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What is OR?

Operations Research or Operational Research (OR) is an interdisciplinary branch of mathematics which uses methods like mathematical modeling, statistics, and algorithms to arrive at optimal or good decisions in complex problems which are concerned with optimizing the maxima (profit, faster assembly line, greater crop yield, higher bandwidth, etc) or minima (cost loss, lowering of risk, etc) of some objective function. The eventual intention behind using Operations Research is to elicit a best possible solution to a problem mathematically, which improves or optimizes the performance of the system.

The terms operations research and management science are often used synonymously. When a distinction is drawn, management science generally implies a closer relationship to the problems of business management. Operations research also closely relates to Industrial engineering. Industrial engineering takes more of an engineering point of view, and industrial engineers typically consider OR techniques to be a major part of their toolset.

Some of the primary tools used by operations researchers are statistics, optimization, stochastics, queueing theory, game theory, graph theory, decision analysis, and simulation. Because of the computational nature of these fields, OR also has ties to computer science, and operations researchers regularly use custom-written or off-the-shelf software.

Operations research is distinguished by its ability to look at and improve an entire system, rather than concentrating only on specific elements (though this is often done as well). An operations researcher faced with a new problem is expected to determine which techniques are most appropriate given the nature of the system, the goals for improvement, and constraints on time and computing power. For this and other reasons, the human element of OR is vital. Like any other tools, OR techniques cannot solve problems by themselves.

Scope of operations research

A few examples of applications in which operations research is currently used include:

  • designing the layout of a factory for efficient flow of materials
  • constructing a telecommunications network at low cost while still guaranteeing QoS (quality of service) or QoE (Quality of Experience) if particular connections become very busy or get damaged
  • road traffic management and 'one way' street allocations i.e. allocation problems.
  • determining the routes of school buses (or city buses) so that as few buses are needed as possible
  • designing the layout of a computer chip to reduce manufacturing time (therefore reducing cost)
  • managing the flow of raw materials and products in a supply chain based on uncertain demand for the finished products
  • efficient messaging and customer response tactics
  • roboticizing or automating human-driven operations processes
  • globalizing operations processes in order to take advantage of cheaper materials, labor, land or other productivity inputs
  • 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 queuing models or queuing systems.
    • sports events and their television coverage
  • blending of raw materials in oil refineries

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

History of OR

The modern field of operations research arose during World War II. Scientists in the United Kingdom including Patrick Blackett, Cecil Gordon, C. H. Waddington, Owen Wansbrough-Jones and Frank Yates, and in the United States with George Dantzig looked for ways to make better decisions in such areas as logistics and training schedules. After the war it began to be applied to similar problems in industry.

Blackett's team made a number of crucial analyses which 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 clearly showed that:[citation needed]

  • Large convoys were more efficient
  • The probability of detection by U-boat was statistically unrelated to the size of the convoy
  • Slow convoys were at greater risk (though considered overall, large convoys were still to be preferred)

In another piece of work, Blackett's team analysed a report of a survey carried out by RAF Bomber Command.[citation needed] For the survey, Bomber Command inspected all bombers returning from bombing raids over Germany over a particular period. All damage inflicted by German air defenses was noted and the recommendation was given that armour be added in the most heavily damaged areas. Their suggestion to remove some of the crew so that an aircraft loss would result in fewer personnel loss was rejected by RAF command.

Blackett's team instead made the surprising and counter-intuitive recommendation that the armour be placed in the areas which were completely untouched by damage, according to the survey. They reasoned that the survey was biased, since it only included aircraft that successfully came back from Germany. The untouched areas were probably vital areas, which if hit would result in the loss of the aircraft.[citation needed]

When the Germans organised their air defences into the Kammhuber Line, it was realised that if the RAF bombers were to fly in a bomber stream they could overwhelm the night fighters who flew in individual cells directed to their targets by ground controllers. It was then a matter of calculating the statistical loss from collisions against the statistical loss from night fighters to calculate how close the bombers should fly to minimise RAF losses.[1]

It is known as "operational research" in the United Kingdom ("operational analysis" within the UK military and UK Ministry of Defence, where OR stands for "Operational Requirement") and as "operations research" in most other English-speaking countries, though OR is a common abbreviation everywhere. With expanded techniques and growing awareness, OR is no longer limited to only operations, and the proliferation of computer data collection has relieved analysts of much of the more mundane research. But the OR analyst must still know how a system operates, and learn to perform even more sophisticated research than ever before. In every sense the name OR still applies, more than a half century later.


