2021년 2월 17일 (수) 07:56에 Pythagoras0님의 편집

2021-02-17T07:56:24Z

Pythagoras0: /* 메타데이터 */ 새 문단

2020-12-26T12:11:57Z

메타데이터: 새 문단

Pythagoras0: /* 노트 */ 새 문단

2020-12-21T14:56:24Z

노트: 새 문단

새 문서

== 노트 ==

===위키데이터===
* ID : [https://www.wikidata.org/wiki/Q202843 Q202843]
===말뭉치===
# Linear programming, mathematical modeling technique in which a linear function is maximized or minimized when subjected to various constraints.<ref name="ref_cbdf84c9">[https://www.britannica.com/science/linear-programming-mathematics linear programming | Definition & Facts]</ref>
# During World War II, linear programming was used extensively to deal with transportation, scheduling, and allocation of resources subject to certain restrictions such as costs and availability.<ref name="ref_cbdf84c9" />
# Linear programming is the process of taking various linear inequalities relating to some situation, and finding the "best" value obtainable under those conditions.<ref name="ref_bfba0ec9">[https://www.purplemath.com/modules/linprog.htm Linear Programming: Introduction]</ref>
# In "real life", linear programming is part of a very important area of mathematics called "optimization techniques".<ref name="ref_bfba0ec9" />
# Linear programming (LP) is one of the simplest ways to perform optimization.<ref name="ref_cc6bb3a3">[https://www.analyticsvidhya.com/blog/2017/02/lintroductory-guide-on-linear-programming-explained-in-simple-english/ Applications Of Linear Programming]</ref>
# For some reason, LP doesn’t get as much attention as it deserves while learning data science.<ref name="ref_cc6bb3a3" />
# I decided to write an article that explains Linear programming in simple English.<ref name="ref_cc6bb3a3" />
# Linear programming is a simple technique where we depict complex relationships through linear functions and then find the optimum points.<ref name="ref_cc6bb3a3" />
# Linear programming can be applied to various fields of study.<ref name="ref_0396107d">[https://en.wikipedia.org/wiki/Linear_programming Linear programming]</ref>
# Industries that use linear programming models include transportation, energy, telecommunications, and manufacturing.<ref name="ref_0396107d" />
# Linear programming is a widely used field of optimization for several reasons.<ref name="ref_0396107d" />
# A number of algorithms for other types of optimization problems work by solving LP problems as sub-problems.<ref name="ref_0396107d" />
# Linear programming techniques are common approaches to solve optimization problems that can be expressed in the standard form given by Eq.<ref name="ref_20482149">[https://www.sciencedirect.com/topics/engineering/linear-programming Linear Programming - an overview]</ref>
# However, any other mixed integer linear programming solver also can be used.<ref name="ref_20482149" />
# Based on the selected literature (52 papers), LP can be applied to a variety of diet problems, from food aid, national food programmes, and dietary guidelines to individual issues.<ref name="ref_cf2e89c8">[https://www.frontiersin.org/articles/10.3389/fnut.2018.00048/full A Review of the Use of Linear Programming to Optimize Diets, Nutritiously, Economically and Environmentally]</ref>
# Future possibilities lie in finding LP solutions for diets by combining nutritional, costs, ecological and acceptability constraints.<ref name="ref_cf2e89c8" />
# This paper reviews the application of linear programming to optimize diets with nutritional, economic, and environmental constraints.<ref name="ref_cf2e89c8" />
# These results led to upper bounds being added to LP for the first time (10).<ref name="ref_cf2e89c8" />
# The first step in any linear programming problem is to define the variables and the objective function.<ref name="ref_0c9d8c1b">[https://www.accaglobal.com/uk/en/student/exam-support-resources/fundamentals-exams-study-resources/f5/technical-articles/linear-programming.html F5 Performance Management]</ref>
# Linear programming (LP) is a powerful framework for describing and solving optimization problems.<ref name="ref_8affeeab">[https://www.gurobi.com/resource/linear-programming-basics/ Linear Programming (LP)]</ref>
# The set of applications of linear programming is literally too long to list.<ref name="ref_8affeeab" />
# The first algorithm for solving linear programming problems was the simplex method, proposed by George Dantzig in 1947.<ref name="ref_8affeeab" />
# However, the sheer variety of different LP models, and the many different ways in which LP is used, mean that neither algorithm dominates the other in practice.<ref name="ref_8affeeab" />
# There were three models produced by linear programming.<ref name="ref_e09afd8d">[https://bmcpublichealth.biomedcentral.com/articles/10.1186/s12889-019-6872-4 Diet optimization using linear programming to develop low cost cancer prevention food plan for selected adults in Kuala Lumpur, Malaysia]</ref>
# Table 2 shows all nutrients constrains and the food groups of the three different models produced by LP based on the dietary guidelines of WCRF/AICR 2007, MDG 2010 and RNI 2017.<ref name="ref_e09afd8d" />
# Table 3 shows the three menus produced, according to raw food items at the lowest possible cost based on WCRF/AICR, MDG, RNI and palatability constraints by using LP.