Operations research

# Operations research

Discussion

Encyclopedia
Operations research is an interdisciplinary mathematical science that focuses on the effective use of technology by organizations. In contrast, many other science & engineering disciplines focus on technology giving secondary considerations to its use.

Employing techniques from other mathematical sciences – such as mathematical model
Mathematical model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used not only in the natural sciences and engineering disciplines A mathematical model is a...

ing, statistical analysis
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

, 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
Industrial engineering
Industrial engineering is a branch of engineering dealing with the optimization of complex processes or systems. It is concerned with the development, improvement, implementation and evaluation of integrated systems of people, money, knowledge, information, equipment, energy, materials, analysis...

and operations management
Operations management
Operations management is an area of management concerned with overseeing, designing, and redesigning business operations in the production of goods and/or services. It involves the responsibility of ensuring that business operations are efficient in terms of using as little resources as needed, and...

, and draws on psychology
Psychology
Psychology is the study of the mind and behavior. Its immediate goal is to understand individuals and groups by both establishing general principles and researching specific cases. For many, the ultimate goal of psychology is to benefit society...

and organization science. Operations Research is often concerned with determining the maximum
Maxima and minima
In mathematics, the maximum and minimum of a function, known collectively as extrema , are the largest and smallest value that the function takes at a point either within a given neighborhood or on the function domain in its entirety .More generally, the...

(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.

## Overview

Operational research (OR) encompasses a wide range of problem-solving techniques and methods applied in the pursuit of improved decision-making and efficiency. Some of the tools used by operational researchers are statistics, optimization, probability theory
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...

, queuing theory, game theory
Game theory
Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...

, graph theory
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...

, decision analysis
Decision analysis
Decision analysis is the discipline comprising the philosophy, theory, methodology, and professional practice necessary to address important decisions in a formal manner...

, mathematical model
Mathematical model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used not only in the natural sciences and engineering disciplines A mathematical model is a...

ing and simulation
Simulation
Simulation is the imitation of some real thing available, state of affairs, or process. The act of simulating something generally entails representing certain key characteristics or behaviours of a selected physical or abstract system....

. Because of the computational nature of these fields, OR also has strong ties to computer science
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...

and analytics
Analytics
Analytics is the application of computer technology, operational research, and statistics to solve problems in business and industry. Analytics is carried out within an information system: while, in the past, statistics and mathematics could be studied without computers and software, analytics has...

. 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:
• Fundamental or foundational work takes place in three mathematical disciplines: probability theory
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...

, mathematical optimization, and dynamical systems theory
Dynamical systems theory
Dynamical systems theory is an area of applied mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical systems. When difference...

.
• Modeling work is concerned with the construction of models, analysing them mathematically, implementing them on computers, solving them using software tools, and assessing their effectiveness with data. This level is mainly instrumental, and driven mainly by statistics and econometrics
Econometrics
Econometrics has been defined as "the application of mathematics and statistical methods to economic data" and described as the branch of economics "that aims to give empirical content to economic relations." More precisely, it is "the quantitative analysis of actual economic phenomena based on...

.
• Application work in operational research, like other engineering and economics disciplines, attempts to use models to make a practical impact on real-world problems.

The major subdisciplines in modern operational research, as identified by the journal Operations Research, are:
• Computing and information technologies
• Decision analysis
Decision analysis
Decision analysis is the discipline comprising the philosophy, theory, methodology, and professional practice necessary to address important decisions in a formal manner...

• Environment, energy, and natural resources
• Financial engineering
• Manufacturing
Manufacturing
Manufacturing is the use of machines, tools and labor to produce goods for use or sale. The term may refer to a range of human activity, from handicraft to high tech, but is most commonly applied to industrial production, in which raw materials are transformed into finished goods on a large scale...

, service sciences, and supply chain management
Supply chain management
Supply chain management is the management of a network of interconnected businesses involved in the ultimate provision of product and service packages required by end customers...

• Marketing Engineering
• Policy modeling and public sector work
• Revenue management
• Simulation
Simulation
Simulation is the imitation of some real thing available, state of affairs, or process. The act of simulating something generally entails representing certain key characteristics or behaviours of a selected physical or abstract system....

• 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 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 analyse and optimize complex systems, and has become an area of active academic and industrial research.

### 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."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. Other names for it included operational analysis (UK Ministry of Defence from 1962) and quantitative management.

Prior to the formal start of the field, early work in operational research was carried out by individuals such as Charles Babbage
Charles Babbage
Charles Babbage, FRS was an English mathematician, philosopher, inventor and mechanical engineer who originated the concept of a programmable computer...

. 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
Great Western Railway
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...

's broad gauge. 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. The modern field of operational research arose during World War II.

Modern operational research originated at the Bawdsey Research Station
Telecommunications Research Establishment
The Telecommunications Research Establishment was the main United Kingdom research and development organization for radio navigation, radar, infra-red detection for heat seeking missiles, and related work for the Royal Air Force during World War II and the years that followed. The name was...

in the UK in 1937 and was the result of an initiative of the station's superintendent, A. P. Rowe
Albert Percival Rowe
Albert Percival Rowe was a British physicist and senior research administrator who had a major role in the development of Radar before and during World War II....

. Rowe conceived the idea as a means to analyse and improve the working of the UK's early warning radar
An early warning radar is any radar system used primarily for the long-range detection of its targets, i.e., allowing defences to be alerted as early as possible before the intruder reaches its target, giving the defences the maximum time in which to operate...

system, Chain Home
Chain Home
Chain Home was the codename for the ring of coastal Early Warning radar stations built by the British before and during the Second World War. 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...

(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.

Scientists in the United Kingdom including Patrick Blackett (later Lord Blackett OM PRS), Cecil Gordon, C. H. Waddington
Conrad Hal Waddington CBE FRS FRSE was a developmental biologist, paleontologist, geneticist, embryologist and philosopher who laid the foundations for systems biology...

, Owen Wansbrough-Jones
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
Frank Yates FRS was one of the pioneers of 20th century statistics.He was born in Manchester. Yates was the eldest of five children, and the only boy, born to Edith and Percy Yates. His father was a seed merchant. He attended Wadham House, a private school, before gaining a scholarship to Clifton...

, Jacob Bronowski
Jacob Bronowski
Jacob Bronowski was a Polish-Jewish British mathematician, biologist, historian of science, theatre author, poet and inventor...

and Freeman Dyson
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, astronomy and nuclear engineering. Dyson is a member of the Board of Sponsors of the Bulletin of the Atomic Scientists...

, and in the United States with George Dantzig
George Dantzig
George Bernard Dantzig was an American mathematical scientist who made important contributions to operations research, computer science, economics, and statistics....

looked for ways to make better decisions in such areas as logistics
Logistics
Logistics is the management of the flow of goods between the point of origin and the point of destination in order to meet the requirements of customers or corporations. Logistics involves the integration of information, transportation, inventory, warehousing, material handling, and packaging, and...

and training schedules. After the war it began to be applied to similar problems in industry.

### Second World War

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
British Army
The British Army is the land warfare branch of Her Majesty's Armed Forces in the United Kingdom. It came into being with the unification of the Kingdom of England and Scotland into the Kingdom of Great Britain in 1707. The new British Army incorporated Regiments that had already existed in England...

.

Patrick Blackett worked for several different organizations during the war. Early in the war while working for the Royal Aircraft Establishment
Royal Aircraft Establishment
The Royal Aircraft Establishment , was a British research establishment, known by several different names during its history, that eventually came under the aegis of the UK Ministry of Defence , before finally losing its identity in mergers with other institutions.The first site was at Farnborough...

(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
Battle of Britain
The Battle of Britain is the name given to the World War II air campaign waged by the German Air Force against the United Kingdom during the summer and autumn of 1940...

to 4,000 in 1941.

