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100-717: The Weapons Systems Evaluation Group (abbreviated WSEG ) was formed in 1949 to carry out Operational Research work for the Joint Chiefs of Staff of the United States Army and the United States Secretary of Defense . The group oversaw the appraisal of weapons used during the Korean War . The group collaborated with Israel in evaluating the effectiveness of Soviet weapons during the Cold War . The first Research Director

200-413: A liberal education , studying languages, music , history , geography , mathematics , logic , and rhetoric , alongside dancing , fencing and horse riding . In 1644, Huygens had as his mathematical tutor Jan Jansz Stampioen , who assigned the 15-year-old a demanding reading list on contemporary science. Descartes was later impressed by his skills in geometry, as was Mersenne, who christened him

300-590: A broad range of correspondents, though with some difficulty after 1648 due to the five-year Fronde in France. Visiting Paris in 1655, Huygens called on Ismael Boulliau to introduce himself, who took him to see Claude Mylon . The Parisian group of savants that had gathered around Mersenne held together into the 1650s, and Mylon, who had assumed the secretarial role, took some trouble to keep Huygens in touch. Through Pierre de Carcavi Huygens corresponded in 1656 with Pierre de Fermat, whom he admired greatly. The experience

400-525: A career. Huygens generally wrote in French or Latin. In 1646, while still a college student at Leiden, he began a correspondence with his father's friend, Marin Mersenne , who died soon afterwards in 1648. Mersenne wrote to Constantijn on his son's talent for mathematics, and flatteringly compared him to Archimedes on 3 January 1647. The letters show Huygens's early interest in mathematics. In October 1646 there

500-402: A collection of solutions to classical problems at the end of the work under the title Illustrium Quorundam Problematum Constructiones ( Construction of some illustrious problems ). Huygens became interested in games of chance after he visited Paris in 1655 and encountered the work of Fermat, Blaise Pascal and Girard Desargues years earlier. He eventually published what was, at the time,

600-611: A complete explanation of the rectilinear propagation and diffraction effects of light in 1821. Today this principle is known as the Huygens–Fresnel principle . Huygens invented the pendulum clock in 1657, which he patented the same year. His horological research resulted in an extensive analysis of the pendulum in Horologium Oscillatorium (1673), regarded as one of the most important 17th century works on mechanics. While it contains descriptions of clock designs, most of

700-681: 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 sometimes complex systems, and has become an area of active academic and industrial research. In the 17th century, mathematicians Blaise Pascal and Christiaan Huygens solved problems involving sometimes complex decisions ( problem of points ) by using game-theoretic ideas and expected values ; others, such as Pierre de Fermat and Jacob Bernoulli , solved these types of problems using combinatorial reasoning instead. Charles Babbage 's research into

800-559: A full cycle of rotation. His approach was thus equivalent to the principle of virtual work . Huygens was also the first to recognize that, for these homogeneous solids, their specific weight and their aspect ratio are the essentials parameters of hydrostatic stability . Huygens was the leading European natural philosopher between Descartes and Newton. However, unlike many of his contemporaries, Huygens had no taste for grand theoretical or philosophical systems and generally avoided dealing with metaphysical issues (if pressed, he adhered to

900-565: A larger audience until the publication of De Motu Corporum ex Percussione ( Concerning the motion of colliding bodies ) in 1703. In addition to his mathematical and mechanical works, Huygens made important scientific discoveries: he was the first to identify Titan as one of Saturn's moons in 1655, invented the pendulum clock in 1657, and explained Saturn's strange appearance as due to a ring in 1659; all these discoveries brought him fame across Europe. On 3 May 1661, Huygens, together with astronomer Thomas Streete and Richard Reeve, observed

1000-468: 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 to 25 feet, 1% of submerged U-boats were sunk and 14% damaged. After

1100-523: A meeting at Gresham College . Shortly afterwards, he reevaluated Boyle's experimental design and developed a series of experiments meant to test a new hypothesis. It proved a yearslong process that brought to the surface a number of experimental and theoretical issues, and which ended around the time he became a Fellow of the Royal Society. Despite the replication of results of Boyle's experiments trailing off messily, Huygens came to accept Boyle's view of

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1200-562: A new technique specific to the problem at hand (and, afterwards, to that type of problem). The major sub-disciplines (but not limited to) in modern operational research, as identified by the journal Operations Research and The Journal of the Operational Research Society are: In the decades after the two world wars, the tools of operations research were more widely applied to problems in business, industry, and society. Since that time, operational research has expanded into

1300-443: A segment of a circle, resulting in a faster and accurate approximation of the circle quadrature. From these theorems, Huygens obtained two set of values for π : the first between 3.1415926 and 3.1415927, and the second between 3.1415926533 and 3.1415926538. Huygens also showed that, in the case of the hyperbola , the same approximation with parabolic segments produces a quick and simple method to calculate logarithms . He appended

1400-588: A 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 (MoS) were landed in Normandy in 1944 , and they followed British forces in the advance across Europe. They analyzed, among other topics, the effectiveness of artillery, aerial bombing and anti-tank shooting. In 1947, under

1500-439: 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 armor be added in the most heavily damaged areas. This recommendation was not adopted because the fact that the aircraft were able to return with these areas damaged indicated

1600-628: A telescope with two lenses to diminish the amount of dispersion . As a mathematician, Huygens developed the theory of evolutes and wrote on games of chance and the problem of points in Van Rekeningh in Spelen van Gluck , which Frans van Schooten translated and published as De Ratiociniis in Ludo Aleae (1657). The use of expected values by Huygens and others would later inspire Jacob Bernoulli's work on probability theory . Christiaan Huygens

1700-706: A vain mission to meet the French Foreign Minister Arnauld de Pomponne . Leibniz was working on a calculating machine at the time and, after a short visit to London in early 1673, he was tutored in mathematics by Huygens until 1676. An extensive correspondence ensued over the years, in which Huygens showed at first reluctance to accept the advantages of Leibniz's infinitesimal calculus . Huygens moved back to The Hague in 1681 after suffering another bout of serious depressive illness. In 1684, he published Astroscopia Compendiaria on his new tubeless aerial telescope . He attempted to return to France in 1685 but

1800-444: Is an umbrella organization for operational research societies worldwide, representing approximately 50 national societies including those in the US, UK , France, Germany, Italy , Canada, Australia, New Zealand, Philippines, India, Japan and South Africa. For the institutionalization of Operations Research, the foundation of IFORS in 1960 was of decisive importance, which stimulated

1900-578: 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. Some of the fields that have considerable overlap with Operations Research and Management Science include: Applications are abundant such as in airlines, manufacturing companies, service organizations , military branches, and government. The range of problems and issues to which it has contributed insights and solutions

2000-438: Is often concerned with determining the extreme values of some real-world objective: the maximum (of profit, performance, or yield) or minimum (of loss, risk, or cost). Originating in military efforts before World War II , its techniques have grown to concern problems in a variety of industries. Operations research (OR) encompasses the development and the use of a wide range of problem-solving techniques and methods applied in

2100-480: Is the suspension bridge and the demonstration that a hanging chain is not a parabola , as Galileo thought. Huygens would later label that curve the catenaria ( catenary ) in 1690 while corresponding with Gottfried Leibniz . In the next two years (1647–48), Huygens's letters to Mersenne covered various topics, including a mathematical proof of the law of free fall , the claim by Grégoire de Saint-Vincent of circle quadrature , which Huygens showed to be wrong,

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2200-528: Is vast. It includes: Management is also concerned with so-called soft-operational analysis which concerns methods for strategic planning , strategic decision support , problem structuring methods . In dealing with these sorts of challenges, mathematical modeling and simulation may not be appropriate or may not suffice. Therefore, during the past 30 years , a number of non-quantified modeling methods have been developed. These include: The International Federation of Operational Research Societies (IFORS)

2300-617: The British Army . 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. In 1941, Blackett moved from

2400-654: The Cartesian philosophy of his time). Instead, Huygens excelled in extending the work of his predecessors, such as Galileo, to derive solutions to unsolved physical problems that were amenable to mathematical analysis. In particular, he sought explanations that relied on contact between bodies and avoided action at a distance . In common with Robert Boyle and Jacques Rohault , Huygens advocated an experimentally oriented, mechanical natural philosophy during his Paris years. Already in his first visit to England in 1661, Huygens had learnt about Boyle's air pump experiments during

2500-619: The Kammhuber Line , it was realized 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 minimize RAF losses. The "exchange rate" ratio of output to input

2600-724: The Minuteman missile project, which was then starting. Together with George E. Pugh he wrote an influential study The Distribution and Effects of Fallout in Large Nuclear Weapon Campaigns . Operational Research Employing techniques from other mathematical sciences, such as modeling , statistics , and optimization , operations research arrives at optimal or near-optimal solutions to decision-making problems. Because of its emphasis on practical applications, operations research has overlapped with many other disciplines, notably industrial engineering . Operations research

2700-469: The Royal Society of London elected Huygens a Fellow in 1663, making him its first foreign member when he was just 34 years old. The Montmor Academy , started in the mid-1650s, was the form the old Mersenne circle took after his death. Huygens took part in its debates and supported those favouring experimental demonstration as a check on amateurish attitudes. He visited Paris a third time in 1663; when

2800-521: The Second Anglo-Dutch War , was guarded. The war ended in 1667, and Huygens announced his results to the Royal Society in 1668. He later published them in the Journal des Sçavans in 1669. In 1659 Huygens found the constant of gravitational acceleration and stated what is now known as the second of Newton's laws of motion in quadratic form. He derived geometrically the now standard formula for

2900-405: The a priori attitude of Descartes, but neither would he accept aspects of gravitational attractions that were not attributable in principle to contact between particles. The approach used by Huygens also missed some central notions of mathematical physics, which were not lost on others. In his work on pendulums Huygens came very close to the theory of simple harmonic motion ; the topic, however,

3000-474: The centre of gravity of the system remains the same in velocity and direction, which Huygens called the conservation of "quantity of movement" . While others at the time were studying impact, Huygens's theory of collisions was more general. These results became the main reference point and the focus for further debates through correspondence and in a short article in Journal des Sçavans but would remain unknown to

3100-402: The centrifugal force , exerted on an object when viewed in a rotating frame of reference , for instance when driving around a curve. In modern notation: with m the mass of the object, ω the angular velocity , and r the radius . Huygens collected his results in a treatise under the title De vi Centrifuga , unpublished until 1703, where the kinematics of free fall were used to produce

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3200-523: The pendulum clock , the most accurate timekeeper for almost 300 years. A talented mathematician and physicist, his works contain the first idealization of a physical problem by a set of mathematical parameters , and the first mathematical and mechanistic explanation of an unobservable physical phenomenon. Huygens first identified the correct laws of elastic collision in his work De Motu Corporum ex Percussione , completed in 1656 but published posthumously in 1703. In 1659, Huygens derived geometrically

3300-449: The revocation of the Edict of Nantes precluded this move. His father died in 1687, and he inherited Hofwijck, which he made his home the following year. On his third visit to England, Huygens met Isaac Newton in person on 12 June 1689. They spoke about Iceland spar , and subsequently corresponded about resisted motion. Huygens returned to mathematical topics in his last years and observed

3400-531: The Øresund to visit Descartes in Stockholm . This did not happen as Descartes had died in the interim. Although his father Constantijn had wished his son Christiaan to be a diplomat, circumstances kept him from becoming so. The First Stadtholderless Period that began in 1650 meant that the House of Orange was no longer in power, removing Constantijn's influence. Further, he realized that his son had no interest in such

3500-449: The "new Archimedes ." At sixteen years of age, Constantijn sent Huygens to study law and mathematics at Leiden University , where he studied from May 1645 to March 1647. Frans van Schooten was an academic at Leiden from 1646, and became a private tutor to Huygens and his elder brother, Constantijn Jr., replacing Stampioen on the advice of Descartes. Van Schooten brought Huygens's mathematical education up to date, introducing him to

