Operations research

Experiment design, according to Doehlert's method.

Operations research, also called operations research, is a discipline that deals with the application of advanced analytical methods to help make better decisions. It is also known as administrative science, being part of the administrative discipline. The origin of modern OR is located in the 2nd World War and on the allied side. Possibly he contributed greatly to their winning the war. In fact, some of the discoveries of those years (Wald's sequential quality control) remained a military secret until several years after the end of the war. Armies are complex organizations with complex problems of coordination and logistics, of production and distribution of weapons, of quarters, of advance strategies and deployment of troops. The allied command brought together scientists from various areas (mathematicians, physicists, engineers, statisticians, economists, among others) to address these complex problems. IO's name comes from that war objective: to investigate (military) operations.

Often considered to be a subfield of applied mathematics. The terms management science and decision theory are sometimes used interchangeably.

Using techniques from other mathematical sciences, such as mathematical modelling, statistical analysis, and 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 overlaps with other disciplines, particularly industrial engineering and production management, and draws on psychology and science. organization science. Operations research is often concerned with determining the extreme values of some real-world objective: the maximums (of gain, return, or profitability) or minimums (of loss, risk, or cost). Originating in military efforts prior to World War II, its techniques have grown to address problems in a variety of industries.

Overview

Operations Research (OR) encompasses a wide range of problem-solving techniques and methods applied to improve decision-making and efficiency, such as simulation, optimization, queuing theory, and other models of stochastic processes, Markov decision process, econometric methods, data envelopment analysis, neural networks, expert systems, decision analysis, and hierarchical analytic processes. Almost all of these techniques involve building mathematical models that attempt to describe the system. Due to the computational and statistical nature of most of these fields, it also has strong ties to computer science and analytics. Operations researchers faced with a new problem must determine which of these techniques is most appropriate, given the nature of the system, improvement goals, and time and computational constraints.^{[citation required ]}

The major subdisciplines in modern operations research, as identified by the journal Operations Research, are:

• IT and IT technologies;
• Financial engineering;
• manufacturing, service science and supply chain management;
• public sector policy and work model;
• income management;
• simulation;
• stochastic models;
• transport.

History

In the decades after the two world wars, operations research tools were applied more widely to problems in business, industry, and society. Since then, operations research has expanded into a field widely used in industries ranging from petrochemicals to airlines, finance, logistics, and government, focusing on the development of mathematical models that can be used to analyze and optimize complex systems, and has become an area of active academic and industrial research.

Historical origins

In the 17th century, mathematicians such as Christiaan Huygens and Blaise Pascal (addressing the problem of interrupted game ) attempted to solve questions related to complex decisions by using the calculus of probability. Other mathematicians of the 18th and 19th centuries solved this type of problem using combinatorics. Charles Babbage's research into the cost of transportation and mail sorting led to the universal "Penny Post" of England in 1840, and in studies on the dynamic behavior of railway vehicles in defense of the GWR track gauge. From the century XX, the study of inventory management could be considered the origin of modern operations research with the concept of economic order quantity developed by Ford W. Harris in 1913. Operations research may have originated from efforts of military planners during the First World War (convoy theory and Lanchester's Laws). Percy Williams Bridgman brought operations research to problems in physics in the 1920s and would later try to extend it to the social sciences.

Modern operations research originated at the Bawdsey Research Establishment in the UK in 1937 and was the result of an initiative by the establishment's superintendent, A. P. Rowe, who conceived the idea as a means of analyzing and improving performance of the UK Radar Early Warning Radar System and its network of facilities (Chain Home (CH)). Initially, he analyzed the performance of radar equipment and its communication networks, later expanding to include the behavior of operating personnel. This revealed unappreciated limitations of the CH network and allowed corrective action to be taken.

Scientists in the UK, including Patrick Blackett, Cecil Gordon, Solly Zuckerman, C. H. Waddington, Owen Wansbrough-Jones, Frank Yates, Jacob Bronowski and Freeman Dyson, and in the US with George Dantzig searched for ways to make better decisions in areas such as logistics and training schedules.

World War II

The modern field of operations research arose during World War II. In this period, operations research was defined as "a scientific method of providing executive departments with a quantitative basis for decision-making about the operations under their control". The activity was also known as operational analysis. (UK Ministry of Defense since 1962) and quantitative management.