In 1941 Blackett moved from the RAE to the Navy, after first working with RAF Coastal Command
RAF Coastal Command
RAF Coastal Command was a formation within the Royal Air Force . Founded in 1936, it was the RAF's premier maritime arm, after the Royal Navy's secondment of the Fleet Air Arm in 1937. Naval aviation was neglected in the inter-war period, 1919–1939, and as a consequence the service did not receive...

, 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...

. Blackett's team at Coastal Command's Operational Research Section (CC-ORS) included two future Nobel prize
Nobel Prize
The Nobel Prizes are annual international awards bestowed by Scandinavian committees in recognition of cultural and scientific advances. The will of the Swedish chemist Alfred Nobel, the inventor of dynamite, established the prizes in 1895...

winners and many other people who went on to be preeminent in their fields. They undertook a number of crucial analyses that aided the war effort. Britain introduced the convoy
Convoy
A convoy is a group of vehicles, typically motor vehicles or ships, traveling together for mutual support and protection. Often, a convoy is organized with armed defensive support, though it may also be used in a non-military sense, for example when driving through remote areas.-Age of Sail:Naval...

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-boat
U-boat
U-boat is the anglicized version of the German word U-Boot , itself an abbreviation of Unterseeboot , and refers to military submarines operated by Germany, particularly in World War I and World War II...

s 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.

While performing an analysis of the methods used by RAF Coastal Command
RAF Coastal Command
RAF Coastal Command was a formation within the Royal Air Force . Founded in 1936, it was the RAF's premier maritime arm, after the Royal Navy's secondment of the Fleet Air Arm in 1937. Naval aviation was neglected in the inter-war period, 1919–1939, and as a consequence the service did not receive...

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.

Other work by the CC-ORS indicated that on average if the trigger depth of aerial delivered depth charge
Depth charge
A depth charge is an anti-submarine warfare weapon intended to destroy or cripple a target submarine by the shock of exploding near it. Most use explosives and a fuze set to go off at a preselected depth in the ocean. Depth charges can be dropped by either surface ships, patrol aircraft, or from...

s (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 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 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".

Bomber Command's Operational Research Section (BC-ORS), analysed a report of a survey carried out by RAF Bomber Command
RAF Bomber Command
RAF Bomber Command controlled the RAF's bomber forces from 1936 to 1968. During World War II the command destroyed a significant proportion of Nazi Germany's industries and many German cities, and in the 1960s stood at the peak of its postwar military power with the V bombers and a supplemental...

. 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
Anti-aircraft warfare
NATO defines air defence as "all measures designed to nullify or reduce the effectiveness of hostile air action." They include ground and air based weapon systems, associated sensor systems, command and control arrangements and passive measures. It may be to protect naval, ground and air forces...

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.

When Germany organised its air defences into the Kammhuber Line
Kammhuber Line
The Kammhuber Line was the name given to the German night air defense system established in July 1940 by Colonel Josef Kammhuber.- Description :...

, it was realised that if the RAF bombers were to fly in a bomber stream
Bomber stream
The bomber stream was a tactic developed by the Royal Air Force Bomber Command to overwhelm the German aerial defences of the Kammhuber Line during World War II....

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.

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.

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.

On land, the operational research sections of the Army Operational Research Group (AORG) of the Ministry of Supply
Ministry of Supply
The Ministry of Supply was a department of the UK Government formed in 1939 to co-ordinate the supply of equipment to all three British armed forces, headed by the Minister of Supply. There was, however, a separate ministry responsible for aircraft production and the Admiralty retained...

(MoS) were landed in Normandy in 1944
Operation Overlord
Operation Overlord was the code name for the Battle of Normandy, the operation that launched the invasion of German-occupied western Europe during World War II by Allied forces. The operation commenced on 6 June 1944 with the Normandy landings...

, 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.