3600-781: The 1930s. The pendulum clock was much more accurate than the existing verge and foliot clocks and was immediately popular, quickly spreading over Europe. Clocks prior to this would lose about 15 minutes per day, whereas Huygens's clock would lose about 15 seconds per day. Although Huygens patented and contracted the construction of his clock designs to Salomon Coster in The Hague, he did not make much money from his invention. Pierre Séguier refused him any French rights, while Simon Douw in Rotterdam and Ahasuerus Fromanteel in London copied his design in 1658. The oldest known Huygens-style pendulum clock

3700-613: The 1960s, ORSA reached 8000 members. Consulting companies also founded OR groups. In 1953, Abraham Charnes and William Cooper published the first textbook on Linear Programming. In the 1950s and 1960s, chairs of operations research were established in the U.S. and United Kingdom (from 1964 in Lancaster) in the management faculties of universities. Further influences from the U.S. on the development of operations research in Western Europe can be traced here. The authoritative OR textbooks from

3800-499: The CC-ORS indicated that on average if the trigger depth of aerial-delivered depth charges were changed from 100 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

3900-502: The Circle , showing that the ratio of the circumference to its diameter or pi ( π ) must lie in the first third of that interval. Using a technique equivalent to Richardson extrapolation , Huygens was able to shorten the inequalities used in Archimedes's method; in this case, by using the centre of the gravity of a segment of a parabola, he was able to approximate the centre of gravity of

4000-575: The English lecturer John Pell . His time in Breda ended around the time when his brother Lodewijk, who was enrolled at the school, duelled with another student. Huygens left Breda after completing his studies in August 1649 and had a stint as a diplomat on a mission with Henry, Duke of Nassau . It took him to Bentheim , then Flensburg . He took off for Denmark, visited Copenhagen and Helsingør , and hoped to cross

4100-523: The French Académie was not always easy, and in 1670 Huygens, seriously ill, chose Francis Vernon to carry out a donation of his papers to the Royal Society in London, should he die. However, the aftermath of the Franco-Dutch War (1672–78), and particularly England's role in it, may have damaged his later relationship with the Royal Society. Robert Hooke , as a Royal Society representative, lacked

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4200-655: 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 . They are: These are listed in alphabetical order of their titles. Christiaan Huygens Christiaan Huygens , Lord of Zeelhem , FRS ( / ˈ h aɪ ɡ ən z / HY -gənz , US also / ˈ h ɔɪ ɡ ən z / HOY -gənz ; Dutch: [ˈkrɪstijaːn ˈɦœyɣə(n)s] ; also spelled Huyghens ; Latin : Hugenius ; 14 April 1629 – 8 July 1695)

4300-649: The Montmor Academy closed down the next year, Huygens advocated for a more Baconian program in science. Two years later, in 1666, he moved to Paris on an invitation to fill a leadership position at King Louis XIV 's new French Académie des sciences . While at the Académie in Paris, Huygens had an important patron and correspondent in Jean-Baptiste Colbert , First Minister to Louis XIV. However, his relationship with

4400-661: The NATO military command structure , the transfer of NATO headquarters from France to Belgium led to the institutionalization of OR in Belgium, where Jacques Drèze founded CORE, the Center for Operations Research and Econometrics at the Catholic University of Leuven in 1966. With the development of computers over the next three decades, Operations Research can now solve problems with hundreds of thousands of variables and constraints. Moreover,

4500-599: The RAE to the Navy, after first working with RAF Coastal Command , in 1941 and then early in 1942 to the Admiralty . 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. They undertook a number of crucial analyses that aided the war effort. Britain introduced the convoy system to reduce shipping losses, but while

4600-657: The U.S. were published in Germany in German language and in France in French (but not in Italian ), such as the book by George Dantzig "Linear Programming"(1963) and the book by C. West Churchman et al. "Introduction to Operations Research"(1957). The latter was also published in Spanish in 1973, opening at the same time Latin American readers to Operations Research. NATO gave important impulses for

