NPTEL – Fundamentals of Operations Research

By Prof. G. Srinivasan, Department of Management Studies, IT Madras. These videos are part of the National Programme on Technology Enhanced Learning (NPTEL), funded by the Government of India and being carried out by the seven Indian Institutes of Technology and IISc Bangalore as a collaborative project.

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Related Material

For the academic journal, see Operations Research (journal).
"Management science" redirects here. For the academic journal, see Management Science (journal).

Operations research, or operational research in British usage, is a discipline that deals with the application of advanced analytical methods to help make better decisions.[1] It is often considered to be a sub-field of 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 maximum (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.[4]

Contents

  • 1 Overview
  • 2 History
    • 2.1 Historical origins
    • 2.2 Second World War
    • 2.3 After World War II
  • 3 Problems addressed
  • 4 Management science
    • 4.1 Related fields
    • 4.2 Applications
  • 5 Societies and journals
  • 6 See also
  • 7 References
  • 8 Notes
  • 9 Further reading
  • 10 External links

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 subdisciplines in modern operational research, as identified by the journal Operations Research,[6] are:

  • Computing and information technologies
  • Financial engineering
  • Manufacturing, service sciences, and supply chain management
  • Marketing Engineering[7]
  • Policy modeling and public sector work
  • Revenue management
  • Simulation
  • Stochastic models
  • Transportation

History

As a formal discipline, operational research originated in the efforts of military planners during World War II. In the decades after the war, the techniques 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

Early work in operational research was carried out by individuals such as Charles Babbage. 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's broad gauge.[8] 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.[9]

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.[10]

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."[11] Other names for it included operational analysis (UK Ministry of Defence from 1962)[12] and quantitative management.[13]

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.[14]

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.[15]

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.[16] 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.[17] 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.[18]

A Liberator in standard RAF green/dark earth/black night bomber finish as originally used by Coastal Command

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.[19] As a result of these findings Coastal Command changed their aircraft to using white undersurfaces.

A Warwick in the revised RAF Coastal Command green/dark grey/white finish

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".[20]

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 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.[21]

Map of Kammhuber Line

When Germany organised its air defences into the Kammhuber Line, it was realised 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 minimise RAF losses.[22]

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.[23]

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.[23]

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

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 [24]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.” [25]

Problems addressed

  • Critical path analysis or project planning: identifying those processes in a complex project which affect the overall duration of the project
  • Floorplanning: designing the layout of equipment in a factory or components on a computer chip to reduce manufacturing time (therefore reducing cost)
  • Network optimization: for instance, setup of telecommunications networks to maintain quality of service during outages
  • Allocation problems
  • Facility location
  • Assignment Problems:
    • Assignment problem
    • Generalized assignment problem
    • Quadratic assignment problem
    • Weapon target assignment problem
  • Bayesian search theory : looking for a target
  • Optimal search
  • Routing, such as determining the routes of buses so that as few buses are needed as possible
  • Supply chain management: managing the flow of raw materials and products based on uncertain demand for the finished products
  • Efficient messaging and customer response tactics
  • Automation: automating or integrating robotic systems in human-driven operations processes
  • Globalization: globalizing operations processes in order to take advantage of cheaper materials, labor, land or other productivity inputs
  • Transportation: managing freight transportation and delivery systems (Examples: LTL Shipping, intermodal freight transport)
  • Scheduling:
    • Personnel staffing
    • Manufacturing steps
    • Project tasks
    • Network data traffic: these are known as queueing models or queueing systems.
    • Sports events and their television coverage
  • Blending of raw materials in oil refineries
  • Determining optimal prices, in many retail and B2B settings, within the disciplines of pricing science

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".[26] However, in modern times the term management science may also be used to refer to the separate fields of organizational studies or corporate strategy.[citation needed] 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.[27]

The application of these models within the corporate sector became known as management science.[28]

Related fields

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

  • Business Analytics
  • Data mining
  • Decision analysis
  • Engineering
  • Financial engineering
  • Forecasting
  • Game theory
  • Graph theory
  • Industrial engineering
  • Logistics
  • Mathematical modeling
  • Mathematical optimization
  • Probability and statistics
  • Project management
  • Policy analysis
  • Simulation
  • Social network/Transportation forecasting models
  • Stochastic processes
  • Supply chain management

Applications

Applications of management science is 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:[27]

  • scheduling airlines, including both planes and crew,
  • deciding the appropriate place to site new facilities such as a warehouse, factory or fire station,
  • managing the flow of water from reservoirs,
  • identifying possible future development paths for parts of the telecommunications industry,
  • establishing the information needs and appropriate systems to supply them within the health service, and
  • identifying and understanding the strategies adopted by companies for their information systems

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 modeling methods have been developed. These include:

  • stakeholder based approaches including metagame analysis and drama theory
  • morphological analysis and various forms of influence diagrams.
  • approaches using cognitive mapping
  • the Strategic Choice Approach
  • robustness analysis

Societies and journals

Societies

The International Federation of Operational Research Societies (IFORS)[29] is an umbrella organization for operational research societies worldwide, representing approximately 50 national societies including those in the US,[30] UK,[31] France,[32] Germany, Canada,[33] Australia,[34] New Zealand,[35] Philippines,[36] India,[37] Japan and South Africa (ORSSA).[38] The constituent members of IFORS form regional groups, such as that in Europe.[39] Other important operational research organizations are Simulation Interoperability Standards Organization (SISO)[40] and Interservice/Industry Training, Simulation and Education Conference (I/ITSEC)[41]

In 2004 the US-based organization INFORMS began an initiative to market the OR profession better, including a website entitled The Science of Better[42] 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.[43]

Journals

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.[44] They are:

  • Decision Analysis[45]
  • Information Systems Research
  • INFORMS Journal on Computing
  • INFORMS Transactions on Education[46] (an open access journal)
  • Interfaces: An International Journal of the Institute for Operations Research and the Management Sciences
  • 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
  • Service Science
  • Transportation Science.
Other journals
  • 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;[47]
  • 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.[48]
  • 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 Palgrave;[49]
  • Journal of Simulation (JOS): an official journal of The OR Society, published by Palgrave;[49]
  • Mathematical Methods of Operations Research (MMOR): the journal of the German and Dutch OR Societies, published by Springer;[50]
  • Military Operations Research (MOR): published by the Military Operations Research Society;
  • Opsearch: official journal of the Operational Research Society of India;
  • OR Insight: a quarterly journal of The OR Society, published by Palgrave;[49]
  • Production and Operations Management, the official journal of the Production and Operations Management Society
  • TOP: the official journal of the Spanish Society of Statistics and Operations Research.[51]

See also

Operation research topics
  • Assignment problem
  • Decision analysis
  • Dynamic programming
  • Inventory theory
  • Linear programming
  • Mathematical optimization
  • Optimal maintenance
  • Queueing theory
  • Real options analysis
  • Stochastic processes
  • Systems analysis
  • Systems thinking
Operation researchers
  • Operations researcher category
  • Russell L. Ackoff
  • Anthony Stafford Beer
  • Alfred Blumstein
  • C. West Churchman
  • William W. Cooper
  • George Dantzig
  • Richard Karp
  • Ramayya Krishnan
  • Frederick W. Lanchester
  • Thomas L. Magnanti
  • Alvin E. Roth
  • Peter Whittle
Related fields
  • Behavioral operations research
  • Big data
  • Business engineering
  • Database normalization
  • Econometrics
  • Industrial engineering
  • Industrial organization
  • Management engineering
  • Managerial economics
  • Military simulation
  • Modeling and simulation
  • Reliability engineering
  • Scientific management
  • Search-based software engineering
  • Simulation
  • System dynamics
  • System safety
  • Systems theory
  • Wargaming