During World War II, nearly 1,000 men and women were involved in operations research in Britain, and around 200 scientists worked in this field for the British Army.

Patrick Maynard Stuart Blackett worked for several different organizations during the war. Early in the conflict, while working for the Royal Aircraft Establishment (RAE), he created a team known as the 'Circus', which helped reduce the number of air defense rounds required 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.

A Liberator with the standard camouflage of the dark/black RAF night bombers as originally used by the Costas Command

In 1941, Blackett moved from the SAR to the Navy, having worked first with RAF Coastal Command in 1941 and then in early 1942 with the British Admiralty. Blackett's team in the Operational Research Section of the Coastal Command (CC-ORS) included two future Nobel Prize winners and many others who went on to be leading figures in their fields. They carried out a series of crucial analyzes that contributed to the war effort. Britain introduced the convoy system to reduce freighter losses, but while the principle of using warships to accompany merchant ships was accepted, it was not clear whether small or large convoys were better. Convoys travel at the speed of the slower member, so small convoys can travel faster. It was also argued that German U-Boats would be more difficult for small convoys to detect. On the other hand, large convoys could deploy more warships against an attacker. Blackett's staff demonstrated that the losses suffered by the convoys depended largely on the number of escort vessels present, rather than the size of the convoy. His conclusion was that some large convoys are more defensible than many small ones.

When conducting an analysis of the methods used by the RAF Coastal Command to hunt down and destroy submarines, one of the analysts asked what color the planes were. Since most of them were from Bomber Command, they were painted black for night operations. At the suggestion of CC-ORS a test was conducted to see if that was the best color to camouflage the aircraft for daytime operations in the gray skies of the North Atlantic. The tests showed that, on average, planes painted white were not seen until they were 20% closer than those painted black. This change indicated that 30% more U-boats would be attacked and sunk with the same number of sightings. As a result of these findings, Coastal Command changed their aircraft to use white undersides.

Other work done by the CC-ORS indicated that, on average, if the firing depth of depth charges were changed from 100 feet to 25 feet, hit rates would go up. The reason was that if a U-boat saw an aircraft shortly before it reached the target, the charges would do no damage by exploding at 100 feet (because the U-boat would not have had time to descend to that depth) and if it saw the aircraft from well away from the target, it had time to alter its course underwater, so the chances of it being within the 20-foot impact zone of the charges were small. It was more efficient to attack submarines near the surface when the location of the targets was better known than to try to destroy them at greater depths when their positions could only be guessed at. Before the configuration change from 100ft to 25ft, 1% of submerged submarines sank and 14% were damaged. After the change, 7% were sunk and 11% damaged (if subs captured on the surface are counted, even if they were attacked shortly after submerging, the numbers increased to 11% sunk and 15% damaged). Blackett observed that "there can be few cases where so large an operating gain has been realized from so small and simple a change in tactics".

Map of the Kammhuber Line

The Bombing Command Operational Research Section (BC-ORS) reviewed a report from a survey carried out by RAF Bombing Command. For the survey, he inspected all bombers returning from missions over Germany during a particular period. All the damage caused by the German anti-aircraft defense was noted and it was recommended that armor be added in the most damaged areas. This recommendation was not adopted because the fact that the aircraft returned with these damaged areas indicated that these areas were not vital, and adding armor to non-vital areas where damage is acceptable negatively impacts aircraft performance. His suggestion to cut some crew members so that the loss of an aircraft would result in fewer personnel losses was also rejected. Blackett's team made the logical recommendation to place the armor in the areas that were completely untouched by the damage in the returning bombers. They reasoned that the data collection was biased as it only included aircraft that returned to Britain. The intact areas of the returning aircraft were likely the vital points which, if damaged, would result in the loss of the aircraft. A similar story is cited about a similar damage assessment study completed in the United States by the Columbia University Statistical Research Group, and was the result of work done by Abraham Wald.

When Germany organized its air defenses on the Kammhuber Line, the British realized that if RAF bombers flew in a tight linear formation they could overwhelm German night fighters flying individually, aimed at their targets by the ground controllers. It was then a matter of statistically calculating the losses caused by collisions between the bombers versus the losses caused by night fighters to determine the separation at which the bombers should fly to minimize RAF losses.

