Operations Research
As early as the 17th century, scientists began solving complex, real-world problems using mathematics. This led to the development of operations research (OR). It is impossible to imagine almost any branch of industry without these methods in today’s world, because many business processes can be traced back to fundamental mathematical problems that are solved with OR.
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Charles Babbage
In the mid-19th century, the Englishman Charles Babbage, best known today for inventing the forerunner of modern computers, conducted a study on transport costs and letter-sorting for the postal service. He then used mathematics to model a delivery network that showed that, given sufficient mail volume, the distance a letter travels is irrelevant to transport costs. His research led to the introduction of the nationwide Penny Post in 1840, in which each letter delivery cost only one penny. This is now considered the first practical application of OR. But as early as the 17th and 18th centuries, mathematicians, including Leibniz and Newton, were working on calculating problems involving complex decision-making. And the French mathematician Jean Baptiste Joseph Fourier outlined the first methods of linear programming as early as 1827.
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The Four-Colour Problem
If you want to color a political map in such a way that the borders between neighboring countries are easy to recognize, you need different colors for countries that share a border. How many different colors are needed to solve this problem for each map? This question has occupied mathematicians since 1852 and is therefore considered the oldest OR problem. Today, we know that four colors are enough for each map on the globe. However, it took more than a century, or, until computers were used, to solve the four-color problem. And up until today, the four-color theorem has not been proven without a computer.
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Operations research
The origin of the term "operations research" dates back to 1937. It was created by the English to designate a group of scientists who researched the possible applications for radar on behalf of the military. By 1940, the field of application and research groups were expanded. In the Air Ministry as well as in the Navy and the Army, researchers were concerned not only with radar but also with the development of optimal strategies in air combat and anti-submarine warfare.
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The Postman's Problem
In order to distribute mail, letter carriers must walk each side of the street once, especially if the street is wide. In order to reach other areas of the delivery zone, they may have to walk streets that have already been serviced without distributing any mail. This increases the distance they have to cover to do the job. The best solution, however, is an optimized round trip that lays out the minimum route length but includes all streets at least once. OR algorithms solve this problem too. Today, solutions for the letter-carrier problem are used in the planning of garbage disposal, street cleaning, or maintenance trips. The same applies to the planning of a round trip for collecting goods in a high-bay warehouse.
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Leonid Kantorovich
Kantorovich is considered the founder of mathematical optimization and was awarded the Nobel Prize in Economic Sciences in 1975. In a study of the organization and planning of production processes in 1939, he showed that many of the problems arising in this field could be formulated mathematically. When asked to optimize production in a veneer wood factory, he developed the method of linear programming. It is still one of the foundations of OR. .
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The Traveling Salesman Problem
How is it possible to organize a business trip with several stops in such a way that no stop except the first is visited more than once, the total travel distance is as short as possible, and the first stop is the same as the last stop? When planning a tour through the 15 largest cities in Germany, 43,589,145,600 possibilities can be calculated. With OR, the optimal route can be determined with mathematical precision from this almost infinite number of possibilities. This classic OR scenario was first mentioned in 1930 and occurs in route planning and goods distribution. It is also known in production planning as the "sequence problem." The question that is asked is what should be done where and when.
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George B. Dantzig
US mathematician George B. Dantzig developed the first algorithm for solving linear optimization problems in 1947. His simplex method is still considered a standard method today and has been expanded on many times. One of the first applications of the new algorithm was in the military for the diet problem. The goal was to produce a low-cost diet for soldiers that contained a certain minimum and maximum number of vitamins and other ingredients. At the time, nine people worked to find an optimal solution, which working together required about 120 person-days of computational work.
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The Backpack Problem
How many items of a given value fit into a backpack that has a weight constraint such that the backpack is optimally utilized? This isn’t a problem just for thieves who can only carry a small amount of a haul but want to walk away with the biggest profit. In many cases, only a limited capacity is available that cannot satisfy the entire demand. For example, freight forwarders have only a limited amount of cargo space available in their trucks to transport various goods at maximum profit. OR can also be used to determine a solution to this problem with mathematical precision.
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Academic Teaching
In 1948, operations research was first added as an academic discipline at the Massachusetts Institute of Technology in Cambridge, Massachusetts, in the US. The first course in this new discipline was held there and dealt exclusively with economics rather than military applications. A master's and doctoral degree in OR could be obtained for the first time in 1952 at the Case Institute of Technology in Cleveland, Ohio. In 1975, the first continental European degree program was established at RWTH Aachen University, which later became the Chair of Corporate Research. Holder of the chair was INFORM founder Prof. Dr. Dres, Hans-Jürgen Zimmermann.
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The Cutting Stock Problem
Whether pipes, wood, or textiles, as little waste as possible should be produced when cutting raw materials to size. This problem also arises when loading a cargo hold or a container. In these cases, it is important to waste as little free space as possible. Even in this application, operations research helps to calculate the best possible solution.
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INFORM GmbH
In 1969, Prof. Hans-Jürgen Zimmermann founded INFORM GmbH with the goal of proving that mathematical optimization is not just a mental game. Rather, he wanted to show that companies can use pure calculations to optimize their processes and thus save a lot of money. INFORM was one of the first companies to offer optimization solutions based on OR and to apply the methods to economic processes with the help of software systems.
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The Waiting Line Problem
From the supermarket checkout and ATM to the ticket counter, everyone has been in one and no one likes them - the waiting line. While a few minutes of waiting in private life may seem tolerable, in business, these minutes can have major consequences. If trucks carrying production materials cannot be unloaded on time at a plant’s loading dock, horrendous demurrage charges are incurred. And when airplanes are not cleared on time because other planes are first in line, costs increase, and so does passenger dissatisfaction. The adequate and efficient design of such systems using OR therefore has a significant effect on the quality of life and productivity.
FUTURE
Capabilities
Since the 1990s, the speed of algorithms has increased by a factor of more than 1.5 million in terms of the computational time that was and is required to solve large OR problems. In this same period of time, the speed of hardware has increased by a factor of only 2,000. Problems that could take up to 100 years to compute in 1990 can now be solved within seconds. This means that what was more of a theoretical concept 30 years ago can now be applied in everyday life, especially in the optimization of complex business processes. As a result, OR has found its way into almost all areas of industry and business. When combined with AI methods such as machine learning, the power of OR will become even greater.