Operations research

Operations research, or operational research (OR) in British usage, is a discipline that deals with the application of advanced analytical methods to help make better decisions.[1] Further, the term operational analysis is used in the British (and some British Commonwealth) military as an intrinsic part of capability development, management and assurance. In particular, operational analysis forms part of the Combined Operational Effectiveness and Investment Appraisals, which support British defense capability acquisition decision-making.

It is often considered to be a sub-field of applied mathematics.[2] The terms management science and decision science are sometimes used as synonyms.[3]

Employing techniques from other mathematical sciences, such as mathematical modeling, statistical analysis, and mathematical optimization, operations research arrives at optimal or near-optimal solutions to complex decision-making problems. Because of its emphasis on human-technology interaction and because of its focus on practical applications, operations research has overlap with other disciplines, notably industrial engineering and operations management, and draws on psychology and organization science. Operations research is often concerned with determining the extreme values of some real-world objective: the maximum (of profit, performance, or yield) or minimum (of loss, risk, or cost). Originating in military efforts before World War II, its techniques have grown to concern problems in a variety of industries.[4]

Overview

Operational research (OR) encompasses a wide range of problem-solving techniques and methods applied in the pursuit of improved decision-making and efficiency, such as simulation, mathematical optimization, queueing theory and other stochastic-process models, Markov decision processes, econometric methods, data envelopment analysis, neural networks, expert systems, decision analysis, and the analytic hierarchy process.[5] Nearly all of these techniques involve the construction of mathematical models that attempt to describe the system. Because of the computational and statistical nature of most of these fields, OR also has strong ties to computer science and analytics. 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.

The major sub-disciplines in modern operational research, as identified by the journal Operations Research,[6] are:

History

In the decades after the two world wars, the tools of operations research were more widely applied 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 analyse and optimize complex systems, and has become an area of active academic and industrial research.[4]

Historical origins

In the 17th century, mathematicians like Christiaan Huygens and Blaise Pascal (problem of points) tried to solve problems involving complex decisions with probability. Others in the 18th and 19th centuries solved these types of problems with combinatorics. Charles Babbage's 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's broad gauge.[7] Beginning in the 20th century, study of inventory management could be considered the origin of modern operations research with economic order quantity developed by Ford W. Harris in 1913. Operational research may have originated in the efforts of military planners during World War I (convoy theory and Lanchester's laws). Percy Bridgman brought operational research to bear on problems in physics in the 1920s and would later attempt to extend these to the social sciences.[8]

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 (CH). Initially, he analysed 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.[9]

Scientists in the United Kingdom including Patrick Blackett (later Lord Blackett OM PRS), Cecil Gordon, Solly Zuckerman, (later Baron Zuckerman OM, KCB, FRS), C. H. Waddington, Owen Wansbrough-Jones, Frank Yates, Jacob Bronowski and Freeman Dyson, and in the United States with George Dantzig looked for ways to make better decisions in such areas as logistics and training schedules

Second World War

The modern field of operational research arose during World War II. 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".[10] Other names for it included operational analysis (UK Ministry of Defence from 1962)[11] and quantitative management.[12]

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.[13]

Patrick Blackett worked for several different organizations during the war. Early in the war while working for the Royal Aircraft Establishment (RAE) he set up a team known as the "Circus" which helped to reduce the number of anti-aircraft artillery rounds needed to shoot down an enemy aircraft from an average of over 20,000 at the start of the Battle of Britain to 4,000 in 1941.[14]

B 24 in raf service 23 03 05
A Liberator in standard RAF green/dark earth/black night bomber finish as originally used by Coastal Command

In 1941, Blackett moved from the RAE to the Navy, after first working with RAF Coastal Command, in 1941 and then early in 1942 to the Admiralty.[15] Blackett's team at Coastal Command's Operational Research Section (CC-ORS) included two future Nobel prize winners and many other people who went on to be pre-eminent in their fields.[16] They undertook a number of crucial analyses that aided the war effort. Britain introduced the convoy 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 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 the size of the convoy. Their conclusion was that a few large convoys are more defensible than many small ones.[17]

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 night-time 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.[18] As a result of these findings Coastal Command changed their aircraft to using white undersurfaces.