## Problems addressed with operational research

• critical path analysis or project planning
Project planning
Project planning is part of project management, which relates to the use of schedules such as Gantt charts to plan and subsequently report progress within the project environment....

: 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
Manufacturing
Manufacturing is the use of machines, tools and labor to produce goods for use or sale. The term may refer to a range of human activity, from handicraft to high tech, but is most commonly applied to industrial production, in which raw materials are transformed into finished goods on a large scale...

time (therefore reducing cost)
• network optimization
Telecommunications network
A telecommunications network is a collection of terminals, links and nodes which connect together to enable telecommunication between users of the terminals. Networks may use circuit switching or message switching. Each terminal in the network must have a unique address so messages or connections...

: for instance, setup of telecommunications networks to maintain quality of service during outages
• Allocation problems
• Facility location
Facility location
Facility location, also known as location analysis, is a branch of operations research and computational geometry concerning itself with mathematical modeling and solution of problems concerning optimal placement of facilities in order to minimize transportation costs, avoid placing hazardous...

• Assignment Problems:
• Assignment problem
Assignment problem
The assignment problem is one of the fundamental combinatorial optimization problems in the branch of optimization or operations research in mathematics...

• Generalized assignment problem
Generalized assignment problem
In applied mathematics, the maximum generalized assignment problem is a problem in combinatorial optimization. This problem is a generalization of the assignment problem in which both tasks and agents have a size...

The quadratic assignment problem is one of fundamental combinatorial optimization problems in the branch of optimization or operations research in mathematics, from the category of the facilities location problems....

• Weapon target assignment problem
Weapon target assignment problem
The weapon target assignment problem is a class of combinatorial optimization problems present in the fields of optimization and operations research...

• Bayesian search theory
Bayesian search theory
Bayesian search theory is the application of Bayesian statistics to the search for lost objects. It has been used several times to find lost sea vessels, for example the USS Scorpion.-Procedure:The usual procedure is as follows:...

: looking for a target
• optimal search
Search theory
In microeconomics, search theory studies buyers or sellers who cannot instantly find a trading partner, and must therefore search for a partner prior to transacting....

• routing
Routing
Routing is the process of selecting paths in a network along which to send network traffic. Routing is performed for many kinds of networks, including the telephone network , electronic data networks , and transportation networks...

, such as determining the routes of buses so that as few buses are needed as possible
• supply chain management
Supply chain management
Supply chain management is the management of a network of interconnected businesses involved in the ultimate provision of product and service packages required by end customers...

: managing the flow of raw materials and products based on uncertain demand for the finished products
• efficient messaging and customer response tactics
• automation
Automation
Automation is the use of control systems and information technologies to reduce the need for human work in the production of goods and services. In the scope of industrialization, automation is a step beyond mechanization...

: automating or integrating robotic systems in human-driven operations processes
• globalization
Globalization
Globalization refers to the increasingly global relationships of culture, people and economic activity. Most often, it refers to economics: the global distribution of the production of goods and services, through reduction of barriers to international trade such as tariffs, export fees, and import...

: 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
Intermodal freight transport
Intermodal freight transport involves the transportation of freight in an intermodal container or vehicle, using multiple modes of transportation , without any handling of the freight itself when changing modes. The method reduces cargo handling, and so improves security, reduces damages and...

)
• scheduling:
• personnel staffing
• manufacturing steps
Project management
Project management is the discipline of planning, organizing, securing, and managing resources to achieve specific goals. A project is a temporary endeavor with a defined beginning and end , undertaken to meet unique goals and objectives, typically to bring about beneficial change or added value...

• network data traffic: these are known as queueing model
Queueing model
In queueing theory, a queueing model is used to approximate a real queueing situation or system, so the queueing behaviour can be analysed mathematically...

s 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
Pricing science
Pricing science is the application of social and business science methods to the problem of setting prices. Methods include economic modeling, statistics, econometrics, mathematical programming...

