External links

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Operations Research Problem???
Q. A company makes two kinds of leather belts, Belt 'A' is a high quality belt & Belt 'B' is of lower quality. The respective profits are Rs.4 & Rs.3 per belt. Each belt of type A requires twice as much as time as a belt of type B and if all belts were of type B, the company could make 1000 per day. The supply of leather is sufficient for only 800 belts per day (both A & B combined). Belt A requires a fancy buckle and only 400 per day are available. There are only 700 buckles a day available for belt B. Determine the Optimal Product Mix. NOW, can any one, please give me solution for the above "Operations research (OR)" PROBLEM??? It would be good, if it is in proper steps...
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A. This is the classic simplex linear optimization problem. Check these out:
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