Other work by the CC-ORS indicated that on average if the trigger depth of aerial-delivered depth charges (DCs) were 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 had time to descend as far as 100 feet), 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-foot kill zone of the charges was small. It was more efficient to attack those submarines close to the surface when the 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".[19]

Bomber Command's Operational Research Section (BC-ORS), analyzed a report of a survey carried out by RAF Bomber Command. For the survey, Bomber Command inspected all bombers returning from bombing raids over Germany over a particular period. All damage inflicted by German air defences was noted and the recommendation was given that armour be added in the most heavily damaged areas. This recommendation was not adopted because the fact that the aircraft returned with these areas damaged indicated these areas were not vital, and adding armour to non-vital areas where damage is acceptable negatively affects aircraft performance. Their suggestion to remove some of the crew so that an aircraft loss would result in fewer personnel losses, was also rejected by RAF command. Blackett's team made the logical 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.[20] This story has been disputed,[21] with a similar damage assessment study completed in the US by the Statistical Research Group at Columbia University[22] and was the result of work done by Abraham Wald[23].

When Germany organized its air defences into the Kammhuber Line, it was realized by the British 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 minimize RAF losses.[24]

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.[25]

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.[25]

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 analyzed, among other topics, the effectiveness of artillery, aerial bombing and anti-tank shooting.

After World War II

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. Operations Research also grew in many areas other than the military once scientists learned to apply its principles to the civilian sector. With the development of the simplex algorithm for linear programming in 1947[26] and the development of computers over the next three decades, Operations Research can now "solve problems with hundreds of thousands of variables and constraints. Moreover, the large volumes of data required for such problems can be stored and manipulated very efficiently."[26]

Problems addressed

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".[29] 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. Management scientists 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.[30]

The application of these models within the corporate sector became known as management science.[31]

Related fields

Some of the fields that have considerable overlap with Operations Research and Management Science include[32]:

Applications

Applications are abundant such as in airlines, manufacturing companies, service organizations, military branches, and government. The range of problems and issues to which it has contributed insights and solutions is vast. It includes:[30]

  • Scheduling (of airlines, trains, buses etc.)
  • Assignment (assigning crew to flights, trains or buses; employees to projects; commitment and dispatch of power generation facilities)
  • Facility location (deciding most appropriate location for new facilities such as warehouse; factory or fire station)
  • Hydraulics & Piping Engineering (managing flow of water from reservoirs)
  • Health Services (information and supply chain management)
  • Game Theory (identifying, understanding; developing strategies adopted by companies)
  • Urban Design
  • Computer Network Engineering (packet routing; timing; analysis)
  • Telecom & Data Communication Engineering (packet routing; timing; analysis)

[33]

Management is also concerned with so-called 'soft-operational analysis' which concerns methods for strategic planning, strategic decision support, problem structuring methods. In dealing with these sorts of challenges, mathematical modeling and simulation may not be appropriate or may not suffice. Therefore, during the past 30 years, a number of non-quantified modeling methods have been developed. These include:

Societies and journals

Societies

The International Federation of Operational Research Societies (IFORS)[34] is an umbrella organization for operational research societies worldwide, representing approximately 50 national societies including those in the US,[35] UK,[36] France,[37] Germany, Italy,[38] Canada,[39] Australia,[40] New Zealand,[41] Philippines,[42] India,[43] Japan and South Africa.[44] The constituent members of IFORS form regional groups, such as that in Europe, the Association of European Operational Research Societies (EURO).[45] Other important operational research organizations are Simulation Interoperability Standards Organization (SISO)[46] and Interservice/Industry Training, Simulation and Education Conference (I/ITSEC)[47]

In 2004 the US-based organization INFORMS began an initiative to market the OR profession better, including a website entitled The Science of Better[48] 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.[49]

Journals of INFORMS

The Institute for Operations Research and the Management Sciences (INFORMS) publishes thirteen scholarly journals about operations research, including the top two journals in their class, according to 2005 Journal Citation Reports.[50] They are:

Other journals

These are listed in alphabetical order of their titles.

