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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Home · DataEnvelopmentAnalysis</title><script data-outdated-warner src="assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.039/juliamono-regular.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.3/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.3/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.3/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.11/katex.min.css" rel="stylesheet" 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type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li class="is-active"><a class="tocitem" href>Home</a><ul class="internal"><li><a class="tocitem" href="#Installation"><span>Installation</span></a></li><li><a class="tocitem" href="#Tutorial"><span>Tutorial</span></a></li><li><a class="tocitem" href="#Available-models"><span>Available models</span></a></li><li><a class="tocitem" href="#Authors"><span>Authors</span></a></li></ul></li><li><span class="tocitem">Technical Efficiency Models</span><ul><li><a class="tocitem" href="technical/radial/">Radial Models</a></li><li><a class="tocitem" href="technical/radialbigdata/">Radial Big Data Models</a></li><li><a class="tocitem" href="technical/directional/">Directional Distance Function Models</a></li><li><a class="tocitem" href="technical/additive/">Additive Models</a></li><li><a class="tocitem" href="technical/generalizeddf/">Generalized Distance Function Models</a></li><li><a class="tocitem" href="technical/russell/">Russell Models</a></li><li><a class="tocitem" href="technical/enhancedrussell/">Enhanced Russell Graph Slack Based Measure</a></li><li><a class="tocitem" href="technical/modifiedddf/">Modified Directional Distance Function</a></li><li><a class="tocitem" href="technical/holder/">Hölder Distance Function</a></li><li><a class="tocitem" href="technical/reverseddf/">Reverse Directional Distance Function</a></li><li><a class="tocitem" href="technical/commontechnical/">Common functions for technical models</a></li></ul></li><li><span class="tocitem">Economic Efficiency Models</span><ul><li><a class="tocitem" href="economic/cost/">Cost Models</a></li><li><a class="tocitem" href="economic/revenue/">Revenue Models</a></li><li><a class="tocitem" href="economic/profit/">Profit Models</a></li><li><a class="tocitem" href="economic/profitability/">Profitability Models</a></li><li><a class="tocitem" href="economic/commoneconomic/">Common functions for economic models</a></li></ul></li><li><span class="tocitem">Productivity Change Models</span><ul><li><a class="tocitem" href="productivity/malmquist/">Malmquist Index</a></li><li><a class="tocitem" href="productivity/commonproductivity/">Common functions for productivity change models</a></li></ul></li><li><a class="tocitem" href="optimizer/">Configuring Optimizer</a></li><li><a class="tocitem" href="bibliography/">Bibliography</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Home</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Home</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/javierbarbero/DataEnvelopmentAnalysis.jl/blob/master/docs/src/index.md" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="DataEnvelopmentAnalysis.jl"><a class="docs-heading-anchor" href="#DataEnvelopmentAnalysis.jl">DataEnvelopmentAnalysis.jl</a><a id="DataEnvelopmentAnalysis.jl-1"></a><a class="docs-heading-anchor-permalink" href="#DataEnvelopmentAnalysis.jl" title="Permalink"></a></h1><p>DataEnvelopmentAnalysis.jl is a Julia package that provides functions for efficiency and productivity measurement using Data Envelopment Analysis (DEA). Particularly, it implements a variety of technical efficiency models, economic efficiency models and productivity change models.</p><p>The package is being developed for Julia <code>1.0</code> and above on Linux, macOS, and Windows.</p><p>The packes uses internally the <a href="https://github.com/JuliaOpt/JuMP.jl">JuMP</a> modelling language for mathematicall optimization with solvers <a href="https://github.com/jump-dev/GLPK.jl">GLPK</a> and <a href="https://github.com/jump-dev/Ipopt.jl">Ipopt</a>.