# Operations research

**operational researchoperation researchoperational analysismanagement scientistmanagement scienceoperations analysisArmy Operational Research Groupmathematics of operational researchOperational Research Sectionoperations analyst**

Operations research (OR) is a discipline that deals with the application of advanced analytical methods to help make better decisions.wikipedia

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### Mathematical optimization

**optimizationmathematical programmingoptimal**

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. Operational research (OR) encompasses the development and the use of 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.

Optimization problems of sorts arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.

### Industrial engineering

**industrial engineerindustrialIndustrial Engineering and Management**

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.

Depending on the sub-specialties involved, industrial engineering may also overlap with, operations research, systems engineering, manufacturing engineering, production engineering, supply chain 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.

### Operations management

**operations manageroperationsoperation**

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.

The synergy of operations research and systems engineering allowed for the realization of solving large scale and complex problems in the modern era.

### Data envelopment analysis

Operational research (OR) encompasses the development and the use of 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.

Data envelopment analysis (DEA) is a nonparametric method in operations research and economics for the estimation of production frontiers.

### Analytics

**data analyticsanalyticadvanced analytics**

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

Especially valuable in areas rich with recorded information, analytics relies on the simultaneous application of statistics, computer programming and operations research to quantify performance.

### George Dantzig

**George B. DantzigDantzigDantzig, George**

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 (George Dantzig) looked for ways to make better decisions in such areas as logistics and training schedules

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.

### Management science

**Management Sciencesmanagement theorymanagement scientist**

The terms management science and decision science are sometimes used as synonyms.

Its origins can be traced to operations research, which became influential during World War II when the Allied forces recruited scientists of various disciplines to assist with military operations.

### Patrick Blackett

**Patrick Blackett, Baron BlackettPatrick Maynard Stuart BlackettP.M.S. Blackett**

Patrick Blackett worked for several different organizations during the war.

He also made a major contribution in World War II advising on military strategy and developing operational research.

### Jacob Bronowski

**BronowskiBronowski, JacobJ. Bronowski**

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 (George Dantzig) looked for ways to make better decisions in such areas as logistics and training schedules

During World War II he led the field of operations research and worked to increase the effectiveness of Allied bombing.

### Freeman Dyson

**Freeman J. DysonDysonFreeman John Dyson**

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 (George Dantzig) looked for ways to make better decisions in such areas as logistics and training schedules

At age 17 he studied mathematics with G.H. Hardy at Trinity College, Cambridge (where he won a scholarship at age 15) and at age 19 was assigned to war work in the Operational Research Section (ORS) of the Royal Air Force's Bomber Command, where he developed analytical methods for calculating the ideal density for bomber formations to help the Royal Air Force bomb German targets during the Second World War.

### Stochastic

**stochasticsstochastic musicstochasticity**

In the 1950s they were used at Los Alamos for early work relating to the development of the hydrogen bomb, and became popularized in the fields of physics, physical chemistry, and operations research.

### Charles Babbage

**BabbageBabbage, CharlesBabbage engines**

Charles Babbage's research into the cost of transportation and sorting of mail led to England's universal "Penny Post" in 1840, and to studies into the dynamical behaviour of railway vehicles in defence of the GWR's broad gauge.

It was an influential early work of operational research.

### Facility location problem

**facilities locationFacility locationFacility location (optimization problem)**

The study of facility location problems (FLP), also known as location analysis, is a branch of operations research and computational geometry concerned with the optimal placement of facilities to minimize transportation costs while considering factors like avoiding placing hazardous materials near housing, and competitors' facilities.

### Convoy

**convoyscaravanAtlantic convoys**

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.

The enormous number of vessels involved and the frequency of engagements meant that statistical techniques could be applied to evaluate tactics: an early use of operational research in war.

### Applied mathematics

**applied mathematicianappliedapplications of mathematics**

It is often considered to be a sub-field of applied mathematics.

Operations research and management science are often taught in faculties of engineering, business, and public policy.

### Travelling salesman problem

**traveling salesman problemTSPtraveling salesman**

It is an NP-hard problem in combinatorial optimization, important in operations research and theoretical computer science.

### Queueing theory

**queuing theoryfirst-come first-servedqueueing model**

Operational research (OR) encompasses the development and the use of 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.

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.

### Project management

**projectproject developmentproject manager**

The secondary—and more ambitious—challenge is to optimize the allocation of necessary inputs and apply them to meet pre-defined objectives.

### Cutting stock problem

**cutting stocknesting of irregular shapes**

In operations research, the cutting-stock problem is the problem of cutting standard-sized pieces of stock material, such as paper rolls or sheet metal, into pieces of specified sizes while minimizing material wasted.

### Nurse scheduling problem

**nurse rosteringnurse rostering optimisationNurse rostering problem**

The nurse scheduling problem (NSP), also called the nurse rostering problem (NRP), is the operations research problem of finding an optimal way to assign nurses to shifts, typically with a set of hard constraints which all valid solutions must follow, and a set of soft constraints which define the relative quality of valid solutions.

### Quadratic assignment problem

**Quadratic Assignment**

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

### Stafford Beer

**Anthony Stafford BeerBeerBeer, Anthony Stafford**

In 1967 Stafford Beer characterized the field of management science as "the business use of operations research".

He is best known for his work in the fields of operational research and management cybernetics.

### Linear programming

**linear programlinear optimizationlinear**

With the development of the simplex algorithm for linear programming in 1947 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."

Many practical problems in operations research can be expressed as linear programming problems.

### Weapon target assignment problem

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

### Analytic hierarchy process

**(AHP)AHPAHP (Analytic Hierarchy Process):**

Operational research (OR) encompasses the development and the use of 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.