  • 4OR-A Quarterly Journal of Operations Research: jointly published the Belgian, French and Italian Operations Research Societies (Springer);
  • Decision Sciences published by Wiley-Blackwell on behalf of the Decision Sciences Institute
  • European Journal of Operational Research (EJOR): Founded in 1975 and is presently by far the largest operational research journal in the world, with its around 9,000 pages of published papers per year. In 2004, its total number of citations was the second largest amongst Operational Research and Management Science journals;
  • INFOR Journal: published and sponsored by the Canadian Operational Research Society;
  • International Journal of Operations Research and Information Systems (IJORIS): an official publication of the Information Resources Management Association, published quarterly by IGI Global;[58]
  • Journal of Defense Modeling and Simulation (JDMS): Applications, Methodology, Technology: a quarterly journal devoted to advancing the science of modeling and simulation as it relates to the military and defense.[59]
  • Journal of the Operational Research Society (JORS): an official journal of The OR Society; this is the oldest continuously published journal of OR in the world, published by Taylor & Francis;
  • Military Operations Research (MOR): published by the Military Operations Research Society;
  • Omega - The International Journal of Management Science;
  • Operations Research Letters;
  • Opsearch: official journal of the Operational Research Society of India;
  • OR Insight: a quarterly journal of The OR Society, published by Palgrave;[60]
  • Production and Operations Management, the official journal of the Production and Operations Management Society
  • TOP: the official journal of the Spanish Statistics and Operations Research Society.[61]