The ratio of the rate of change of output to input was a hallmark of operations research. By comparing the number of flight hours of Allied aircraft to the number of submarine sightings in a given area, it was possible to redeploy the aircraft to more productive patrol areas. The comparison of these rates allowed us to establish "effectiveness ratios" useful in planning. The ratio of 60 sea mines laid per ship sunk was common to several campaigns: German mines in British ports, British mines in German routes, and US mines in Japanese routes.

Operational research doubled the hit rate of bombing attacks on intended targets by Boeing B-29 Superfortresses attacking Japan from the Mariana Islands by increasing the training ratio from 4 to 10 percent of flight hours; revealed that wolf packs from three US submarines were the most effective number; showed that glossy enamel paint was a more effective camouflage for night fighters than the traditional dull camouflage paint finish, and that the smooth paint finish increased aircraft speed by reducing airframe drag..

On land, operational research sections of the Ministry of Supply (MoS) Army Operations Research Group (AORG) were deployed to the Battle of Normandy in 1944, and followed British forces in the advance towards the center of Europe. They discussed, among other topics, the effectiveness of artillery, aerial bombardments, and anti-tank fire.

After World War II

With expanded techniques and increased awareness of the field at the end of the war, operational research was no longer limited to just tactics, but expanded to encompass equipment acquisition, training, logistics, and security. infrastructure. Operations research also grew in many other areas besides the military once scientists learned to apply its principles to the civilian sector. With the development of the simplex algorithm for linear programming in 1947 and the development of computers in the next three decades."

Issues Addressed

• Critical route method or project planning: identification of processes that affect the overall duration of a complex project
• Floorplanning: design of a factory equipment or components of an integrated circuit to reduce manufacturing time (so reduce cost)
• Network optimization: for example, the configuration of telecommunications networks or the energy system to maintain service quality during service interruptions
• Allocation problems
• Location of facilities
• Assignment problems:
  • Assignment problem
  • Generalized allocation problem
  • Problem of quadratic allocation
  • Target mapping problem
• Bayesiana search theory: search for targets
• Optimized search
• Encamination, how to determine bus routes so that as many buses as possible are needed
• Supply Chain Management: Management of the flow of raw materials and products according to the uncertain demand of finished products
• Project production activities: management of the flow of work activities in a capital project in response to system variability through operations research tools for reducing variability and allocation of buffers using a combination of capacity assignment, inventory and time
• Efficient messages and customer response tactics
• Industrial automation or integration of robotic systems into human-driven operations processes
• Globalization: operations globalization processes to take advantage of materials, labour, land or other cleaner productivity inputs
• Transport: management of transport and delivery systems freight (Examples: LTL shipping, intermodal transport, traveler's problem)
• Planning:
  • Staff organization
  • Manufacturing steps
  • Project management
  • Network data traffic: these are known as queue theory or queue systems
  • Sports events and their television coverage
• Mixing of raw materials in oil refineries
• Optimal pricing determination, in many retail and B2B configurations, within pricing science disciplines
• Value Cutting Problem: Cutting Small Items from Larger Sizes

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

Management Science

In 1967, Stafford Beer characterized the field of management science as "the business use of operations research". The term management science can also be used to refer to the separate fields of organizational studies or business strategy. Management science is an interdisciplinary branch of applied mathematics devoted to optimal decision planning, with strong links to economics, business, engineering, and other sciences. It uses various research-based principles, strategies, and analytical techniques, including mathematical modelling, statistics, and numerical analysis, to improve an organization's ability to make rational and meaningful management decisions in arriving at optimal or near-optimal solutions to complex problems. decision. Management scientists help companies achieve their goals using the scientific methods of operations research.

The management scientist's mandate is to use rational, systematic, and science-based techniques to inform and improve decisions of all kinds. Of course, management science techniques are not limited to commercial applications, but can be applied to the military, medical, public administration, charitable groups, political groups, or communities.

Management science is concerned with the development and application of models and concepts that can be useful in helping to illuminate management problems and solve management problems, as well as in designing and developing new and improved models. of organizational excellence.

