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Cutting Stock Problem
In operations research, the cutting-stock problem is the problem of cutting standard-sized pieces of Inventory, stock material, such as paper rolls or sheet metal, into pieces of specified sizes while minimizing material wasted. It is an optimization (mathematics), optimization problem in mathematics that arises from applications in industry. In terms of Analysis of algorithms, computational complexity, the problem is an NP-hard problem reducible to the knapsack problem. The problem can be formulated as an integer linear programming problem. Illustration of one-dimensional cutting-stock problem A paper machine can produce an unlimited number of master (jumbo) rolls, each 5600 mm wide. The following 13 items must be cut, in the table below. The important thing about this kind of problem is that many different product units can be made from the same master roll, and the number of possible combinations is itself very large, in general, and not trivial to enumerate. The probl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Operations Research
Operations research () (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a branch of applied mathematics that deals with the development and application of analytical methods to improve management and decision-making. Although the term management science is sometimes used similarly, the two fields differ in their scope and emphasis. Employing techniques from other mathematical sciences, such as mathematical model, modeling, statistics, and mathematical optimization, 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 is often concerned with determining the extreme values of some real-world objective: the Maxima and minima, maximum (of profit, performance, or yield) or minimum (of loss, risk, or cost). Originating in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Letter (paper Size)
Letter (officially ANSI A) is a paper size standard defined in ANSI/ASME Y14.1 by the American National Standards Institute, commonly used as home or office stationery primarily in the United States, Canada, and the Philippines, and variably across Latin America."US Letter" is the primary paper size used in Belize, Canada, Chile, Colombia, Costa Rica, El Salvador, Guatemala, Mexico, Nicaragua, Panama, Philippines, Puerto Rico, United States, Venezuela according to It measures and is similar in use to the A4 paper standard at used by most other countries, defined in ISO 216 by the International Organization for Standardization. Details The Reagan administration made Letter-size paper the norm for US federal forms in the early 1980s; previously, the smaller "official" Government Letter size, (aspect ratio: 1.3125), was used in government, while paper was standard in most other offices. The aspect ratio is ≈ 1.294 and the diagonal is ≈ in length. In the US, paper den ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Linear Program
Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements and objective are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization). More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints. Its feasible region is a convex polytope, which is a set defined as the intersection of finitely many half spaces, each of which is defined by a linear inequality. Its objective function is a real-valued affine (linear) function defined on this polytope. A linear programming algorithm finds a point in the polytope where this function has the largest (or smallest) value if such a point exists. Linear programs are problems that can be expressed in standard form as: : \beg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Delayed Column-generation
Column generation or delayed column generation is an efficient algorithm for solving large linear programs. The overarching idea is that many linear programs are too large to consider all the variables explicitly. The idea is thus to start by solving the considered program with only a subset of its variables. Then iteratively, variables that have the potential to improve the objective function are added to the program. Once it is possible to demonstrate that adding new variables would no longer improve the value of the objective function, the procedure stops. The hope when applying a column generation algorithm is that only a very small fraction of the variables will be generated. This hope is supported by the fact that in the optimal solution, most variables will be non-basic and assume a value of zero, so the optimal solution can be found without them. In many cases, this method allows to solve large linear programs that would otherwise be intractable. The classical example of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Bin Packing Problem
The bin packing problem is an optimization problem, in which items of different sizes must be packed into a finite number of bins or containers, each of a fixed given capacity, in a way that minimizes the number of bins used. The problem has many applications, such as filling up containers, loading trucks with weight capacity constraints, creating file backups in media, splitting a network prefix into multiple subnets, and technology mapping in FPGA semiconductor chip design. Computationally, the problem is NP-hard, and the corresponding decision problem, deciding if items can fit into a specified number of bins, is NP-complete. Despite its worst-case hardness, optimal solutions to very large instances of the problem can be produced with sophisticated algorithms. In addition, many approximation algorithms exist. For example, the first fit algorithm provides a fast but often non-optimal solution, involving placing each item into the first bin in which it will fit. It requires ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Zalgaller