See also

Operations research topics
Operations researchers
Related fields

References

  1. ^ "About Operations Research". INFORMS.org. Retrieved 7 January 2012.
  2. ^ "Mathematics Subject Classification". American Mathematical Society. 23 May 2011. Retrieved 7 January 2012.
  3. ^ Wetherbe, James C. (1979), Systems analysis for computer-based information systems, West series in data processing and information systems, West Pub. Co., ISBN 9780829902280, A systems analyst who contributes in the area of DSS must be skilled in such areas as management science (synonymous with decision science and operation research), modeling, simulation, and advanced statistics.
  4. ^ a b "What is OR". HSOR.org. Retrieved 13 November 2011.
  5. ^ "Operations Research Analysts". Bls.gov. Retrieved 27 January 2012.
  6. ^ "OR / Pubs / IOL Home". INFORMS.org. 2 January 2009. Archived from the original on 27 May 2009. Retrieved 13 November 2011.
  7. ^ 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
  8. ^ P. W. Bridgman, The Logic of Modern Physics, The MacMillan Company, New York, 1927
  9. ^ "operations research (industrial engineering) :: History – Britannica Online Encyclopedia". Britannica.com. Retrieved 13 November 2011.
  10. ^ "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 Operation Research, 1st edition revised, MIT Press & J Wiley, 5th printing, 1954.
  11. ^ 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 the Army Operational Research Establishment based at West Byfleet."
  12. ^ http://brochure.unisa.ac.za/myunisa/data/subjects/Quantitative%20Management.pdf
  13. ^ Kirby, p. 117 Archived 27 August 2013 at the Wayback Machine
  14. ^ Kirby, pp. 91–94 Archived 27 August 2013 at the Wayback Machine
  15. ^ Kirby, p. 96,109 Archived 2 October 2013 at the Wayback Machine
  16. ^ Kirby, p. 96 Archived 27 March 2014 at the Wayback Machine
  17. ^ ""Numbers are Essential": Victory in the North Atlantic Reconsidered, March–May 1943". Familyheritage.ca. 24 May 1943. Retrieved 13 November 2011.
  18. ^ Kirby, p. 101
  19. ^ (Kirby, pp. 102,103)
  20. ^ James F. Dunnigan (1999). Dirty Little Secrets of the Twentieth Century. Harper Paperbacks. pp. 215–217.
  21. ^ http://lesswrong.com/lw/bbv/examine_your_assumptions/
  22. ^ Wallis, W. Allen (1980). "The Statistical Research Group, 1942–1945". Journal of the American Statistical Association. 75 (370): 320–330. doi:10.1080/01621459.1980.10477469.
  23. ^ Mangel, Marc; Samaniego, Francisco J (1984). "Abraham Wald's Work on Aircraft Survivability". Journal of the American Statistical Association. 79 (386): 259. doi:10.2307/2288257. JSTOR 2288257.
  24. ^ "RAF History – Bomber Command 60th Anniversary". Raf.mod.uk. Retrieved 13 November 2011.
  25. ^ a b Milkman, Raymond H. (May 1968). "Operation Research in World War II". United States Naval Institute Proceedings.
  26. ^ a b "1.2 A HISTORICAL PERSPECTIVE". PRINCIPLES AND APPLICATIONS OF OPERATIONS RESEARCH.
  27. ^ “Factory Physics for Managers”, E. S. Pound, J. H. Bell, and M. L. Spearman, McGraw-Hill, 2014, p 47
  28. ^ “New Era of Project Delivery – Project as Production System”, R. G. Shenoy and T. R. Zabelle, Journal of Project Production Management, Vol 1, pp Nov 2016, pp 13-24 https://www.researchgate.net/publication/312602707_New_Era_of_Project_Delivery_-_Project_as_Production_System
  29. ^ Stafford Beer (1967) Management Science: The Business Use of Operations Research
  30. ^ a b What is Management Science? Archived 14 September 2008 at the Wayback Machine Lancaster University, 2008. Retrieved 5 June 2008.
  31. ^ What is Management Science? The University of Tennessee, 2006. Retrieved 5 June 2008.
  32. ^ Merigó, José M; Yang, Jian-Bo (2017). "A bibliometric analysis of operations research and management science". Omega - International Journal of Management Science. 73: 37–48. doi:10.1016/j.omega.2016.12.004. ISSN 0305-0483.
  33. ^ http://nak-architecture.com/index.php/en/services/blog/55-urban-operations-research-uor
  34. ^ "IFORS". IFORS. Retrieved 13 November 2011.
  35. ^ Leszczynski, Mary (8 November 2011). "Informs". Informs. Retrieved 13 November 2011.
  36. ^ "The OR Society". Orsoc.org.uk. Archived from the original on 24 April 2006. Retrieved 13 November 2011.
  37. ^ "Société française de Recherche Opérationnelle et d'Aide à la Décision". ROADEF. Retrieved 13 November 2011.
  38. ^ www.airo.org. "AIRO". airo.org. Retrieved 31 March 2018.
  39. ^ www.cors.ca. "CORS". Cors.ca. Retrieved 13 November 2011.
  40. ^ "ASOR". ASOR. 1 January 1972. Retrieved 13 November 2011.
  41. ^ "ORSNZ". ORSNZ. Retrieved 13 November 2011.
  42. ^ "ORSP". ORSP. Retrieved 13 November 2011.
  43. ^ "ORSI". Orsi.in. Retrieved 13 November 2011.
  44. ^ "ORSSA". ORSSA. 23 September 2011. Retrieved 13 November 2011.
  45. ^ "EURO (EURO)". Euro-online.org. Retrieved 13 November 2011.
  46. ^ "SISO". Sisostds.org. Retrieved 13 November 2011.
  47. ^ "I/Itsec". I/Itsec. Retrieved 13 November 2011.
  48. ^ "The Science of Better". The Science of Better. Retrieved 13 November 2011.
  49. ^ "Learn about OR". Learn about OR. Retrieved 13 November 2011.
  50. ^ "INFORMS Journals". Informs.org. Retrieved 13 November 2011.
  51. ^ "Decision Analysis". Informs.org. Retrieved 19 March 2015.
  52. ^ "Information Systems Research". Informs.org. Retrieved 19 March 2015.
  53. ^ "INFORMS Journal on Computing". Informs.org. Retrieved 19 March 2015.
  54. ^ "INFORMS Transactions on Education". Informs.org. Retrieved 19 March 2015.
  55. ^ "Interfaces". Informs.org. Retrieved 19 March 2015.
  56. ^ "Organization Science". Informs.org. Retrieved 19 March 2015.
  57. ^ "Service Science". Informs.org. Retrieved 19 March 2015.
  58. ^ "International Journal of Operations Research and Information Systems (IJORIS) (1947–9328)(1947–9336): John Wang: Journals". IGI Global. Retrieved 13 November 2011.
  59. ^ The Society for Modeling & Simulation International. "JDMS". Scs.org. Retrieved 13 November 2011.
  60. ^ The OR Society Archived 24 April 2006 at the Library of Congress Web Archives;
  61. ^ "TOP". Springer.com. Retrieved 13 November 2011.