OR/IE Relationship

In recent years industrial engineering has broadened significantly as a discipline, and the support it now provides to production and manufacturing managers comes from staff specialists drawn not only from the field of industrial engineering but also from operations research, management science, computer science, and information systems. In the 1970s and 1980s industrial engineering became a more quantitative and computer-based profession, and operations research techniques were adopted as the core of most industrial engineering academic curricula in both the United States and Europe.

Since many of the problems of operations research originate in industrial production systems, it is often difficult to determine where the engineering discipline ends and the more basic scientific discipline begins (operations research is a branch of applied mathematics). Indeed, many academic industrial engineering departments now use the term industrial engineering and operations research or the reverse, further clouding the distinction.


OR/IE Departments

The University of Texas at Austin

UC Berkeley

Columbia University

IIT Bombay

New Mexico State University

Cornell University

Georgia Institute of Technology

University of Wisconsin-Madison

Rutgers Center for Operations Research


OR Around the world


Italian Interuniversity Center for Operations Research

The Italian Society of Operations Research, Optimisation and Decision Sciences

The Belgian Operations Research Society

The Operational Research Society


OR/IE Applications

Examples and Case Studies in Optimization

How OR can help your organization

Capgemini success stories

Operations Research: the science of better

OR/IE and Pollution Prevention

Dynamic Modeling of a Supply Chain

From Bioterrorism to Natural Disasters

Sport Scheduling

Predicting the future -A case study of Volvo CE's forecasting process

Sales Forecasting: A "Job Shop" Case Study Revisited

Project Management Case studies


OR/IE Software

Free Student/Trial Versions of MPL/CPLEX and OptiMax 2000

Free and open-source software for Operations Research and Industrial Engineering


LogMeIn IT Reach

Key-Stock Stock Management System



Scheduling Software

Interval Global Solver

MINOPT for Mixed Integer Nonlinear Programming

GAMS/DICOPT Solver for Mixed Integer Nonlinear Programming

XPRESS-MP mixed integer LP, QP and MINLP solver

TOMLAB modeling and optimization environment.

OptQuest Tabu and Scatter search, etc.

OptiREX, Cutting optimizer for rectangular sheets

Koalog Constraint Solver

HEURO, Integrated Optimization Environment for large scale black box global optimization with expensive objective function

DistOpt: a distributed optimization software


Decision Tree for Optimization Software

OOP-Web Algorithms Directory

Semidefinite Programming

Traveling Salesman Problem Software

Algorithms and Data Structure Group

egf’s Algorithms

Computational Optimization and Applications Software Forum

Constraints Archives – Cork Constraint Computation Center

Local Optimization Software

Global Optimization Software

Web Work Enterprise


OM Software

Forecasting Software

Project Management Software


OR/IE Selected Books

Production Planning And Inventory Control (1967), by Magee, John F.; Boodman, David M

Inventory Management and Production Planning and Scheduling, 3rd Edition (1998), by Edward A. Silver, David F. Pyke, Rein Peterson

Decision Systems for Inventory Management and Production Planning (1991), by Edward A. Silver, Rein Peterson

Integrated Models in Production Planning, Inventory, Quality, and Maintenance (2001), by M.A. Rahim, Mohamed Ben-Daya

Operations Management (2004), by Nigel Slack, Stuart Chambers, Robert Johnston

Cases in Operations Management (2002), by Robert Johnston, Stuart Chambers, Nigel Slack, Alan Harrison, Christine Harland

Operations Management (2004), by Terry Hill

Project Management (2005), by Jack R. Meredith, Samuel J. Mantel, Jr.

Advances in Industrial Engineering and Operations Research (2008), by Chan, Alan H.S.; Ao, Sio-Iong

Models for Public Systems Analysis (Operations research and industrial engineering), by Edward J. Beltrami (1977)


OR Libraries

Optimization Online

IIASA Publications catalog

The Virtual Library for Operations Research and the Management Sciences

Online Resources on Scheduling

International Abstracts in Operations Research




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