Operational research is also used extensively in government where evidence-based policy
Evidence-based policy
Evidence-based policy is public policy informed by rigorously established objective evidence. It is an extension of the idea of evidence-based medicine to all areas of public policy...

is used.

## Management science

In 1967 Stafford Beer characterized the field of management science as "the business use of operations research". However, in modern times the term management science may also be used to refer to the separate fields of organizational studies
Organizational studies
Organizational studies, sometimes known as organizational science, encompass the systematic study and careful application of knowledge about how people act within organizations...

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 model
Mathematical model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used not only in the natural sciences and engineering disciplines A mathematical model is a...

ing, 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 concept
Concept
The word concept is used in ordinary language as well as in almost all academic disciplines. Particularly in philosophy, psychology and cognitive sciences the term is much used and much discussed. WordNet defines concept: "conception, construct ". However, the meaning of the term concept is much...

s 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.

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

### Techniques

Some of the fields that have considerable overlap with Management Science include:
• Data mining
Data mining
Data mining , a relatively young and interdisciplinary field of computer science is the process of discovering new patterns from large data sets involving methods at the intersection of artificial intelligence, machine learning, statistics and database systems...

• Decision analysis
Decision analysis
Decision analysis is the discipline comprising the philosophy, theory, methodology, and professional practice necessary to address important decisions in a formal manner...

• Engineering
• Forecasting
Forecasting
Forecasting is the process of making statements about events whose actual outcomes have not yet been observed. A commonplace example might be estimation for some variable of interest at some specified future date. Prediction is a similar, but more general term...

• Game theory
Game theory
Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...

• Industrial engineering
Industrial engineering
Industrial engineering is a branch of engineering dealing with the optimization of complex processes or systems. It is concerned with the development, improvement, implementation and evaluation of integrated systems of people, money, knowledge, information, equipment, energy, materials, analysis...

• Logistics
Logistics
Logistics is the management of the flow of goods between the point of origin and the point of destination in order to meet the requirements of customers or corporations. Logistics involves the integration of information, transportation, inventory, warehousing, material handling, and packaging, and...

• Mathematical modeling

• Mathematical optimization
• Probability and statistics
Probability and statistics
See the separate articles on probability or the article on statistics. Statistical analysis often uses probability distributions, and the two topics are often studied together. However, probability theory contains much that is of mostly mathematical interest and not directly relevant to statistics...

• Project management
Project management
Project management is the discipline of planning, organizing, securing, and managing resources to achieve specific goals. A project is a temporary endeavor with a defined beginning and end , undertaken to meet unique goals and objectives, typically to bring about beneficial change or added value...

• Simulation
Simulation
Simulation is the imitation of some real thing available, state of affairs, or process. The act of simulating something generally entails representing certain key characteristics or behaviours of a selected physical or abstract system....

• Social network
Social network
A social network is a social structure made up of individuals called "nodes", which are tied by one or more specific types of interdependency, such as friendship, kinship, common interest, financial exchange, dislike, sexual relationships, or relationships of beliefs, knowledge or prestige.Social...

/Transportation forecasting
Transportation forecasting
Transportation forecasting is the process of estimating the number of vehicles or people that will use a specific transportation facility in the future. For instance, a forecast may estimate the number of vehicles on a planned road or bridge, the ridership on a railway line, the number of...

models
• Supply chain management
Supply chain management
Supply chain management is the management of a network of interconnected businesses involved in the ultimate provision of product and service packages required by end customers...