Further reading

Classic books and articles

  • R. E. Bellman, Dynamic Programming, Princeton University Press, Princeton, 1957
  • Abraham Charnes, William W. Cooper, Management Models and Industrial Applications of Linear Programming, Volumes I and II, New York, John Wiley & Sons, 1961
  • Abraham Charnes, William W. Cooper, A. Henderson, An Introduction to Linear Programming, New York, John Wiley & Sons, 1953
  • C. West Churchman, Russell L. Ackoff & E. L. Arnoff, Introduction to Operations Research, New York: J. Wiley and Sons, 1957
  • George B. Dantzig, Linear Programming and Extensions, Princeton, Princeton University Press, 1963
  • Lester K. Ford, Jr., D. Ray Fulkerson, Flows in Networks, Princeton, Princeton University Press, 1962
  • Jay W. Forrester, Industrial Dynamics, Cambridge, MIT Press, 1961
  • L. V. Kantorovich, "Mathematical Methods of Organizing and Planning Production" Management Science, 4, 1960, 266–422
  • Ralph Keeney, Howard Raiffa, Decisions with Multiple Objectives: Preferences and Value Tradeoffs, New York, John Wiley & Sons, 1976
  • H. W. Kuhn, "The Hungarian Method for the Assignment Problem," Naval Research Logistics Quarterly, 1–2, 1955, 83–97
  • H. W. Kuhn, A. W. Tucker, "Nonlinear Programming," pp. 481–492 in Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability
  • B. O. Koopman, Search and Screening: General Principles and Historical Applications, New York, Pergamon Press, 1980
  • Tjalling C. Koopmans, editor, Activity Analysis of Production and Allocation, New York, John Wiley & Sons, 1951
  • Charles C. Holt, Franco Modigliani, John F. Muth, Herbert A. Simon, Planning Production, Inventories, and Work Force, Englewood Cliffs, NJ, Prentice-Hall, 1960
  • Philip M. Morse, George E. Kimball, Methods of Operations Research, New York, MIT Press and John Wiley & Sons, 1951
  • Robert O. Schlaifer, Howard Raiffa, Applied Statistical Decision Theory, Cambridge, Division of Research, Harvard Business School, 1961

Classic textbooks

  • Frederick S. Hillier & Gerald J. Lieberman, Introduction to Operations Research, McGraw-Hill: Boston MA; 10th Edition, 2014
  • Taha, Hamdy A., "Operations Research: An Introduction", Pearson, 10th Edition, 2016
  • Robert J. Thierauf & Richard A. Grosse, "Decision Making Through Operations Research", John Wiley & Sons, INC, 1970
  • Harvey M. Wagner, Principles of Operations Research, Englewood Cliffs, Prentice-Hall, 1969

History

  • Saul I. Gass, Arjang A. Assad, An Annotated Timeline of Operations Research: An Informal History. New York, Kluwer Academic Publishers, 2005.
  • Saul I. Gass (Editor), Arjang A. Assad (Editor), Profiles in Operations Research: Pioneers and Innovators. Springer, 2011
  • Maurice W. Kirby (Operational Research Society (Great Britain)). Operational Research in War and Peace: The British Experience from the 1930s to 1970, Imperial College Press, 2003. ISBN 1-86094-366-7, ISBN 978-1-86094-366-9
  • J. K. Lenstra, A. H. G. Rinnooy Kan, A. Schrijver (editors) History of Mathematical Programming: A Collection of Personal Reminiscences, North-Holland, 1991
  • Charles W. McArthur, Operations Analysis in the U.S. Army Eighth Air Force in World War II, History of Mathematics, Vol. 4, Providence, American Mathematical Society, 1990
  • C. H. Waddington, O. R. in World War 2: Operational Research Against the U-boat, London, Elek Science, 1973.

