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Reduced Cost
In linear programming, reduced cost, or opportunity cost, is the amount by which an objective function coefficient would have to improve (so increase for maximization problem, decrease for minimization problem) before it would be possible for a corresponding variable to assume a positive value in the optimal solution. It is the cost for increasing a variable by a small amount, i.e., the first derivative from a certain point on the polyhedron that constrains the problem. When the point is a vertex in the polyhedron, the variable with the most extreme cost, negatively for minimization and positively maximization, is sometimes referred to as the steepest edge. Given a system minimize \mathbf^T\mathbf subject to \mathbf\leq\mathbf, \mathbf\geq 0, the reduced cost vector can be computed as \mathbf - \mathbf^T \mathbf, where \mathbf is the dual cost vector. It follows directly that for a minimization problem, any non- basic variables at their lower bounds with strictly negative reduce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Programming
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 function#As a polynomial function, 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 mathematical optimization, optimization of a linear objective function, subject to linear equality and linear inequality Constraint (mathematics), constraints. Its feasible region is a convex polytope, which is a set defined as the intersection (mathematics), intersection of finitely many Half-space (geometry), half spaces, each of which is defined by a linear inequality. Its objective function is a real number, real-valued affine function, affine (linear) function defined on this polytope. A linear programming algorithm finds a point in the po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Opportunity Cost
In microeconomic theory, the opportunity cost of a choice is the value of the best alternative forgone where, given limited resources, a choice needs to be made between several mutually exclusive alternatives. Assuming the best choice is made, it is the "cost" incurred by not enjoying the ''benefit'' that would have been had if the second best available choice had been taken instead. The '' New Oxford American Dictionary'' defines it as "the loss of potential gain from other alternatives when one alternative is chosen". As a representation of the relationship between scarcity and choice, the objective of opportunity cost is to ensure efficient use of scarce resources. It incorporates all associated costs of a decision, both explicit and implicit. Thus, opportunity costs are not restricted to monetary or financial costs: the real cost of output forgone, lost time, pleasure, or any other benefit that provides utility should also be considered an opportunity cost. Types Expl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Objective Function
In mathematical optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cost" associated with the event. An optimization problem seeks to minimize a loss function. An objective function is either a loss function or its opposite (in specific domains, variously called a reward function, a profit function, a utility function, a fitness function, etc.), in which case it is to be maximized. The loss function could include terms from several levels of the hierarchy. In statistics, typically a loss function is used for parameter estimation, and the event in question is some function of the difference between estimated and true values for an instance of data. The concept, as old as Laplace, was reintroduced in statistics by Abraham Wald in the middle of the 20th century. In the context of economics, for example, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polyhedron
In geometry, a polyhedron (: polyhedra or polyhedrons; ) is a three-dimensional figure with flat polygonal Face (geometry), faces, straight Edge (geometry), edges and sharp corners or Vertex (geometry), vertices. The term "polyhedron" may refer either to a solid figure or to its boundary surface (mathematics), surface. The terms solid polyhedron and polyhedral surface are commonly used to distinguish the two concepts. Also, the term ''polyhedron'' is often used to refer implicitly to the whole structure (mathematics), structure formed by a solid polyhedron, its polyhedral surface, its faces, its edges, and its vertices. There are many definitions of polyhedron. Nevertheless, the polyhedron is typically understood as a generalization of a two-dimensional polygon and a three-dimensional specialization of a polytope, a more general concept in any number of dimensions. Polyhedra have several general characteristics that include the number of faces, topological classification by Eule ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Basic Variable
Basic or BASIC may refer to: Science and technology * BASIC, a computer programming language * Basic (chemistry), having the properties of a base * Basic access authentication, in HTTP Entertainment * ''Basic'' (film), a 2003 film * Basic, one of the languages in ''Star Wars'' Music * ''Basic'' (Glen Campbell album), 1978 * ''Basic'' (Robert Quine and Fred Maher album), 1984 * ''B.A.S.I.C.'' (Alpinestars album), 2000 * ''Basic'' (Brown Eyed Girls album), 2015 * ''B.A.S.I.C.'' (The Basics album), 2019 Places * Basic, Mississippi, a community in the US * BASIC countries, Brazil, South Africa, India and China in climate change negotiations Organizations * BASIC Bank Limited, government owned bank in Bangladesh * Basic Books, an American publisher Other uses * Basic (cigarette), a brand of cigarettes manufactured by the Altria Group (Philip Morris Company) * Basic (dance move), the dance move that defines the character of a particular dance * Basic (slang), a pejorative te ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pivot Strategy
Pivot may refer to: *Pivot, the point of rotation in a lever system *More generally, the center point of any rotational system *Pivot joint, a kind of joint between bones in the body *Pivot turn, a dance move Companies *Incitec Pivot, an Australian chemicals and explosives manufacturer *Pivot Legal Society, a legal advocacy organization based in Vancouver, British Columbia *Pivot Wireless, a cell phone service, created by a joint venture between Sprint and multiple cable companies Computing *Apache Pivot, an open-source platform for building applications in Java *Microsoft Live Labs Pivot, a data search application *Morrow Pivot and Morrow Pivot II, early laptop computers *Pivot, an element of the quicksort algorithm *Pivot display, a display which can change orientation * Pivot Stickfigure Animator, stick-figure animation software *Pivot table, a data summarization tool in spreadsheets *Pivotal Games, a former UK video game developer *Pivoting, a computer security exploit used ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Devex Algorithm
In applied mathematics, the devex algorithm is a pivot rule for the simplex method developed by Paula M. J. Harris. It identifies the steepest-edge approximately in its search for the optimal solution.Forrest, John J., and Donald Goldfarb Donald Goldfarb (born August 14, 1941 in New York City) is an American mathematician, best known for his works in mathematical optimization and numerical analysis. Biography Goldfarb studied Chemical Engineering at Cornell University, earning a B ....Steepest-edge simplex algorithms for linear programming" Mathematical programming 57.1–3 (1992): 341–374. References Algorithms {{algorithm-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Programming
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 function#As a polynomial function, 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 mathematical optimization, optimization of a linear objective function, subject to linear equality and linear inequality Constraint (mathematics), constraints. Its feasible region is a convex polytope, which is a set defined as the intersection (mathematics), intersection of finitely many Half-space (geometry), half spaces, each of which is defined by a linear inequality. Its objective function is a real number, real-valued affine function, affine (linear) function defined on this polytope. A linear programming algorithm finds a point in the po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shadow Price
A shadow price is the monetary value assigned to an abstract or intangible commodity which is not traded in the marketplace. This often takes the form of an externality. Shadow prices are also known as the recalculation of known market prices in order to account for the presence of distortionary market instruments (e.g. quotas, tariffs, taxes or subsidies). Shadow prices are the real economic prices given to goods and services after they have been appropriately adjusted by removing distortionary market instruments and incorporating the societal impact of the respective good or service. A shadow price is often calculated based on a group of assumptions and estimates because it lacks reliable data, so it is subjective and somewhat inaccurate. The need for shadow prices arises as a result of “externalities” and the presence of distortionary market instruments. An externality is defined as a cost or benefit incurred by a third party as a result of production or consumption of a g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