<ref name="ref_e09afd8d" />
# The production of every menu is different from another as it follows the list of food ingredients selected according to the LP models.<ref name="ref_e09afd8d" />
# A linear programming problem involves constraints that contain inequalities.<ref name="ref_3e5c3852">[https://courses.lumenlearning.com/sanjacinto-finitemath1/chapter/reading-meeting-demands-with-linear-programming/ 3.2a. Solving Linear Programming Problems Graphically]</ref>
# The objective function along with the three corner points above forms a bounded linear programming problem.<ref name="ref_3e5c3852" />
# If this is the case, then you have a bounded linear programming problem.<ref name="ref_3e5c3852" />
# If a solution exists to a bounded linear programming problem, then it occurs at one of the corner points.<ref name="ref_3e5c3852" />
# Linear programming is a form of mathematical optimisation that seeks to determine the best way of using limited resources to achieve a given objective.<ref name="ref_22854ff1">[https://www.fm-magazine.com/issues/2019/feb/linear-programming-microsoft-excel.html Solve problems with linear programming and Excel]</ref>
# Before we continue, it's important to note that this article is not intended to be an exhaustive course in linear programming.<ref name="ref_22854ff1" />
# This example provides one setting where linear programming can be applied.<ref name="ref_22854ff1" />
# A short explanation is given what Linear programming is and some basic knowledge you need to know.<ref name="ref_fa3161a7">[http://web.mit.edu/lpsolve/lpsolve-default/doc/LPBasics.htm Linear programming basics]</ref>
# So a linear programming model consists of one objective which is a linear equation that must be maximized or minimized.<ref name="ref_fa3161a7" />
# It is the usual and most intuitive form of describing a linear programming problem.<ref name="ref_fa3161a7" />
# See Formulation of an lp problem in lpsolve for a practical example.<ref name="ref_fa3161a7" />
# If you think about the geometry in the above graph, in any linear optimization problem at least one vertex of the feasible region must be an optimal solution.<ref name="ref_07d2bfa0">[https://developers.google.com/optimization/lp/glop The Glop Linear Solver]</ref>
# Linear programming is a mathematical technique that determines the best way to use available resources.<ref name="ref_75a878c7">[https://www.mindtools.com/pages/article/newTED_82.htm Decision-Making Skills Training from MindTools.com]</ref>
# Note: You can use linear programming only if there is a linear relationship between the variables you're looking at.<ref name="ref_75a878c7" />
# To help you understand linear programming, we'll work through an example.<ref name="ref_75a878c7" />
# Linear programming software programs can solve the equations quickly and easily, and they provide a great deal of information about the various points within the possible set.<ref name="ref_75a878c7" />
# This paper studies the problem of tangible assets acquisition within the company by proposing a new hybrid model that uses linear programming and fuzzy numbers.<ref name="ref_ba865c30">[https://www.mdpi.com/1099-4300/22/1/121 Linear Programming and Fuzzy Optimization to Substantiate Investment Decisions in Tangible Assets]</ref>
# Regarding linear programming, two methods were implemented in the model, namely: the graphical method and the primal simplex algorithm.<ref name="ref_ba865c30" />
# Solving the primal simplex algorithm using fuzzy numbers and coefficients, allowed the results of the linear programming problem to also be in the form of fuzzy variables.<ref name="ref_ba865c30" />
# Linear programming, sometimes known as linear optimization, is the problem of maximizing or minimizing a linear function over a convex polyhedron specified by linear and non-negativity constraints.<ref name="ref_5252cc22">[https://mathworld.wolfram.com/LinearProgramming.html Linear Programming -- from Wolfram MathWorld]</ref>
# Linear programming theory falls within convex optimization theory and is also considered to be an important part of operations research.<ref name="ref_5252cc22" />
# Linear programming can be solved using the simplex method (Wood and Dantzig 1949, Dantzig 1949) which runs along polytope edges of the visualization solid to find the best answer.<ref name="ref_5252cc22" />
# Linear programming has proven to be an extremely powerful tool, both in modeling real-world problems and as a widely applicable mathematical theory.<ref name="ref_38a60640">[http://home.ubalt.edu/ntsbarsh/opre640a/partviii.htm Linear Optimization]</ref>
# Linear Programming (LP) is a mathematical procedure for determining optimal allocation of scarce resources.<ref name="ref_38a60640" />
# LP is a procedure that has found practical application in almost all facets of business, from advertising to production planning.<ref name="ref_38a60640" />
# Linear programming deals with a class of programming problems where both the objective function to be optimized is linear and all relations among the variables corresponding to resources are linear.<ref name="ref_38a60640" />
# Linear programming (LP) is one of the most widely-applied techniques in operations research.