External links

Applied mathematics

Applied mathematics is the application of mathematical methods by different fields such as science, engineering, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models. In the past, practical applications have motivated the development of mathematical theories, which then became the subject of study in pure mathematics where abstract concepts are studied for their own sake. The activity of applied mathematics is thus intimately connected with research in pure mathematics.

Clifford Stein

Clifford Seth Stein (born December 14, 1965), a computer scientist, is a professor of industrial engineering and operations research at Columbia University in New York, NY, where he also holds an appointment in the Department of Computer Science. Stein is chair of the Industrial Engineering and Operations Research Department at Columbia University. Prior to joining Columbia, Stein was a professor at Dartmouth College in New Hampshire.

Stein's research interests include the design and analysis of algorithms, combinatorial optimization, operations research, network algorithms, scheduling, algorithm engineering and computational biology.

Stein has published many influential papers in the leading conferences and journals in his fields of research, and has occupied a variety of editorial positions including in the journals ACM Transactions on Algorithms, Mathematical Programming, Journal of Algorithms, SIAM Journal on Discrete Mathematics and Operations Research Letters. His work has been funded by the National Science Foundation and the Sloan Foundation. As of November 1, 2015, his publications have been cited over 46,000 times, and he has an h-index of 42.Stein is the winner of several prestigious awards including an NSF Career Award, an Alfred Sloan Research Fellowship and the Karen Wetterhahn Award for Distinguished Creative or Scholarly Achievement. He is also the co-author of two textbooks:

Introduction to Algorithms, with T. Cormen, C. Leiserson and R. Rivest, which is currently the best-selling textbook in algorithms and has been translated into 8 languages. About 39,500 of Stein's 46,000 citations are made to this book.

Discrete Math for Computer Science, with Ken Bogart and Scot Drysdale, which is a new textbook that covers discrete math at an undergraduate level.Stein earned his B.S.E. from Princeton University in 1987, a Master of Science from The Massachusetts Institute of Technology in 1989, and a PhD also from the Massachusetts Institute of Technology in 1992.In recent years, Stein has built up close ties with the Norwegian research community which earned him an honorary doctorate from the University of Oslo (May 2010).

Decision tree

A decision tree is a decision support tool that uses a tree-like model of decisions and their possible consequences, including chance event outcomes, resource costs, and utility. It is one way to display an algorithm that only contains conditional control statements.

Decision trees are commonly used in operations research, specifically in decision analysis, to help identify a strategy most likely to reach a goal, but are also a popular tool in machine learning.

Discrete mathematics

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic – do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus or Euclidean geometry. Discrete objects can often be enumerated by integers. More formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets (finite sets or sets with the same cardinality as the natural numbers). However, there is no exact definition of the term "discrete mathematics." Indeed, discrete mathematics is described less by what is included than by what is excluded: continuously varying quantities and related notions.

The set of objects studied in discrete mathematics can be finite or infinite. The term finite mathematics is sometimes applied to parts of the field of discrete mathematics that deals with finite sets, particularly those areas relevant to business.

Research in discrete mathematics increased in the latter half of the twentieth century partly due to the development of digital computers which operate in discrete steps and store data in discrete bits. Concepts and notations from discrete mathematics are useful in studying and describing objects and problems in branches of computer science, such as computer algorithms, programming languages, cryptography, automated theorem proving, and software development. Conversely, computer implementations are significant in applying ideas from discrete mathematics to real-world problems, such as in operations research.

Although the main objects of study in discrete mathematics are discrete objects, analytic methods from continuous mathematics are often employed as well.

In university curricula, "Discrete Mathematics" appeared in the 1980s, initially as a computer science support course; its contents were somewhat haphazard at the time. The curriculum has thereafter developed in conjunction with efforts by ACM and MAA into a course that is basically intended to develop mathematical maturity in first year students; therefore it is nowadays a prerequisite for mathematics majors in some universities as well. Some high-school-level discrete mathematics textbooks have appeared as well. At this level, discrete mathematics is sometimes seen as a preparatory course, not unlike precalculus in this respect.The Fulkerson Prize is awarded for outstanding papers in discrete mathematics.

George Dantzig

George Bernard Dantzig (; November 8, 1914 – May 13, 2005) was an American mathematical scientist who made contributions to industrial engineering, operations research, computer science, economics, and statistics.