• Financial engineering

### 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:
• 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
Metagame analysis
Metagame analysis involves framing a problem situation as a strategic game in which participants try to realise their objectives by means of the options available to them...

and drama theory
• morphological analysis and various forms of influence diagram
Influence diagram
An influence diagram is a compact graphical and mathematical representation of a decision situation...

s.
• approaches using cognitive mapping
• the Strategic Choice Approach
• robustness analysis

## Societies and journals

Societies
The International Federation of Operational Research Societies (IFORS) is an umbrella organization
Umbrella organization
An umbrella organization is an association of institutions, who work together formally to coordinate activities or pool resources. In business, political, or other environments, one group, the umbrella organization, provides resources and often an identity to the smaller organizations...

for operational research societies worldwide, representing approximately 50 national societies including those in the US, UK, France, Germany, Canada, Australia, New Zealand, Philippines, India, Japan and South Africa (ORSSA
Operations Research Society of South Africa
The Operations Research Society of South Africa is South Africa's national, professional body for operations research. Founded in 1969, its aim is to further the interests of those engaged in, or interested in the discipline...

). The constituent members of IFORS form regional groups, such as that in Europe. Other important operational research organizations are Simulation Interoperability Standards Organization
Simulation Interoperability Standards Organization
The Simulation Interoperability Standards Organization is an organization dedicated to the promotion of modeling and simulation interoperability and reuse for the benefit of diverse M&S communities, including developers, procurers, and users, world-wide.-History:The Simulation Interoperability...

(SISO) and Interservice/Industry Training, Simulation and Education Conference
Interservice/Industry Training, Simulation and Education Conference
The Interservice/Industry Training, Simulation and Education Conference is an organization dedicated to the promotion of cooperation among the Armed Services, Industry, Academia and various Government agencies that are in pursuit of improved training and education programs, identification of...

(I/ITSEC)

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

Journals
INFORMS publishes twelve scholarly journals about operations research, including the top two journals in their class, according to 2005 Journal Citation Reports
Journal Citation Reports
Journal Citation Reports is an annual publication by the Healthcare & Science division of Thomson Reuters. It has been integrated with the Web of Knowledge, by Thomson Reuters, and is accessed from the Web of Science to JCR Web. It provides information about academic journals in the sciences and...

. They are:
• Decision Analysis
• Information Systems Research
Information Systems Research
Information Systems Research is a peer-reviewed academic journal that covers research in the areas of information systems and information technology. It is published by the Institute for Operations Research and the Management Sciences, and was recently selected as one of the top 20...

• INFORMS Journal on Computing
• INFORMS Transactions on Education (an open access journal)
• Interfaces: An International Journal of the Institute for Operations Research and the Management Sciences
• Management Science: A 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
Management Science: A Journal of the Institute for Operations Research and the Management Sciences is a peer-reviewed academic journal covering the techniques of operations research and scientific approaches to problems of management, marketing, manufacturing, and related fields...

• Manufacturing & Service Operations Management
Manufacturing & Service Operations Management
Manufacturing & Service Operations Management is a scholarly, refereed journal that is published quarterly by INFORMS. M&SOM contains research about innovative mathematical methods of implementation in the manufacturing industry and service operations. The research draws heavily from the tools of...

• Marketing Science
Marketing Science
Marketing Science is a peer-reviewed academic journal published by the Institute for Operations Research and the Management Sciences. It covers operations research and mathematical modeling to analyze marketing...

• Mathematics of Operations Research
Mathematics of Operations Research
Mathematics of Operations Research is a scholarly journal published since 1976. The founding editor was Arthur F. Veinott, Jr. of Stanford University, who served as editor-in-chief 1976-1980. MOR is published quarterly by INFORMS and indexed by Journal Citation Reports...

• Operations Research: A Journal of the Institute for Operations Research and the Management Sciences
Operations Research: A Journal of the Institute for Operations Research and the Management Sciences
Operations Research was founded after World War II by the Operations Research Society of America , which became part of the Institute for Operations Research and the Management Science . The refereed journal includes studies related to linear programming, optimization, revenue management, and the...

• Organization Science
• Transportation Science
Transportation Science
Transportation Science is a peer-reviewed academic journal published by the Institute for Operations Research and the Management Sciences . The studies published in the journal apply operations research techniques to problems in the full range of transportation sectors, including air travel, rail...

.