4700-636: 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 . The Institute for Operations Research and

4800-576: 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. The modern field of operational research arose during World War II. In

4900-642: 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". Other names for it included operational analysis (UK Ministry of Defence from 1962) and quantitative management. 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

5000-501: The acoustical phenomenon now known as flanging in 1693. Two years later, on 8 July 1695, Huygens died in The Hague and was buried, like his father before him, in an unmarked grave at the Grote Kerk . Huygens never married. Huygens first became internationally known for his work in mathematics, publishing a number of important results that drew the attention of many European geometers. Huygens's preferred method in his published works

5100-449: The areas of hyperbolas, ellipses, and circles that paralleled Archimedes's work on conic sections, particularly his Quadrature of the Parabola . The second part included a refutation to Grégoire de Saint-Vincent's claims on circle quadrature, which he had discussed with Mersenne earlier. Huygens demonstrated that the centre of gravity of a segment of any hyperbola , ellipse , or circle

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5200-437: The areas were not vital, and adding armor to non-vital areas where damage is acceptable reduces 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 armor be placed in the areas which were completely untouched by damage in the bombers who returned. They reasoned that

5300-567: The auspices of the British Association , a symposium was organized in Dundee . In his opening address, Watson-Watt offered a definition of the aims of OR: 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

5400-522: The book is an analysis of pendular motion and a theory of curves . In 1655, Huygens began grinding lenses with his brother Constantijn to build refracting telescopes . He discovered Saturn's biggest moon, Titan, and was the first to explain Saturn's strange appearance as due to "a thin, flat ring, nowhere touching, and inclined to the ecliptic." In 1662 Huygens developed what is now called the Huygenian eyepiece ,

5500-405: The change, 7% were sunk and 11% damaged; if submarines were caught on the surface but had time to submerge just before being attacked, 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), analyzed a report of

5600-475: The concepts of a "fair game" and equitable contract (i.e., equal division when the chances are equal), and extended the argument to set up a non-standard theory of expected values. His success in applying algebra to the realm of chance, which hitherto seemed inaccessible to mathematicians, demonstrated the power of combining Euclidean synthetic proofs with the symbolic reasoning found in the works of Viète and Descartes. Huygens included five challenging problems at

5700-442: 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, or develop

5800-664: The correct laws, including the conservation of the product of mass times the square of the speed for hard bodies, and the conservation of quantity of motion in one direction for all bodies. An important step was his recognition of the Galilean invariance of the problems. Huygens had worked out the laws of collision from 1652 to 1656 in a manuscript entitled De Motu Corporum ex Percussione , though his results took many years to be circulated. In 1661, he passed them on in person to William Brouncker and Christopher Wren in London. What Spinoza wrote to Henry Oldenburg about them in 1666, during

5900-484: 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. Beginning in the 20th century, study of inventory management could be considered the origin of modern operations research with economic order quantity developed by Ford W. Harris in 1913. Operational research may have originated in

6000-527: The efforts of military planners during World War I (convoy theory and Lanchester's laws ). 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. Modern operational research originated at the Bawdsey Research Station in the UK in 1937 as the result of an initiative of the station's superintendent, A. P. Rowe and Robert Watson-Watt . Rowe conceived

6100-466: The end of the book that became the standard test for anyone wishing to display their mathematical skill in games of chance for the next sixty years. People who worked on these problems included Abraham de Moivre , Jacob Bernoulli, Johannes Hudde , Baruch Spinoza , and Leibniz. Huygens had earlier completed a manuscript in the manner of Archimedes's On Floating Bodies entitled De Iis quae Liquido Supernatant ( About parts floating above liquids ). It

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6200-525: The finesse to handle the situation in 1673. The physicist and inventor Denis Papin was an assistant to Huygens from 1671. One of their projects, which did not bear fruit directly, was the gunpowder engine . Huygens made further astronomical observations at the Académie using the observatory recently completed in 1672. He introduced Nicolaas Hartsoeker to French scientists such as Nicolas Malebranche and Giovanni Cassini in 1678. The young diplomat Leibniz met Huygens while visiting Paris in 1672 on

6300-460: The first generalized conception of force prior to Newton. The general idea for the centrifugal force, however, was published in 1673 and was a significant step in studying orbits in astronomy. It enabled the transition from Kepler's third law of planetary motion to the inverse square law of gravitation. Yet, the interpretation of Newton's work on gravitation by Huygens differed from that of Newtonians such as Roger Cotes : he did not insist on

6400-477: The first graph of a continuous distribution function under the assumption of a uniform death rate , and used it to solve problems in joint annuities . Contemporaneously, Huygens, who played the harpsichord , took an interest in Simon Stevin's theories on music; however, he showed very little concern to publish his theories on consonance , some of which were lost for centuries. For his contributions to science,

6500-404: The formula in classical mechanics for the centrifugal force in his work De vi Centrifuga , a decade before Newton . In optics, he is best known for his wave theory of light , which he described in his Traité de la Lumière (1690). His theory of light was initially rejected in favour of Newton's corpuscular theory of light , until Augustin-Jean Fresnel adapted Huygens's principle to give

6600-667: The foundation of national OR societies in Austria, Switzerland and Germany. IFORS held important international conferences every three years since 1957. The constituent members of IFORS form regional groups, such as that in Europe, the Association of European Operational Research Societies (EURO). Other important operational research organizations are Simulation Interoperability Standards Organization (SISO) and Interservice/Industry Training, Simulation and Education Conference (I/ITSEC) In 2004,

6700-494: The idea as a means to analyse and improve the working of the UK's early-warning radar system, code-named " Chain Home " (CH). Initially, Rowe 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

6800-961: The lack of data, there are also no computer applications in the textbooks. Operational research is also used extensively in government where evidence-based policy is used. The field of management science (MS) is known as using operations research models in business. Stafford Beer characterized this in 1967. Like operational research itself, management science 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 sometimes complex decision problems. Management scientists help businesses to achieve their goals using

6900-599: The large volumes of data required for such problems can be stored and manipulated very efficiently." Much of operations research (modernly known as 'analytics') relies upon stochastic variables and a therefore access to truly random numbers. Fortunately, the cybernetics field also required the same level of randomness. The development of increasingly better random number generators has been a boon to both disciplines. Modern applications of operations research includes city planning, football strategies, emergency planning, optimizing all facets of industry and economy, and undoubtedly with

7000-400: The likelihood of the inclusion of terrorist attack planning and definitely counterterrorist attack planning. More recently, the research approach of operations research, which dates back to the 1950s, has been criticized for being collections of mathematical models but lacking an empirical basis of data collection for applications. How to collect data is not presented in the textbooks. Because of

7100-474: 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. 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

7200-413: The mathematics of Thomas Hobbes . Persisting in trying to explain the errors Hobbes had fallen into, he made an international reputation. Huygens's next publication was De Circuli Magnitudine Inventa ( New findings in the measurement of the circle ), published in 1654. In this work, Huygens was able to narrow the gap between the circumscribed and inscribed polygons found in Archimedes's Measurement of

7300-502: The military once scientists learned to apply its principles to the civilian sector. The development of the simplex algorithm for linear programming was in 1947. In the 1950s, the term Operations Research was used to describe heterogeneous mathematical methods such as game theory , dynamic programming, linear programming, warehousing, spare parts theory , queue theory , simulation and production control, which were used primarily in civilian industry. Scientific societies and journals on

7400-472: The most coherent presentation of a mathematical approach to games of chance in De Ratiociniis in Ludo Aleae ( On reasoning in games of chance ). Frans van Schooten translated the original Dutch manuscript into Latin and published it in his Exercitationum Mathematicarum (1657). The work contains early game-theoretic ideas and deals in particular with the problem of points . Huygens took from Pascal

7500-530: 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 conventional dull camouflage paint finish, and

7600-463: The paraboloid by a clever application of Torricelli's principle (i.e., that bodies in a system move only if their centre of gravity descends). He then proves the general theorem that, for a floating body in equilibrium, the distance between its centre of gravity and its submerged portion is at a minimum. Huygens uses this theorem to arrive at original solutions for the stability of floating cones , parallelepipeds , and cylinders , in some cases through

7700-554: The planet Mercury transit over the Sun using Reeve's telescope in London. Streete then debated the published record of Hevelius , a controversy mediated by Henry Oldenburg . Huygens passed to Hevelius a manuscript of Jeremiah Horrocks on the transit of Venus in 1639 , printed for the first time in 1662. In that same year, Sir Robert Moray sent Huygens John Graunt 's life table , and shortly after Huygens and his brother Lodewijk dabbled on life expectancy . Huygens eventually created

7800-437: 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

7900-409: 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 , ordinal priority approach , neural networks , expert systems , decision analysis , and the analytic hierarchy process . Nearly all of these techniques involve

8000-459: The rectification of the ellipse, projectiles, and the vibrating string . Some of Mersenne's concerns at the time, such as the cycloid (he sent Huygens Torricelli 's treatise on the curve), the centre of oscillation , and the gravitational constant , were matters Huygens only took seriously later in the 17th century. Mersenne had also written on musical theory. Huygens preferred meantone temperament ; he innovated in 31 equal temperament (which

8100-421: 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

8200-555: The spread of Operations Research in Western Europe; NATO headquarters (SHAPE) organised four conferences on OR in the 1950s – the one in 1956 with 120 participants – bringing OR to mainland Europe. Within NATO, OR was also known as "Scientific Advisory" (SA) and was grouped together in the Advisory Group of Aeronautical Research and Development (AGARD). SHAPE and AGARD organized an OR conference in April 1957 in Paris. When France withdrew from

8300-662: The subject of operations research were founded in the 1950s, such as the Operation Research Society of America (ORSA) in 1952 and the Institute for Management Science (TIMS) in 1953. Philip Morse, the head of the Weapons Systems Evaluation Group of the Pentagon, became the first president of ORSA and attracted the companies of the military-industrial complex to ORSA, which soon had more than 500 members. In

8400-504: 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. As a result of these findings Coastal Command changed their aircraft to using white undersurfaces. Other work by

8500-519: The survey was biased, since it only included aircraft that returned to Britain. The areas untouched in returning aircraft were probably vital areas, which, if hit, would result in the loss of the aircraft. This story has been disputed, with a similar damage assessment study completed in the US by the Statistical Research Group at Columbia University , the result of work done by Abraham Wald . When Germany organized its air defences into

8600-492: The universe this way made the theory of collisions central to physics, as only explanations that involved matter in motion could be truly intelligible. While Huygens was influenced by the Cartesian approach, he was less doctrinaire. He studied elastic collisions in the 1650s but delayed publication for over a decade. Huygens concluded quite early that Descartes's laws for elastic collisions were largely wrong, and he formulated

8700-492: The void against the Cartesian denial of it. Newton's influence on John Locke was mediated by Huygens, who assured Locke that Newton's mathematics was sound, leading to Locke's acceptance of a corpuscular-mechanical physics. The general approach of the mechanical philosophers was to postulate theories of the kind now called "contact action." Huygens adopted this method but not without seeing its limitations, while Leibniz, his student in Paris, later abandoned it. Understanding

8800-548: The work of Viète , Descartes, and Fermat . After two years, starting in March 1647, Huygens continued his studies at the newly founded Orange College , in Breda , where his father was a curator . Constantijn Huygens was closely involved in the new College, which lasted only to 1669; the rector was André Rivet . Christiaan Huygens lived at the home of the jurist Johann Henryk Dauber while attending college, and had mathematics classes with