Dantzig is known for his development of the simplex algorithm, an algorithm for solving linear programming problems, and for his other work with linear programming. In statistics, Dantzig solved two open problems in statistical theory, which he had mistaken for homework after arriving late to a lecture by Jerzy Neyman.Dantzig was the Professor Emeritus of Transportation Sciences and Professor of Operations Research and of Computer Science at Stanford.

Hugh Everett III

Hugh Everett III (; November 11, 1930 – July 19, 1982) was an American physicist who first proposed the many-worlds interpretation (MWI) of quantum physics, which he termed his "relative state" formulation.

Discouraged by the scorn of other physicists for MWI, Everett ended his physics career after completing his Ph.D. Afterwards, he developed the use of generalized Lagrange multipliers for operations research and applied this commercially as a defense analyst and a consultant. He was married to Nancy Everett née Gore. They had two children: Elizabeth Everett and Mark Oliver Everett, who became frontman of the musical band Eels.

Indian Statistical Institute

Indian Statistical Institute (ISI) is an academic institute of national importance as recognised by a 1959 act of the Indian parliament. It grew out of the Statistical Laboratory set up by Prasanta Chandra Mahalanobis in Presidency College, Kolkata. Established in 1931, this public university of India is one of the oldest and most prestigious institutions focused on statistics, and its early reputation led it to being adopted as a model for the first US institute of Statistics set up at the Research Triangle, North Carolina by Gertrude Mary Cox.Mahalanobis, the founder of ISI, was deeply influenced by wisdom and guidance of Rabindranath Tagore and Brajendranath Seal. Under his leadership, the institute initiated and promoted the interaction of Statistics with natural and social sciences to advance the role of Statistics as a key technology by explicating the twin aspects – its general applicability and its dependence on other disciplines for its own development. The institute is now considered as one of the foremost centres in the world for training and research in Computer science, Statistics, Quantitative Economics and related sciences.

ISI has its headquarters in Baranagar, Kolkata, West Bengal. It has four subsidiary centres focused in academics at Delhi, Bangalore, Chennai and Tezpur, and a branch at Giridih. In addition, the Institute has a network of units of Statistical Quality Control and Operations Research at Vadodara, Coimbatore, Hyderabad, Mumbai and Pune engaged in guiding the industries, within and outside India, in developing the most up–to–date quality management systems and solving critical problems of quality, reliability and productivity.

Primary activities of ISI are research and training of Statistics, development of theoretical Statistics and its applications in various natural and social sciences. Originally affiliated with the University of Calcutta, the institute was declared an institute of national importance in 1959, through an act of Indian parliament, Indian Statistical Institute act, 1959. ISI functions under the Ministry of Statistics and Programme Implementation (MOSPI) of the Government of India.Key areas of expertise of ISI are Computer science, Statistics, Mathematics, Mathematical economics, Operations Research and Information Science and it is one of the few research oriented Indian schools offering courses at both the undergraduate and graduate level.

Industrial engineering

Industrial engineering is an inter-disciplinary profession that is concerned with the optimization of complex processes, systems, or organizations by developing, improving and implementing integrated systems of people, money, knowledge, information, equipment, energy and materials.

Industrial engineers use specialized knowledge and skills in the mathematical, physical, and social sciences, together with the principles and methods of engineering analysis and design, to specify, predict, and evaluate the results obtained from systems and processes. From these results, they are able to create new systems, processes or situations for the useful coordination of man, materials and machines and also improve the quality and productivity of systems, physical or social. Depending on the sub-specialties involved, industrial engineering may also overlap with, operations research, systems engineering, manufacturing engineering, production engineering, management science, management engineering, financial engineering, ergonomics or human factors engineering, safety engineering, or others, depending on the viewpoint or motives of the user.

Even though its underlying concepts overlap considerably with certain business-oriented disciplines, such as operations management, industrial engineering is a longstanding engineering discipline subject to (and eligible for) professional engineering licensure in most jurisdictions.