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
Decision Sciences Institute
The Decision Sciences Institute is a professional association of university professors, graduate students, and practitioners whose interest lies in the application of quantitative research and qualitative research to the decision problems of individuals, organizations, and society...

• 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;
• 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.
• 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;
• Journal of Simulation (JOS): an official journal of The OR Society, published by Palgrave;
• Mathematical Methods of Operations Research (MMOR): the journal of the German and Dutch OR Societies, published by Springer;
• Military Operations Research (MOR): published by the Military Operations Research Society
Military Operations Research Society
The Military Operations Research Society is a society for professionals active within defense applications of operations research in the United States...

;
• Opsearch: official journal of the Operational Research Society of India;
• OR Insight: a quarterly journal of The OR Society, published by Palgrave;
• Production and Operations Management
Production and Operations Management
Production and Operations Management is a peer-reviewed academic journal covering research on all topics in product and process design, operations, and supply chain management....

, the official journal of the Production and Operations Management Society
• TOP: the official journal of the Spanish Society of Statistics and Operations Research.

Operation research topics
• Assignment problem
Assignment problem
The assignment problem is one of the fundamental combinatorial optimization problems in the branch of optimization or operations research in mathematics...

• Decision Analysis
Decision analysis
Decision analysis is the discipline comprising the philosophy, theory, methodology, and professional practice necessary to address important decisions in a formal manner...

• Dynamic programming
Dynamic programming
In mathematics and computer science, dynamic programming is a method for solving complex problems by breaking them down into simpler subproblems. It is applicable to problems exhibiting the properties of overlapping subproblems which are only slightly smaller and optimal substructure...

• Linear programming
Linear programming
Linear programming is a mathematical method for determining a way to achieve the best outcome in a given mathematical model for some list of requirements represented as linear relationships...

• Inventory theory
Inventory theory
Inventory theory is the sub-specialty within operations research that is concerned with the design of production/inventory systems to minimize costs...

• Optimal Maintenance
Optimal maintenance
Optimal maintenance is the discipline within operations research concerned with maintaining a system in a manner that maximizes profit or minimizes cost. Cost functions depending on the reliability and maintainability characteristics of the system of interest determine the parameters to minimize...

• Mathematical optimization
• Real options analysis
Real options analysis
Real options valuation, also often termed Real options analysis, applies option valuation techniques to capital budgeting decisions. A real option itself, is the right — but not the obligation — to undertake some business decision; typically the option to make, abandon, expand, or contract a...

• Stochastic processes
• Systems analysis
Systems analysis
Systems analysis is the study of sets of interacting entities, including computer systems analysis. This field is closely related to requirements analysis or operations research...

• Systems thinking
Systems thinking
Systems thinking is the process of understanding how things influence one another within a whole. In nature, systems thinking examples include ecosystems in which various elements such as air, water, movement, plants, and animals work together to survive or perish...

Operation researchers
Operations researcher category
• Russell L. Ackoff
Russell L. Ackoff
Russell Lincoln Ackoff 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...

• Anthony Stafford Beer
Anthony Stafford Beer
Anthony Stafford Beer was a British theorist, consultant and professor at the Manchester Business School. He is best known for his work in the fields of operational research and management cybernetics.- Biography :...

• Alfred Blumstein
Alfred Blumstein
Alfred Blumstein is an American scientist and the J. Erik Jonsson University Professor of Urban Systems and Operations Research at the Heinz College and Department of Engineering and Public Policy at Carnegie Mellon University...

• C. West Churchman
C. West Churchman
Charles West Churchman was an American philosopher and systems scientist, who was Professor at the School of Business Administration and Professor of Peace and Conflict Studies at the University of California, Berkeley...

• George Dantzig
George Dantzig
George Bernard Dantzig was an American mathematical scientist who made important contributions to operations research, computer science, economics, and statistics....

