Operations Research (OR) in North America, South Africa and Australia, and Operational Research in Europe, is an interdisciplinary branch of applied mathematics and formal science that uses methods such as mathematical modeling, statistics, and algorithms to arrive at optimal or near optimal solutions to complex problems. It is typically concerned with optimizing the maxima (profit, assembly line performance, crop yield, bandwidth, etc) or minima (loss, risk, etc.) of some objective function. Operations research helps management achieve its goals using scientific methods.
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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. The field is closely related to Industrial engineering, but takes more of an engineering point of view. Industrial engineers typically consider Operations Research (OR) techniques to be a major part of their toolset.
Some of the primary tools used by operations researchers are statistics, optimization, probability theory, queuing 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 use custom-written and off-the-shelf software.
Operations research is distinguished by its frequent use to examine an entire management information 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.
Examples of applications in which operations research is currently used include:
Operations research is also used extensively in government where evidence-based policy is used.
Some say that Charles Babbage (1791-1871) is the "father of operations research" because 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.[1] 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 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.[2]
In another piece of work, Blackett's team analysed a report of a survey carried out by RAF Bomber Command. For the survey, Bomber Command inspected all bombers returning from bombing raids over Germany over a particular period. All damage inflicted by German air 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 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 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.[2]
The "exchange rate" ratio of output to input was a characteristic feature of operations 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.[3]
Operations research doubled the success rate of aerial attacks on submarines by recommending a shallower detonation setting on the depth charges being dropped by aircraft. The depth charges had previously been set to detonate at the depth where the shock of the explosion would be most efficiently transferred through the water, but submarines were unable to reach that depth in the limited time available after being spotted by the aircraft. Shallower detonation depth settings reduced the distance of the detonation from the submarine: a close detonation with lower shock transmission efficiency was more destructive than a more distant detonation with better transmission.[3]
Operations 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.[3]
It is known as "operational research" in the United Kingdom (and "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, but "OR" is the common abbreviation everywhere. With expanded techniques and growing awareness, OR is no longer limited to only operations, and the introduction of computer data collection and processing has relieved analysts of much of the more mundane labour.
The International Federation of Operational Research Societies[4] is an umbrella organization for operations research societies worldwide. Significant among these are:
In 2004 INFORMS began an initiative to better market the OR profession, including a website entitled The Science of Better[16] which provides an introduction to OR and examples of successful applications of OR to industrial problems.
INFORMS publishes twelve scholarly journals about operations research, including the top two journals in their class, according to 2005 Journal Citation Reports.[17] They are:
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