8900-507: Was Philip M. Morse , who served a year and a half before returning to MIT in the summer of 1950. From 1957 until 1960 John H. Sides was director of WSEG. Lt. Gen. Harvey T. Alness was director from Sept. 1, 1962 until March 1, 1964. Hugh Everett III worked at the WSEG from 1956 until 1964. Much of his works remains classified. During his time with the WSEG Everett worked on various studies of

9000-464: Was a Dutch mathematician , physicist , engineer , astronomer , and inventor who is regarded as a key figure in the Scientific Revolution . In physics, Huygens made seminal contributions to optics and mechanics , while as an astronomer he studied the rings of Saturn and discovered its largest moon, Titan . As an engineer and inventor, he improved the design of telescopes and invented

9100-594: 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

9200-451: Was a diplomat and advisor to the House of Orange , in addition to being a poet and a musician. He corresponded widely with intellectuals across Europe; his friends included Galileo Galilei , Marin Mersenne , and René Descartes . Christiaan was educated at home until the age of sixteen, and from a young age liked to play with miniatures of mills and other machines. From his father he received

9300-552: Was bittersweet and somewhat puzzling since it became clear that Fermat had dropped out of the research mainstream, and his priority claims could probably not be made good in some cases. Besides, Huygens was looking by then to apply mathematics to physics, while Fermat's concerns ran to purer topics. Like some of his contemporaries, Huygens was often slow to commit his results and discoveries to print, preferring to disseminate his work through letters instead. In his early days, his mentor Frans van Schooten provided technical feedback and

9400-469: Was born on 14 April 1629 in The Hague , into a rich and influential Dutch family, the second son of Constantijn Huygens . Christiaan was named after his paternal grandfather. His mother, Suzanna van Baerle , died shortly after giving birth to Huygens's sister. The couple had five children: Constantijn (1628), Christiaan (1629), Lodewijk (1631), Philips (1632) and Suzanna (1637). Constantijn Huygens

9500-482: Was cautious for the sake of his reputation. Between 1651 and 1657, Huygens published a number of works that showed his talent for mathematics and his mastery of classical and analytical geometry , increasing his reach and reputation among mathematicians. Around the same time, Huygens began to question Descartes's laws of collision , which were largely wrong, deriving the correct laws algebraically and later by way of geometry. He showed that, for any system of bodies,

9600-559: Was covered fully for the first time by Newton in Book II of the Principia Mathematica (1687). In 1678 Leibniz picked out of Huygens's work on collisions the idea of conservation law that Huygens had left implicit. In 1657, inspired by earlier research into pendulums as regulating mechanisms, Huygens invented the pendulum clock, which was a breakthrough in timekeeping and became the most accurate timekeeper for almost 300 years until

9700-408: Was directly related to the area of that segment. He was then able to show the relationships between triangles inscribed in conic sections and the centre of gravity for those sections. By generalizing these theorems to cover all conic sections, Huygens extended classical methods to generate new results. Quadrature was a live issue in the 1650s and, through Mylon, Huygens intervened in the discussion of

9800-507: Was not itself a new idea but known to Francisco de Salinas ), using logarithms to investigate it further and show its close relation to the meantone system. In 1654, Huygens returned to his father's house in The Hague and was able to devote himself entirely to research. The family had another house, not far away at Hofwijck , and he spent time there during the summer. Despite being very active, his scholarly life did not allow him to escape bouts of depression. Subsequently, Huygens developed

9900-533: Was that of Archimedes, though he made use of Descartes's analytic geometry and Fermat's infinitesimal techniques more extensively in his private notebooks. Huygens's first publication was Theoremata de Quadratura Hyperboles, Ellipsis et Circuli ( Theorems on the quadrature of the hyperbola, ellipse, and circle ), published by the Elzeviers in Leiden in 1651. The first part of the work contained theorems for computing

10000-401: Was written around 1650 and was made up of three books. Although he sent the completed work to Frans van Schooten for feedback, in the end Huygens chose not to publish it, and at one point suggested it be burned. Some of the results found here were not rediscovered until the eighteenth and nineteenth centuries. Huygens first re-derives Archimedes's solutions for the stability of the sphere and

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