<ref name="ref_5c23f6c5">[http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0120-56092012000200013 A new algorithm for solving linear programming problems]</ref>
# Many methods have been developed and several others are being proposed for solving LP problems, including the famous simplex method and interior point algorithms.<ref name="ref_5c23f6c5" />
# This study was aimed at introducing a new method for solving LP problems.<ref name="ref_5c23f6c5" />
# Linear programming (LP) dates from 1939 when Leonid Kan-tarovich first expressed a problem in economics in linear form (Bazaraa et al., 1998).<ref name="ref_5c23f6c5" />
# As was stated earlier, a linear programming problem that has minimum constraints does not work with the simplex algorithm.<ref name="ref_8de10776">[https://brilliant.org/wiki/linear-programming/ Brilliant Math & Science Wiki]</ref>
# This method is viable for any linear programming problem that does not match the forms of the previous section .<ref name="ref_8de10776" />
# All linear programming problems aim to either maximize or minimize some numerical value representing profit, cost, production quantity, etc.<ref name="ref_8b56966f">[https://towardsdatascience.com/elements-of-a-linear-programming-problem-lpp-325075688c18 Elements of a Linear Programming Problem (LPP)]</ref>
# A feasible solution to the linear programming problem should satisfy the constraints and non-negativity restrictions.<ref name="ref_8b56966f" />
# In Mathematics, linear programming is a method of optimising operations with some constraints.<ref name="ref_88a291d6">[https://byjus.com/maths/linear-programming/ Linear Programming (Definition, Characteristics, Method & Example)]</ref>
# The main objective of linear programming is to maximize or minimize the numerical value.<ref name="ref_88a291d6" />
# Linear programming is considered as an important technique which is used to find the optimum resource utilisation.<ref name="ref_88a291d6" />
# The term “linear programming” consists of two words such as linear and programming.<ref name="ref_88a291d6" />
# To obtain the initial feasible vertex, one can set up another LP problem (called the phase I problem) to which there is always a known feasible vertex, and apply the simplex method to that problem.<ref name="ref_2fccf8fd">[https://www.nap.edu/read/2026/chapter/10 9 Probabilistic Analysis in Linear Programming]</ref>
# Within a few years of its introduction, LP had become a central—perhaps the central—paradigm of operations research.<ref name="ref_2fccf8fd" />
# The Linear Programming FAQ, established by John W. Gregory and maintained for many years by Robert Fourer, was last updated in 2005.<ref name="ref_26e6660e">[https://neos-guide.org/content/lp-faq Linear Programming FAQ]</ref>
# Since the LP FAQ is no longer maintained, the content has been incorporated into the relevant sections of the NEOS Optimization Guide.<ref name="ref_26e6660e" />
# The importance of linear programming derives in part from its many applications (see further below) and in part from the existence of good general-purpose techniques for finding optimal solutions.<ref name="ref_a201174e">[https://engineering.purdue.edu/~engelb/abe565/linear-programming-faq.html Linear Programming FAQ]</ref>
# These techniques take as input only an LP in the above Standard Form, and determine a solution without reference to any information concerning the LP's origins or special structure.<ref name="ref_a201174e" />
# The related problem of integer programming (or integer linear programming, strictly speaking) requires some or all of the variables to take integer (whole number) values.<ref name="ref_a201174e" />
# Industries that make use of LP and its extensions include transportation, energy, telecommunications, and manufacturing of many kinds.<ref name="ref_a201174e" />
# This problem involves the allocation of resources and can be modeled as a linear programming problem as we will discuss.<ref name="ref_730a8744">[https://www.intechopen.com/books/engineering-management/modeling-and-linear-programming-in-engineering-management Modeling and Linear Programming in Engineering Management]</ref>
# To model and solve this problem, we can use linear programming.<ref name="ref_730a8744" />
# Modern linear programming was the result of a research project undertaken by the US Department of Air Force under the title of Project SCOOP (Scientific Computation of Optimum Programs).<ref name="ref_730a8744" />
# One of the SCOOP team members, George Dantzig, developed the simplex algorithm for solving simultaneous linear programming problems.<ref name="ref_730a8744" />
# In Section 4, the problem is formulated as a mixed integer linear programming model.<ref name="ref_49168980">[https://www.hindawi.com/journals/jat/2020/3809734/ A Mixed Integer Linear Programming Model for Rolling Stock Deadhead Routing before the Operation Period in an Urban Rail Transit Line]</ref>
# However, even though the proposed model is a MILP model, it can be further transformed into a pure 0-1 linear programming model.<ref name="ref_49168980" />
===소스===
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2021년 2월 17일 (수) 07:56에 Pythagoras0님의 편집

Pythagoras0: /* 메타데이터 */ 새 문단

Pythagoras0: /* 노트 */ 새 문단