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

Related fields

Some of the fields that have considerable overlap with Operations Research and Management Science include:

Applications

Applications are plentiful, such as in airlines, manufacturing companies, service club, military branches and government. The range of problems and problems to which he has contributed ideas and solutions is very wide. Includes:

• Programming (of airlines, trains, buses, etc.)
• Allocation (assignment of personnel to flights, trains or buses; employees to projects; commitment and dispatch of power generation facilities)
• Installation location (deciding the most suitable location for new facilities such as warehouse, factory or fire station)
• Hydraulic and pipe engineering (water flow management of reservoirs)
• Health services (information and supply chain management).
• Theory of games (identification, understanding, development of strategies adopted by companies)
• Urban design
• Computer network engineering (package routing; temporization; analysis)
• Telecommunications engineering and data communication (package routing; time; analysis)

Management is also concerned about the so-called 'soft operational analysis' which refers to methods for strategic planning, decision support systems, and problem structuring methods.

When dealing with these types of challenges, mathematical modeling and simulation may not be appropriate or may not be sufficient. Therefore, since the 1990s several non-quantified modeling methods have been developed. These include:

• Approaches based on stakeholders, including metagame analysis and drama theory
• Morphological analysis and various forms of influence diagrams
• Cognitive Correspondence
• Strategic choice
• Robust analysis

Societies and magazines

Society

The International Federation of Operational Research Societies (IFORS) is an umbrella organization for operations research societies worldwide, representing approximately 50 national societies, including those in the United States United Kingdom (Operational Research Society), France, Germany, Italy (Italian Operations Research Society), Canada, Australia, New Zealand, the Philippines, India, Japan, and South Africa IFORS constituent members form regional groups, such as Europe, Association of European Operational Research Societies (EURO). Other important operations research organizations include the Simulation Interoperability Standards Organization (SISO) and the Interservice/Industry Training, Simulation and Education Conference (I/ITSEC).

In 2004, the United States-based organization INFORMS began an initiative to better market the practice of operations research practitioners, including a website titled "The Science of Better" which provides an introduction to operations research and examples of its successful application to industrial problems. This initiative has been taken up by the Operational Research Society in the UK, including a website entitled "Learn about OR.

INFORMS magazines

The Institute for Operations Research and the Management Sciences (INFORMS) publishes thirteen academic journals on operations research, including the two largest journals of their kind, according to the 2005 Journal Citation Reports:

• Decision analysis
• Research of information systems
• INFORMS Journal on Computing
• INFORMS Transactions on Education(an open access journal)
• Interfaces
• Management Science
• Manufacturing " Service Operations Management "
• Marketing Science
• Mathematics of Operations Research
• Operations Research
• Science of the Organization
• Service Science
• Transportation Science

Other magazines

Listed in alphabetical order of their titles:

• 4OR-A Quarterly Journal of Operations Research (A quarterly business research journal): joint publication of the Operations Research Societies of Belgium, France and Italy (Springer);
• Decision Sciences: published by Wiley-Blackwell on the commission of the Sciences Institute Decision;
• European Journal of Operational Research (European Journal of Operational Research) (EJOR): founded in 1975, it is with much the world's largest operational research magazine, with about 9000 pages of articles published per year. In 2004, its total number of appointments was the second largest among operational research journals and management sciences;
• 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 Defence Modeling and Simulation (JDMS): Applications, Methodology, Technology (Review of Defense Modeling and Simulation: Applications, Methodology, Technology).: a quarterly publication dedicated to the advancement of modelling science and simulation in terms of the military and the defense;
• Journal of the Operational Research Society: The OR Society's official journal; it is the world's oldest publication on IO that continues to be active, published by Taylor and Francis;
• Military Operations Research (Investigation of Military Operations) (MOR): published by Military Operations Research Society;
• Omega - The International Journal of Management Science (The International Journal of Management Sciences);
• Operations Research Letters;
• Opsearch: official journal of the Operational Research Society of India;
• OR Insight: a quarterly magazine of The OR Society, published by Palgrave;
• Production and Operations Management: official journal of the Production and Operations Management Society
• TOP: official journal of the Spanish Society of IO.

Further reading

Classic books and articles