• Richard Karp
Richard Karp
Richard Manning Karp is a computer scientist and computational theorist at the University of California, Berkeley, notable for research in the theory of algorithms, for which he received a Turing Award in 1985, The Benjamin Franklin Medal in Computer and Cognitive Science in 2004, and the Kyoto...

• Frederick W. Lanchester
• Thomas L. Magnanti
Thomas L. Magnanti
Thomas L. Magnanti is an American engineer and Institute Professor and former Dean of the School of Engineering at the Massachusetts Institute of Technology...

• Alvin E. Roth
Alvin E. Roth
Alvin E. "Al" Roth is an American economist currently serving as the George Gund Professor of Economics and Business Administration at Harvard Business School...

• Peter Whittle
Peter Whittle
Peter Whittle is a mathematician and statistician, working in the fields of stochastic nets, optimal control, time series analysis, stochastic optimization and stochastic dynamics...

Related fields
• Behavioral operations research
Behavioral Operations Research
Behavioral operations research examines the behavior of actual human agents in complex decision problems. BOR is the operations management analog of experimental economics and behavioral finance, and is part of the field known as management science....

• Database normalization
Database normalization
In the design of a relational database management system , the process of organizing data to minimize redundancy is called normalization. The goal of database normalization is to decompose relations with anomalies in order to produce smaller, well-structured relations...

• Econometrics
Econometrics
Econometrics has been defined as "the application of mathematics and statistical methods to economic data" and described as the branch of economics "that aims to give empirical content to economic relations." More precisely, it is "the quantitative analysis of actual economic phenomena based on...

• Industrial Engineering
Industrial engineering
Industrial engineering is a branch of engineering dealing with the optimization of complex processes or systems. It is concerned with the development, improvement, implementation and evaluation of integrated systems of people, money, knowledge, information, equipment, energy, materials, analysis...

• Industrial organization
Industrial organization
Industrial organization is the field of economics that builds on the theory of the firm in examining the structure of, and boundaries between, firms and markets....

• Management engineering
Management engineering
Management engineering is a branch of engineering that focuses on optimizing complex processes or systems. It is concerned with the development, improvement, implementation and evaluation of integrated systems of people, money, knowledge, information, equipment, energy, materials and/or processes....

• Managerial economics
Managerial economics
Managerial economics as defined by Edwin Mansfield is "concerned with application of economic concepts and economic analysis to the problems of formulating rational managerial decision." It is sometimes referred to as business economics and is a branch of economics that applies microeconomic...

• Military simulation
Military simulation
Military simulations, also known informally as war games, are simulations in which theories of warfare can be tested and refined without the need for actual hostilities. Many professional contemporary analysts object to the term wargames as this is generally taken to be referring to the civilian...

• Modeling & Simulation
• Reliability engineering
Reliability engineering
Reliability engineering is an engineering field, that deals with the study, evaluation, and life-cycle management of reliability: the ability of a system or component to perform its required functions under stated conditions for a specified period of time. It is often measured as a probability of...

• Search Based Software Engineering
• Simulation
Simulation
Simulation is the imitation of some real thing available, state of affairs, or process. The act of simulating something generally entails representing certain key characteristics or behaviours of a selected physical or abstract system....

• System Dynamics
System dynamics
System dynamics is an approach to understanding the behaviour of complex systems over time. It deals with internal feedback loops and time delays that affect the behaviour of the entire system. What makes using system dynamics different from other approaches to studying complex systems is the use...

• System Safety
System safety
The system safety concept calls for a risk management strategy based on identification, analysis of hazards and application of remedial controls using a systems-based approach...

• Systems theory
Systems theory
Systems theory is the transdisciplinary study of systems in general, with the goal of elucidating principles that can be applied to all types of systems at all nesting levels in all fields of research...

• Wargaming
Wargaming
A wargame is a strategy game that deals with military operations of various types, real or fictional. Wargaming is the hobby dedicated to the play of such games, which can also be called conflict simulations, or consims for short. When used professionally to study warfare, it is generally known as...

• 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
• 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.