Institute for Operations Research and the Management Sciences

The Institute for Operations Research and the Management Sciences (INFORMS) is an international society for practitioners in the fields of operations research (O.R.), management science, and analytics. It was established in 1995 with the merger of the Operations Research Society of America (ORSA) and The Institute of Management Sciences (TIMS). The 2018 president of the institute is Professor Nicholas G. Hall of Ohio State University.

International Abstracts in Operations Research

International Abstracts in Operations Research is an official publication of the International Federation of Operational Research Societies.

Management science

Management science (MS) is the broad interdisciplinary study of problem solving and decision making in human organizations, with strong links to management, economics, business, engineering, management consulting, 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 accurate management decisions by arriving at optimal or near optimal solutions to complex decision problems. Management science helps businesses to achieve goals using various scientific methods.

The field was initially an outgrowth of applied mathematics, where early challenges were problems relating to the optimization of systems which could be modeled linearly, i.e., determining the optima (maximum value of profit, assembly line performance, crop yield, bandwidth, etc. or minimum of loss, risk, costs, etc.) of some objective function. Today, management science encompasses any organizational activity for which the problem can be structured as a functional system so as to obtain a solution set with identifiable characteristics.

Managerial economics

Managerial economics deals with the application of the economic concepts, theories, tools, and methodologies to solve practical problems in a business. It helps the manager in decision making and acts as a link between practice and theory". It is sometimes referred to as business economics and is a branch of economics that applies microeconomic analysis to decision methods of businesses or other management units.

As such, it bridges economic theory and economics in practice. It draws heavily from quantitative techniques such as regression analysis, correlation and calculus. If there is a unifying theme that runs through most of managerial economics, it is the attempt to optimize business decisions given the firm's objectives and given constraints imposed by scarcity, for example through the use of operations research, mathematical programming, game theory for strategic decisions, and other computational methods.

Mathematical optimization

In mathematics, computer science and operations research, mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element (with regard to some criterion) from some set of available alternatives.In the simplest case, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. More generally, optimization includes finding "best available" values of some objective function given a defined domain (or input), including a variety of different types of objective functions and different types of domains.

Operations Research (journal)

Operations Research is a bimonthly peer-reviewed academic journal covering operations research that is published by INFORMS. It was established in 1952 as the Journal of the Operations Research Society of America and obtained its current name in 1955. The journal is indexed by Mathematical Reviews and Zentralblatt MATH. Its 2009 MCQ was 0.23. According to the Journal Citation Reports, the journal has a 2016 impact factor of 1.779.

Philip M. Morse

Philip McCord Morse (August 6, 1903 – 5 September 1985), was an American physicist, administrator and pioneer of operations research (OR) in World War II. He is considered to be the father of operations research in the U.S.

Queueing theory

Queueing theory is the mathematical study of waiting lines, or queues. A queueing model is constructed so that queue lengths and waiting time can be predicted. Queueing theory is generally considered a branch of operations research because the results are often used when making business decisions about the resources needed to provide a service.

Queueing theory has its origins in research by Agner Krarup Erlang when he created models to describe the Copenhagen telephone exchange. The ideas have since seen applications including telecommunication, traffic engineering, computing

and, particularly in industrial engineering, in the design of factories, shops, offices and hospitals, as well as in project management.

Russell L. Ackoff

Russell Lincoln Ackoff (12 February 1919 – 29 October 2009) was an American organizational theorist, consultant, and Anheuser-Busch Professor Emeritus of Management Science at the Wharton School, University of Pennsylvania. Ackoff was a pioneer in the field of operations research, systems thinking and management science.

System dynamics

System dynamics (SD) is an approach to understanding the nonlinear behaviour of complex systems over time using stocks, flows, internal feedback loops, table functions and time delays.

White-collar worker

A white-collar worker is a person who performs professional, managerial, or administrative work. White-collar work may be performed in an office or other administrative setting. White-collar includes business management, customer support, market research, finance, engineering, operations research, marketing, information technology, networking, attorneys, medical professional, public relation, talent professionals, architects, graphics design, stockbrokers, accounting, auditor, actuary, customs professional, research and development and contracting. Other types of work are those of a blue-collar worker, whose job requires manual labor and a pink-collar worker, whose labor is related to customer interaction, entertainment, sales, or other service-oriented work. Many occupations blend blue, white and pink (service) industry categorizations.

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