</p><h2 id="Installation"><a class="docs-heading-anchor" href="#Installation">Installation</a><a id="Installation-1"></a><a class="docs-heading-anchor-permalink" href="#Installation" title="Permalink"></a></h2><p>The package can be installed with the Julia package manager:</p><pre><code class="language-julia hljs">julia> using Pkg; Pkg.add("DataEnvelopmentAnalysis")</code></pre><h2 id="Tutorial"><a class="docs-heading-anchor" href="#Tutorial">Tutorial</a><a id="Tutorial-1"></a><a class="docs-heading-anchor-permalink" href="#Tutorial" title="Permalink"></a></h2><p>For a tutorial on how to use the package, check the documentation on the <a href="technical/radial/#Radial-Input-Oriented-Model">Radial Input Oriented Model</a>.</p><h2 id="Available-models"><a class="docs-heading-anchor" href="#Available-models">Available models</a><a id="Available-models-1"></a><a class="docs-heading-anchor-permalink" href="#Available-models" title="Permalink"></a></h2><p>Technical efficiency DEA models:</p><ul><li><a href="technical/radial/#Radial-Models">Radial Models</a></li><li class="no-marker"><ul><li><a href="technical/radial/#Radial-Input-Oriented-Model">Radial Input Oriented Model</a></li><li><a href="technical/radial/#Radial-Output-Oriented-Model">Radial Output Oriented Model</a></li><li><a href="technical/radial/#Radial-Model-in-Multiplier-Form">Radial Model in Multiplier Form</a></li></ul></li><li><a href="technical/radialbigdata/#Radial-Big-Data-Models">Radial Big Data Models</a></li><li><a href="technical/directional/#Directional-Distance-Function-Models">Directional Distance Function Models</a></li><li><a href="technical/additive/#Additive-Models">Additive Models</a></li><li class="no-marker"><ul><li><a href="technical/additive/#Weighted-Additive-Model">Weighted Additive Model</a></li><li><a href="technical/additive/#Measure-of-Inefficiency-Proportions-(MIP)">Measure of Inefficiency Proportions (MIP)</a></li><li><a href="technical/additive/#Normalized-Weighted-Additive-Model">Normalized Weighted Additive Model</a></li><li><a href="technical/additive/#Range-Adjusted-Measure-(RAM)">Range Adjusted Measure (RAM)</a></li><li><a href="technical/additive/#Bounded-Adjusted-Measure-(BAM)">Bounded Adjusted Measure (BAM)</a></li></ul></li><li><a href="technical/generalizeddf/#Generalized-Distance-Function-Models">Generalized Distance Function Models</a></li><li><a href="technical/russell/#Russell-Models">Russell Models</a></li><li class="no-marker"><ul><li><a href="technical/russell/#Russell-Input-Model">Russell Input Model</a></li><li><a href="technical/russell/#Russell-Output-Model">Russell Output Model</a></li><li><a href="technical/russell/#Russell-Graph-Model">Russell Graph Model</a></li></ul></li><li><a href="technical/enhancedrussell/#Enhanced-Russell-Graph-Slack-Based-Measure">Enhanced Russell Graph Slack Based Measure</a></li><li><a href="technical/modifiedddf/#Modified-Directional-Distance-Function">Modified Directional Distance Function</a></li><li><a href="technical/holder/#Hölder-Distance-Function-Models">Hölder Distance Function Models</a></li><li class="no-marker"><ul><li><a href="technical/holder/#Hölder-L1">Hölder L1</a></li><li><a href="technical/holder/#Hölder-L2">Hölder L2</a></li><li><a href="technical/holder/#Hölder-LInf">Hölder LInf</a></li></ul></li><li><a href="technical/reverseddf/#Reverse-Directional-Distance-Function">Reverse Directional Distance Function</a></li></ul><p>Economic efficiency DEA models:</p><ul><li><a href="economic/cost/#Cost-Models">Cost Models</a></li><li><a href="economic/revenue/#Revenue-Models">Revenue Models</a></li><li><a href="economic/profit/#Profit-Models">Profit Models</a></li><li><a href="economic/profitability/#Profitability-Models">Profitability Models</a></li></ul><p>Productivity change models:</p><ul><li><a href="productivity/malmquist/#The-Malmquist-index">The Malmquist index</a></li></ul><h2 id="Authors"><a class="docs-heading-anchor" href="#Authors">Authors</a><a id="Authors-1"></a><a class="docs-heading-anchor-permalink" href="#Authors" title="Permalink"></a></h2><p>DataEnvelopmentAnalysis.jl is being developed by <a href="http://www.javierbarbero.net">Javier Barbero</a> and <a href="http://www.joselzofio.net">José Luís Zofío</a>.</p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="technical/radial/">Radial Models »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.10 on <span class="colophon-date" title="Wednesday 12 January 2022 19:43">Wednesday 12 January 2022</span>. 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