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 operations 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. Retrieved 13 November 2011. 
  7. ^ "DecisionPro, Inc. – Makers of Marketing Engineering Software – Home Page". Decisionpro.biz. Retrieved 13 November 2011. 
  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, 1927
  10. ^ "operations research (industrial engineering) :: History – Britannica Online Encyclopedia". Britannica.com. Retrieved 13 November 2011. 
  11. ^ "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.
  12. ^ 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."
  13. ^ http://brochure.unisa.ac.za/myunisa/data/subjects/Quantitative%20Management.pdf
  14. ^ Kirby, p. 117[dead link]
  15. ^ Kirby, pp. 91–94[dead link]
  16. ^ Kirby, p. 96,109[dead link]
  17. ^ Kirby, p. 96[dead link]
  18. ^ ""Numbers are Essential": Victory in the North Atlantic Reconsidered, March–May 1943". Familyheritage.ca. 24 May 1943. Retrieved 13 November 2011. 
  19. ^ Kirby, p. 101
  20. ^ (Kirby, pp. 102,103)
  21. ^ James F. Dunnigan (1999). Dirty Little Secrets of the Twentieth Century. Harper Paperbacks. pp. 215–217. 
  22. ^ "RAF History – Bomber Command 60th Anniversary". Raf.mod.uk. Retrieved 13 November 2011. 
  23. ^ a b Milkman, Raymond H. (May 1968). "Operations Research in World War II". United States Naval Institute Proceedings. 
  24. ^ http://www.pitt.edu/~jrclass/or/or-intro.html#history
  25. ^ http://www.pitt.edu/~jrclass/or/or-intro.html#history
  26. ^ Stafford Beer (1967) Management Science: The Business Use of Operations Research
  27. ^ a b What is Management Science? Lancaster University, 2008. Retrieved 5 June 2008.
  28. ^ What is Management Science? The University of Tennessee, 2006. Retrieved 5 June 2008.
  29. ^ "IFORS". IFORS. Retrieved 13 November 2011. 
  30. ^ Leszczynski, Mary (8 November 2011). "Informs". Informs. Retrieved 13 November 2011. 
  31. ^ "The OR Society". Orsoc.org.uk. Retrieved 13 November 2011. 
  32. ^ "Société française de Recherche Opérationnelle et d'Aide à la Décision". ROADEF. Retrieved 13 November 2011. 
  33. ^ www.cors.ca. "CORS". Cors.ca. Retrieved 13 November 2011. 
  34. ^ "ASOR". ASOR. 1 January 1972. Retrieved 13 November 2011. 
  35. ^ "ORSNZ". ORSNZ. Retrieved 13 November 2011. 
  36. ^ "ORSP". ORSP. Retrieved 13 November 2011. 
  37. ^ "ORSI". Orsi.in. Retrieved 13 November 2011. 
  38. ^ "ORSSA". ORSSA. 23 September 2011. Retrieved 13 November 2011. 
  39. ^ "EURO". Euro-online.org. Retrieved 13 November 2011. 
  40. ^ "SISO". Sisostds.org. Retrieved 13 November 2011. 
  41. ^ "I/Itsec". I/Itsec. Retrieved 13 November 2011. 
  42. ^ "The Science of Better". The Science of Better. Retrieved 13 November 2011. 
  43. ^ "Learn about OR". Learn about OR. Retrieved 13 November 2011. 
  44. ^ "INFORMS Journals". Informs.org. Retrieved 13 November 2011. 
  45. ^ "''Decision Analysis''". Informs.org. Retrieved 13 November 2011. 
  46. ^ "INFORMS Transactions on Education". Informs.org. Retrieved 13 November 2011. 
  47. ^ "International Journal of Operations Research and Information Systems (IJORIS) (1947–9328)(1947–9336): John Wang: Journals". IGI Global. Retrieved 13 November 2011. 
  48. ^ The Society for Modeling & Simulation International. "JDMS". Scs.org. Retrieved 13 November 2011. 
  49. ^ a b c The OR Society;
  50. ^ "Mathematical Methods of Operations Research website". Springer.com. Retrieved 13 November 2011. 
  51. ^ "TOP". Springer.com. Retrieved 13 November 2011. 

Notes

  • Kirby, M. W. (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

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
  • 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; 9th. Edition, 2011
  • Wayne Winston, Operations Research: Applications and Algorithms, Duxbury Press; 4th. Edition, 2003
  • Kenneth R. Baker, Dean H. Kropp (1985). Management Science: An Introduction to the Use of Decision Models
  • David Charles Heinze (1982). Management Science: Introductory Concepts and Applications
  • Lee J. Krajewski, Howard E. Thompson (1981). "Management Science: Quantitative Methods in Context"
  • Thomas W. Knowles (1989). Management science: Building and Using Models
  • Kamlesh Mathur, Daniel Solow (1994). Management Science: The Art of Decision Making
  • Laurence J. Moore, Sang M. Lee, Bernard W. Taylor (1993). Management Science
  • William Thomas Morris (1968). Management Science: A Bayesian Introduction.
  • William E. Pinney, Donald B. McWilliams (1987). Management Science: An Introduction to Quantitative Analysis for Management
  • Shrader, Charles R. (2006). History of Operations Research in the United States Army, Volume 1:1942–1962. Washington, D.C.: United States Army Center of Military History. CMH Pub 70-102-1. 
  • Gerald E. Thompson (1982). Management Science: An Introduction to Modern Quantitative Analysis and Decision Making. New York : McGraw-Hill Publishing Co.
  • Saul I. Gass & Arjang A. Assad (2005). An Annotated Timeline of Operations Research: An Informal History. New York : Kluwer Academic Publishers.
  • C. H. Waddington. "O. R. in World War 2: Operational Research against the U-boat", Elek Science, London, 1973.

External links

  • INFORMS OR/MS Resource Collection: a comprehensive set of OR links.
  • International Federation of Operational Research Societies
  • Occupational Outlook Handbook, U.S. Department of Labor Bureau of Labor Statistics
  • "Operation Everything: It Stocks Your Grocery Store, Schedules Your Favorite Team's Games, and Helps Plan Your Vacation. The Most Influential Academic Discipline You've Never Heard Of." Boston Globe, 27 June 2004
  • "Optimal Results: IT-powered advances in operations research can enhance business processes and boost the corporate bottom line." Computerworld, 20 November 2000

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