Victor (Viktor) Abramovich Zalgaller (; ; 25 December 1920 – 2 October 2020) was a Russian-Israeli mathematician in the fields of geometry and optimization. He is best known for the results he achieved on convex polyhedra, linear and dynamic programming, isoperimetry, and differential geometry. Biography Zalgaller was born in Parfino, Novgorod Governorate on 25 December 1920. In 1936, he was one of the winners of the Leningrad Mathematics Olympiads for high school students. He started his studies at the Leningrad State University, however, World War II intervened in 1941, and Zalgaller joined the Red Army. He took part in the defence of Leningrad, and in 1945 marched into Germany. He worked as a teacher at the Saint Petersburg Lyceum 239, and received his 1963 doctoral dissertation on polyhedra with the aid of his high school students who wrote the computer programs for the calculation. Zalgaller did his early work under direction of Aleksandr Aleksandrov and Leonid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Kantorovich
Leonid Vitalyevich Kantorovich (, ; 19 January 19127 April 1986) was a Soviet mathematician and economist, known for his theory and development of techniques for the optimal allocation of resources. He is regarded as the founder of linear programming. He was the winner of the USSR State Prize, Stalin Prize in 1949 and the Nobel Memorial Prize in Economic Sciences in 1975. Biography Kantorovich was born on 19 January 1912, to a History of the Jews in Russia, Russian Jewish family. His father was a doctor practicing in Saint Petersburg. In 1926, at the age of fourteen, he began his studies at Saint Petersburg State University, Leningrad State University. He graduated from the Faculty of Mathematics and Mechanics in 1930, and began his graduate studies. In 1934, at the age of 22 years, he became a full professor. In 1935 he received his doctoral degree. Later, Kantorovich worked for the Government of the Soviet Union, Soviet government. He was given the task of Mathematical optimiz ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Guillotine Problem
Guillotine cutting is the process of producing small rectangular items of fixed dimensions from a given large rectangular sheet, using only guillotine-cuts. A guillotine-cut (also called an edge-to-edge cut) is a straight bisecting line going from one edge of an existing rectangle to the opposite edge, similarly to a paper guillotine. Guillotine cutting is particularly common in the glass industry. Glass sheets are scored along horizontal and vertical lines, and then broken along these lines to obtain smaller panels. It is also useful for cutting steel plates, cutting of wood sheets to make furniture, and cutting of cardboard into boxes. There are various optimization problems related to guillotine cutting, such as: maximize the total area of the produced pieces, or their total value; minimize the amount of waste (unused parts) of the large sheet, or the total number of sheets. They have been studied in combinatorial geometry, operations research and industrial engineering. A re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Corrugated Fiberboard
Corrugated fiberboard, corrugated cardboard, or corrugated is a type of packaging material consisting of a fluted corrugated sheet and one or two flat linerboards. It is made on "flute lamination machines" or "corrugators" and is used for making corrugated boxes. The corrugated medium sheet and the linerboard(s) are made of kraft containerboard, a paperboard material usually over thick. History Corrugated (also called pleated) paper was patented in England in 1856, and used as a liner for tall hats, but corrugated boxboard was not patented and used as a shipping material until 20 December 1871. The patent was issued to Albert Jones of New York City for single-sided (single-face) corrugated board. Jones used the corrugated board for wrapping bottles and glass lantern chimneys. The first machine for producing large quantities of corrugated board was built in 1874 by G. Smyth, and in the same year Oliver Long improved upon Jones' design by inventing corrugated board with lin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Tyvek
Tyvek () is a brand of synthetic flashspun high-density polyethylene fibers. The name ''Tyvek'' is a registered trademark of the American multinational chemical company DuPont, which discovered and commercialized Tyvek in the late 1950s and early 1960s. Tyvek's properties—such as being difficult to tear but easily cut, and waterproof against liquids while allowing water vapor to penetrate—have led to it being used in a variety of applications. Tyvek is often used as housewrap, a synthetic material used to protect buildings during construction, or as personal protective equipment (PPE). History Tyvek is a nonwoven product consisting of spun bond olefin fiber. It was first discovered in 1955 by a researcher for the DuPont textile company working in an experimental lab, who noticed a type of white fluff coming out of a pipe. That fluff was a form of polyethylene, which DuPont requested a patent for within a year of the discovery. After technologies improved during the next ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |