<html><head></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">Daniel, boa noite!<div><br></div><div>Não compreendi o seu problema postado na lista, possivelmente pq não utilizo o pacote DEA, onde posso baixar o pacote DEA para testes?</div><div>Também utilizo o R para analisar eficiência por meio de análise envoltória de dados. Estou trabalhando com o pacote Benchmarking, que além do excelente help tem o livro do mesmo autores que criaram o pacote que é bastante útil:</div><div>Bogetoft and Otto (2011), Benchmarking with DEA, SFA, and R.</div><div><br></div><div>Como exemplo do uso do pacote Benchmarking segue medidas de eficiência para o modelos básicos de DEA utilizando os dados da Tabela 2.1 de Coll e Blasco (2006) Evaluación de la Eficiencia mediante el Análisis Envolvente de Datos. Vale ressaltar que no seu caso o arquivo é grande, e nesse exemplo o arquivo .csv tem poucas linhas, mas acredito que não terá problema em manipular suas matrizes ou data.frames utilizando o Benchmarking.</div><div><br></div><div>Espero que o exemplo sejá útil, caso encontre algum erro pode corrigir e postar a versão corrigida.</div><div><br></div><div>Att</div><div>Roney</div><div><br></div><div>####################</div><div><br></div><div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 4px; text-indent: -4px; font: normal normal normal 11px/normal Monaco; color: rgb(30, 22, 153); "><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># <span style="color: rgb(50, 149, 113); ">TODO</span>: Dados da Tabla 2.1 Valores observados concesionarios, do livro de Coll e Blasco (2006) </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># INPUTS</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># x1 = Número de empleados </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># x2 = Depreciación del Inmovilizado, como proxy del capital</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># OUTPUTS</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># y1 = Número de vehículos vendidos </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># y2 = Número de órdenes de trabajo recibidas en taller</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># Coll e Blasco (2006) Evaluación de la Eficiencia mediante el Análisis Envolvente de Datos</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># Ferreira e Gomes (2009) Introdução à Análise Envoltória de Dados. Teoria, Modelos e Aplicações</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># Bogetoft, Otto (2011) Benchmark and frontier analysis using DEA and SFA and R</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># Author: roney</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); ">###############################################################################</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">rm(list=ls(all=<span style="color: rgb(162, 0, 149); ">TRUE</span>))</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">getwd()</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(92, 70, 193); "><span style="color: rgb(0, 0, 0); ">setwd(</span>"/Users/roney/Documents/Economia/R-workspace/DEA"<span style="color: rgb(0, 0, 0); ">)</span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">dir()</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">library(Benchmarking)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">help(package=<span style="color: rgb(92, 70, 193); ">"Benchmarking"</span>)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; "><span style="color: rgb(189, 68, 147); ">?</span>dea </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); ">## dea(X, Y, RTS="vrs", ORIENTATION="in", XREF=NULL, YREF=NULL,</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); ">#<span class="Apple-tab-span" style="white-space: pre; "> </span>FRONT.IDX=NULL, SLACK=FALSE, DUAL=FALSE, DIRECT=NULL, param=NULL,</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); ">#<span class="Apple-tab-span" style="white-space: pre; "> </span>TRANSPOSE=FALSE, FAST=FALSE, LP=FALSE, CONTROL=NULL, LPK=NULL)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); ">#</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># Tabla 2.1 Valores observados concesionarios</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); ">#<span class="Apple-tab-span" style="white-space: pre; "> </span>x1<span class="Apple-tab-span" style="white-space: pre; "> </span>x2<span class="Apple-tab-span" style="white-space: pre; "> </span>y1<span class="Apple-tab-span" style="white-space: pre; "> </span>y2</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); ">#<span class="Apple-tab-span" style="white-space: pre; "> </span>A<span class="Apple-tab-span" style="white-space: pre; "> </span>8<span class="Apple-tab-span" style="white-space: pre; "> </span>8<span class="Apple-tab-span" style="white-space: pre; "> </span>14<span class="Apple-tab-span" style="white-space: pre; "> </span>20</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); ">#<span class="Apple-tab-span" style="white-space: pre; "> </span>B<span class="Apple-tab-span" style="white-space: pre; "> </span>11<span class="Apple-tab-span" style="white-space: pre; "> </span>15<span class="Apple-tab-span" style="white-space: pre; "> </span>25<span class="Apple-tab-span" style="white-space: pre; "> </span>42</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); ">#<span class="Apple-tab-span" style="white-space: pre; "> </span>C<span class="Apple-tab-span" style="white-space: pre; "> </span>14<span class="Apple-tab-span" style="white-space: pre; "> </span>12<span class="Apple-tab-span" style="white-space: pre; "> </span>8<span class="Apple-tab-span" style="white-space: pre; "> </span>30</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); ">#<span class="Apple-tab-span" style="white-space: pre; "> </span>D<span class="Apple-tab-span" style="white-space: pre; "> </span>12<span class="Apple-tab-span" style="white-space: pre; "> </span>13<span class="Apple-tab-span" style="white-space: pre; "> </span>25<span class="Apple-tab-span" style="white-space: pre; "> </span>8</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); ">#<span class="Apple-tab-span" style="white-space: pre; "> </span>E<span class="Apple-tab-span" style="white-space: pre; "> </span>11<span class="Apple-tab-span" style="white-space: pre; "> </span>18<span class="Apple-tab-span" style="white-space: pre; "> </span>40<span class="Apple-tab-span" style="white-space: pre; "> </span>22</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); ">#<span class="Apple-tab-span" style="white-space: pre; "> </span>F<span class="Apple-tab-span" style="white-space: pre; "> </span>18<span class="Apple-tab-span" style="white-space: pre; "> </span>20<span class="Apple-tab-span" style="white-space: pre; "> </span>24<span class="Apple-tab-span" style="white-space: pre; "> </span>30</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># link baixar o arquivo .csv # <a href="http://www.datafilehost.com/download-b7ad5202.html">http://www.datafilehost.com/download-b7ad5202.html</a></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(92, 70, 193); "><span style="color: rgb(0, 0, 0); ">read.csv(</span>"Coll-Blasco_exemplo.csv"<span style="color: rgb(0, 0, 0); ">, header=</span><span style="color: rgb(162, 0, 149); ">TRUE</span><span style="color: rgb(0, 0, 0); ">)</span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">coll.blasco <- read.csv(<span style="color: rgb(92, 70, 193); ">"Coll-Blasco_exemplo.csv"</span>, header=<span style="color: rgb(162, 0, 149); ">TRUE</span>)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">namesAF <- c(<span style="color: rgb(92, 70, 193); ">"A"</span>, <span style="color: rgb(92, 70, 193); ">"B"</span>, <span style="color: rgb(92, 70, 193); ">"C"</span>, <span style="color: rgb(92, 70, 193); ">"D"</span>, <span style="color: rgb(92, 70, 193); ">"E"</span>, <span style="color: rgb(92, 70, 193); ">"F"</span>)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">namesX <-c(<span style="color: rgb(92, 70, 193); ">"x1"</span>, <span style="color: rgb(92, 70, 193); ">"x2"</span>)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">namesY <- c(<span style="color: rgb(92, 70, 193); ">"y1"</span>, <span style="color: rgb(92, 70, 193); ">"y2"</span>)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">namesXY <- c(<span style="color: rgb(92, 70, 193); ">"x1"</span>, <span style="color: rgb(92, 70, 193); ">"x2"</span>, <span style="color: rgb(92, 70, 193); ">"y1"</span>, <span style="color: rgb(92, 70, 193); ">"y2"</span>)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">insumos <- matrix(c(coll.blasco<span style="color: rgb(71, 115, 115); ">$</span>x1, coll.blasco<span style="color: rgb(71, 115, 115); ">$</span>x2), nrow=<span style="color: rgb(36, 0, 150); ">6</span>, ncol=<span style="color: rgb(36, 0, 150); ">2</span>, byrow=<span style="color: rgb(162, 0, 149); ">FALSE</span>, dimnames=list(namesAF, namesX))</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">is.matrix(insumos)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">insumos</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">produtos <- matrix(c(coll.blasco<span style="color: rgb(71, 115, 115); ">$</span>y1, coll.blasco<span style="color: rgb(71, 115, 115); ">$</span>y2), nrow=<span style="color: rgb(36, 0, 150); ">6</span>, ncol=<span style="color: rgb(36, 0, 150); ">2</span>, byrow=<span style="color: rgb(162, 0, 149); ">FALSE</span>, dimnames=list(namesAF, namesY))</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">is.matrix(produtos)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">produtos</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); ">######## CCR Input Orientado #######</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># Em benchmarking modelo CCR (crs) input orientado, o problema primal é a minimização do insumos dada a</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># quantidade de produtos. Modelo envoltório (que usa lambda), ver notação página 72 Ferreira e Gomes (2009)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">ccr.in <- dea(insumos, produtos, RTS=<span style="color: rgb(92, 70, 193); ">"crs"</span>, ORIENTATION=<span style="color: rgb(92, 70, 193); ">"in"</span>, SLACK=<span style="color: rgb(162, 0, 149); ">TRUE</span>) <span style="color: rgb(48, 149, 95); "># eff CCR insumo orientado com folgas</span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "><span style="color: rgb(0, 0, 0); ">summary(ccr.in) </span># função que trás o resumo das medidas, como número e % de unidades eficientes em cada</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "><span style="color: rgb(0, 0, 0); "><span class="Apple-tab-span" style="white-space: pre; "> </span></span># faixa de valor, assim como folgas. Muito útil para grande quantidade de DMU's</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "><span style="color: rgb(0, 0, 0); ">lambda(ccr.in)<span class="Apple-tab-span" style="white-space: pre; "> </span></span># equivalente a saída Benchmarking do SAID, indica quais DMU's estão sendo referência,</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "><span style="color: rgb(0, 0, 0); "><span class="Apple-tab-span" style="white-space: pre; "> </span></span># as que estão nas colunas, para as demais DMU's, que estão nas linhas.</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "><span style="color: rgb(0, 0, 0); "><span class="Apple-tab-span" style="white-space: pre; "> </span></span># em outras palavras, parceiros relevantes (peers) para as DMU's ineficientes, e o valor do </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "><span style="color: rgb(0, 0, 0); "><span class="Apple-tab-span" style="white-space: pre; "> </span></span># lambda indica o quanto a DMU eficiente, o benchmarking, é importante para a DMU ineficiente</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "><span style="color: rgb(0, 0, 0); ">lambda(ccr.in, KEEPREF = </span><span style="color: rgb(162, 0, 149); ">TRUE</span><span style="color: rgb(0, 0, 0); ">) </span># quando a opção "KEEPREF = TRUE" é utilizada todas as DMU's são mostradas</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "><span style="color: rgb(0, 0, 0); "><span class="Apple-tab-span" style="white-space: pre; "> </span></span># nas colunas, não penas as eficiêntes.</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "><span style="color: rgb(0, 0, 0); ">print(ccr.in</span><span style="color: rgb(71, 115, 115); ">$</span><span style="color: rgb(0, 0, 0); ">eff, digits=</span><span style="color: rgb(36, 0, 150); ">2</span><span style="color: rgb(0, 0, 0); ">)<span class="Apple-tab-span" style="white-space: pre; "> </span></span># para mostrar a eficiência das DMU's</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "><span style="color: rgb(0, 0, 0); ">which( ccr.in</span><span style="color: rgb(71, 115, 115); ">$</span><span style="color: rgb(0, 0, 0); ">eff </span><span style="color: rgb(189, 68, 147); ">==</span><span style="color: rgb(0, 0, 0); "> </span><span style="color: rgb(36, 0, 150); ">1</span><span style="color: rgb(0, 0, 0); "> </span><span style="color: rgb(189, 68, 147); ">&</span><span style="color: rgb(0, 0, 0); "> </span><span style="color: rgb(189, 68, 147); ">!</span><span style="color: rgb(0, 0, 0); ">ccr.in</span><span style="color: rgb(71, 115, 115); ">$</span><span style="color: rgb(0, 0, 0); ">slack)<span class="Apple-tab-span" style="white-space: pre; "> </span></span># para mostrar apenas as DMU's eficientes e sem folga</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">data.frame(<span style="color: rgb(92, 70, 193); ">"eff"</span>=ccr.in<span style="color: rgb(71, 115, 115); ">$</span>eff, <span style="color: rgb(92, 70, 193); ">"ins"</span>=insumos, <span style="color: rgb(92, 70, 193); ">"rad"</span>=ccr.in<span style="color: rgb(71, 115, 115); ">$</span>eff <span style="color: rgb(189, 68, 147); ">*</span> insumos, <span style="color: rgb(92, 70, 193); ">"fol"</span>=ccr.in<span style="color: rgb(71, 115, 115); ">$</span>sx, <span style="color: rgb(92, 70, 193); ">"alv"</span>=insumos <span style="color: rgb(189, 68, 147); ">-</span> ccr.in<span style="color: rgb(71, 115, 115); ">$</span>sx) </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "><span style="color: rgb(0, 0, 0); "><span class="Apple-tab-span" style="white-space: pre; "> </span></span># i) eff, ii) insumos observados ou atual, iii) movimento radial, iv) folga e v) alvo</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; "><span class="Apple-tab-span" style="white-space: pre; "> </span><span style="color: rgb(48, 149, 95); "># </span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "><span style="color: rgb(0, 0, 0); "><span class="Apple-tab-span" style="white-space: pre; "> </span></span># iii) movimento radial é o cálculo da redução dos insumos em direção a fronteira eficiente</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "><span style="color: rgb(0, 0, 0); "><span class="Apple-tab-span" style="white-space: pre; "> </span></span># <span class="Apple-tab-span" style="white-space: pre; "> </span> e é obtido pela multiplicação dos insumos observados pela eficiência das respectivas</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "><span style="color: rgb(0, 0, 0); "><span class="Apple-tab-span" style="white-space: pre; "> </span></span>#<span class="Apple-tab-span" style="white-space: pre; "> </span> unidades, ou pela multiplicação da unidade do insumo da unidade ineficiente pelo</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "><span style="color: rgb(0, 0, 0); "><span class="Apple-tab-span" style="white-space: pre; "> </span></span>#<span class="Apple-tab-span" style="white-space: pre; "> </span> lambda do(s) seu(s) benchmarks. (ver página 101 de Ferreira e Gomes, 2009)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "><span style="color: rgb(0, 0, 0); "><span class="Apple-tab-span" style="white-space: pre; "> </span></span># iv) mesmo projetando DMU em direção a fronteira eficiente devido a possibilidade</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "><span style="color: rgb(0, 0, 0); "><span class="Apple-tab-span" style="white-space: pre; "> </span></span>#<span class="Apple-tab-span" style="white-space: pre; "> </span> de existir alguns seguimentos da fronteira poliangular linear paralelos aos eixos<span class="Apple-tab-span" style="white-space: pre; "> </span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "><span style="color: rgb(0, 0, 0); "><span class="Apple-tab-span" style="white-space: pre; "> </span></span>#<span class="Apple-tab-span" style="white-space: pre; "> </span> coordenadas é possível ocorrer folgas nesses pontos. Ou seja, mesmo que o movimento</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "><span style="color: rgb(0, 0, 0); "><span class="Apple-tab-span" style="white-space: pre; "> </span></span>#<span class="Apple-tab-span" style="white-space: pre; "> </span> radial tenha projetado a DMU para a fronteira eficiente é possivel existir alguma</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "><span style="color: rgb(0, 0, 0); "><span class="Apple-tab-span" style="white-space: pre; "> </span></span>#<span class="Apple-tab-span" style="white-space: pre; "> </span> ineficiencia, que caracterizamos como folga. (ver página 102 de Ferreira e Gomes, 2009)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "><span style="color: rgb(0, 0, 0); "><span class="Apple-tab-span" style="white-space: pre; "> </span></span># v) o alvo é o movimento radial dimunuido das possíveis folgas</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">data.frame(<span style="color: rgb(92, 70, 193); ">"eff"</span>=ccr.in<span style="color: rgb(71, 115, 115); ">$</span>eff,<span style="color: rgb(92, 70, 193); ">"pro"</span>=produtos,<span style="color: rgb(92, 70, 193); ">"rad"</span>=ccr.in<span style="color: rgb(71, 115, 115); ">$</span>eff<span style="color: rgb(189, 68, 147); ">*</span>produtos,<span style="color: rgb(92, 70, 193); ">"fol"</span>=ccr.in<span style="color: rgb(71, 115, 115); ">$</span>sy,<span style="color: rgb(92, 70, 193); ">"alv"</span>=produtos<span style="color: rgb(189, 68, 147); ">+</span>ccr.in<span style="color: rgb(71, 115, 115); ">$</span>sy)<span class="Apple-tab-span" style="white-space: pre; "> </span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "><span style="color: rgb(0, 0, 0); "><span class="Apple-tab-span" style="white-space: pre; "> </span></span># i) eff, ii) produtos observados ou atual, iii) movimento radial, iv) folga e v) alvo</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "><span style="color: rgb(0, 0, 0); "><span class="Apple-tab-span" style="white-space: pre; "> </span></span># o mesmo do exemplo anterior mas agora aplicado para aos produtos</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); ">## Problema da Dualidade ## </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># no problema dual do modelo CCR (crs) insumos orientado [maximização] é expressa a forma multiplicada desse modelo, </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># onde os lambdas são substituidos pelos peso insumo (u) e peso produto (v). ver notação pág 72 Ferreira e Gomes (2009)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># os pesos, peso insumo (u) e peso produto (v), que permitem calcular os insumos e produtos virtuais conforme são </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># obtidos na saída do SAID e no modelo insumo orientado multiplicadores (primal) de Coll e Blasco (2006) só são </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># encontrados pelo problema dual no pacote Benchmarking</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">ccr.in.dual <- dea.dual(insumos, produtos, RTS=<span style="color: rgb(92, 70, 193); ">"crs"</span>, ORIENTATION=<span style="color: rgb(92, 70, 193); ">"in"</span>)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">names(ccr.in.dual)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">print(cbind(<span style="color: rgb(92, 70, 193); ">"eff"</span>=ccr.in.dual<span style="color: rgb(71, 115, 115); ">$</span>eff, ccr.in.dual<span style="color: rgb(71, 115, 115); ">$</span>u, ccr.in.dual<span style="color: rgb(71, 115, 115); ">$</span>v), digits=<span style="color: rgb(36, 0, 150); ">5</span>) </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "><span style="color: rgb(0, 0, 0); "><span class="Apple-tab-span" style="white-space: pre; "> </span></span># o valor eficiência é exatamente igual aos do SAID e do Excel, mas os pesos apresentam valores diferentes</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "> <br class="webkit-block-placeholder"></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># para detalhes ver tabela 4.8 na página 130 de Ferreira e Gomes (2009) ou nas páginas 117 e 118 tabelas 4.2 e 4.3 </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); ">######## CCR Output Orientado #######</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># Em benchmarking modelo CCR (crs) output orientado, o problema primal é a maximização do produto dada a</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># quantidade de insumos. Modelo envoltório (que usa lambda), ver notação página 130 Ferreira e Gomes (2009)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">ccr.out <- dea(insumos, produtos, RTS=<span style="color: rgb(92, 70, 193); ">"crs"</span>, ORIENTATION=<span style="color: rgb(92, 70, 193); ">"out"</span>, SLACK=<span style="color: rgb(162, 0, 149); ">TRUE</span>)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">summary(ccr.out)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "><span style="color: rgb(0, 0, 0); ">lambda(ccr.out) </span># apresentou uma pequena mudança no valor dos lambdas comparado com o resultado do SAID, mas como </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "><span style="color: rgb(0, 0, 0); "><span class="Apple-tab-span" style="white-space: pre; "> </span></span># o modelo é CCR acredito não deveria acontecer isso</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">lambda(ccr.out, KEEPREF = <span style="color: rgb(162, 0, 149); ">TRUE</span>)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">print(<span style="color: rgb(36, 0, 150); ">1</span><span style="color: rgb(189, 68, 147); ">/</span>ccr.out<span style="color: rgb(71, 115, 115); ">$</span>eff, digits=<span style="color: rgb(36, 0, 150); ">2</span>)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">which(<span style="color: rgb(36, 0, 150); ">1</span><span style="color: rgb(189, 68, 147); ">/</span>ccr.out<span style="color: rgb(71, 115, 115); ">$</span>eff <span style="color: rgb(189, 68, 147); ">==</span> <span style="color: rgb(36, 0, 150); ">1</span> <span style="color: rgb(189, 68, 147); ">&</span> <span style="color: rgb(189, 68, 147); ">!</span>ccr.out<span style="color: rgb(71, 115, 115); ">$</span>slack)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">data.frame(<span style="color: rgb(92, 70, 193); ">"eff"</span>=<span style="color: rgb(36, 0, 150); ">1</span><span style="color: rgb(189, 68, 147); ">/</span>ccr.out<span style="color: rgb(71, 115, 115); ">$</span>eff, <span style="color: rgb(92, 70, 193); ">"ins"</span>=insumos, <span style="color: rgb(92, 70, 193); ">"rad"</span>=(<span style="color: rgb(36, 0, 150); ">1</span><span style="color: rgb(189, 68, 147); ">/</span>ccr.out<span style="color: rgb(71, 115, 115); ">$</span>eff) <span style="color: rgb(189, 68, 147); ">*</span> insumos, <span style="color: rgb(92, 70, 193); ">"fol"</span>=ccr.out<span style="color: rgb(71, 115, 115); ">$</span>sx,</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; "><span class="Apple-tab-span" style="white-space: pre; "> </span><span style="color: rgb(92, 70, 193); ">"alv"</span>=insumos <span style="color: rgb(189, 68, 147); ">-</span> ccr.in<span style="color: rgb(71, 115, 115); ">$</span>sx)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">data.frame(<span style="color: rgb(92, 70, 193); ">"eff"</span>=<span style="color: rgb(36, 0, 150); ">1</span><span style="color: rgb(189, 68, 147); ">/</span>ccr.out<span style="color: rgb(71, 115, 115); ">$</span>eff, <span style="color: rgb(92, 70, 193); ">"pro"</span>=produtos, <span style="color: rgb(92, 70, 193); ">"rad"</span>=<span style="color: rgb(36, 0, 150); ">1</span><span style="color: rgb(189, 68, 147); ">/</span>ccr.out<span style="color: rgb(71, 115, 115); ">$</span>eff <span style="color: rgb(189, 68, 147); ">*</span> produtos, <span style="color: rgb(92, 70, 193); ">"fol"</span>=ccr.out<span style="color: rgb(71, 115, 115); ">$</span>sy, </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; "><span class="Apple-tab-span" style="white-space: pre; "> </span><span style="color: rgb(92, 70, 193); ">"alv"</span>=produtos <span style="color: rgb(189, 68, 147); ">+</span> ccr.out<span style="color: rgb(71, 115, 115); ">$</span>sy)<span class="Apple-tab-span" style="white-space: pre; "> </span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># apresentou pequenas mudanças diante dos resultodos do SAID #</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># o problema dual do modelo CCR (crs) output orientado é a minimização, modelo dos multiplicadores, que considera</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># os pesos insumos (u) e produtos (v)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">ccr.out.dual <- dea.dual(insumos, produtos, RTS=<span style="color: rgb(92, 70, 193); ">"crs"</span>, ORIENTATION=<span style="color: rgb(92, 70, 193); ">"out"</span>) <span style="color: rgb(48, 149, 95); "># problema dual output orientado</span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">names(ccr.out.dual)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">print(cbind(<span style="color: rgb(92, 70, 193); ">"eff"</span>=ccr.out.dual<span style="color: rgb(71, 115, 115); ">$</span>eff, ccr.out.dual<span style="color: rgb(71, 115, 115); ">$</span>u, ccr.out.dual<span style="color: rgb(71, 115, 115); ">$</span>v), digits=<span style="color: rgb(36, 0, 150); ">5</span>)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); ">######## BCC Input Orientado #######</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># Em benchmarking modelo BCC (vrs) input orientado, o problema primal é a minimização do insumos dada a</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># quantidade de produtos. Modelo envoltório (que usa lambda), ver notação página 130 Ferreira e Gomes (2009)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">bcc.in <- dea(insumos, produtos, RTS=<span style="color: rgb(92, 70, 193); ">"vrs"</span>, ORIENTATION=<span style="color: rgb(92, 70, 193); ">"in"</span>, SLACK=<span style="color: rgb(162, 0, 149); ">TRUE</span>) <span style="color: rgb(48, 149, 95); "># eff BCC insumo orientado com folgas</span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">summary(bcc.in)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">lambda(bcc.in)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">lambda(bcc.in, KEEPREF = <span style="color: rgb(162, 0, 149); ">TRUE</span>)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">print(bcc.in<span style="color: rgb(71, 115, 115); ">$</span>eff, digits=<span style="color: rgb(36, 0, 150); ">2</span>)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">which(bcc.in<span style="color: rgb(71, 115, 115); ">$</span>eff <span style="color: rgb(189, 68, 147); ">==</span> <span style="color: rgb(36, 0, 150); ">1</span> <span style="color: rgb(189, 68, 147); ">&</span> <span style="color: rgb(189, 68, 147); ">!</span>bcc.in<span style="color: rgb(71, 115, 115); ">$</span>slack)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">data.frame(<span style="color: rgb(92, 70, 193); ">"eff"</span>=bcc.in<span style="color: rgb(71, 115, 115); ">$</span>eff, <span style="color: rgb(92, 70, 193); ">"ins"</span>=insumos, <span style="color: rgb(92, 70, 193); ">"rad"</span>=bcc.in<span style="color: rgb(71, 115, 115); ">$</span>eff <span style="color: rgb(189, 68, 147); ">*</span> insumos, <span style="color: rgb(92, 70, 193); ">"fol"</span>=bcc.in<span style="color: rgb(71, 115, 115); ">$</span>sx, <span style="color: rgb(92, 70, 193); ">"alv"</span>=insumos <span style="color: rgb(189, 68, 147); ">-</span> bcc.in<span style="color: rgb(71, 115, 115); ">$</span>sx)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">data.frame(<span style="color: rgb(92, 70, 193); ">"eff"</span>=bcc.in<span style="color: rgb(71, 115, 115); ">$</span>eff, <span style="color: rgb(92, 70, 193); ">"ins"</span>=produtos, <span style="color: rgb(92, 70, 193); ">"rad"</span>=bcc.in<span style="color: rgb(71, 115, 115); ">$</span>eff <span style="color: rgb(189, 68, 147); ">*</span> produtos,<span style="color: rgb(92, 70, 193); ">"fol"</span>=bcc.in<span style="color: rgb(71, 115, 115); ">$</span>sy, <span style="color: rgb(92, 70, 193); ">"alv"</span>=produtos <span style="color: rgb(189, 68, 147); ">+</span> bcc.in<span style="color: rgb(71, 115, 115); ">$</span>sy)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); ">## RENDIMENTOS DE ESCALA ## </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># na saida do SAID, além dos pesos do CCR, tem v0 que corresponde ao k da abordagem de Coll e Blasco (2006) </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">bcc.in.irs <- dea(insumos, produtos, RTS=<span style="color: rgb(92, 70, 193); ">"irs"</span>, ORIENTATION=<span style="color: rgb(92, 70, 193); ">"in"</span>, SLACK=<span style="color: rgb(162, 0, 149); ">TRUE</span>) <span style="color: rgb(48, 149, 95); "># eff BCC ins orientado rend crescentes</span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">bcc.in.drs <- dea(insumos, produtos, RTS=<span style="color: rgb(92, 70, 193); ">"drs"</span>, ORIENTATION=<span style="color: rgb(92, 70, 193); ">"in"</span>, SLACK=<span style="color: rgb(162, 0, 149); ">TRUE</span>) <span style="color: rgb(48, 149, 95); "># eff BCC ins orientado rend decrescentes</span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><span class="Apple-tab-span" style="white-space: pre; "> </span><br class="webkit-block-placeholder"></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "><span style="color: rgb(0, 0, 0); "><span class="Apple-tab-span" style="white-space: pre; "> </span></span># Ferreira e Gomes (2009) página 198</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "><span style="color: rgb(0, 0, 0); "><span class="Apple-tab-span" style="white-space: pre; "> </span></span># CCR = BCC rendimentos constantes de escala</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "><span style="color: rgb(0, 0, 0); "><span class="Apple-tab-span" style="white-space: pre; "> </span></span># DRS = RVE rendimentos decrescentes, se DRS != RVE rendimentos crescentes</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "><span style="color: rgb(0, 0, 0); "><span class="Apple-tab-span" style="white-space: pre; "> </span></span># IRS = RVE rendimentos crescentes, se IRS != RVE rendimentos decrescentes </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">data.frame(<span style="color: rgb(92, 70, 193); ">"CRS"</span>=ccr.in<span style="color: rgb(71, 115, 115); ">$</span>eff,<span style="color: rgb(92, 70, 193); ">"VRS"</span>=bcc.in<span style="color: rgb(71, 115, 115); ">$</span>eff, <span style="color: rgb(92, 70, 193); ">"IRS"</span>=bcc.in.irs<span style="color: rgb(71, 115, 115); ">$</span>eff, <span style="color: rgb(92, 70, 193); ">"DRS"</span>=bcc.in.drs<span style="color: rgb(71, 115, 115); ">$</span>eff, <span style="color: rgb(92, 70, 193); ">"E_ESC"</span>=ccr.in<span style="color: rgb(71, 115, 115); ">$</span>eff<span style="color: rgb(189, 68, 147); ">/</span>bcc.in<span style="color: rgb(71, 115, 115); ">$</span>eff,</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; "><span class="Apple-tab-span" style="white-space: pre; "> </span><span style="color: rgb(92, 70, 193); ">"REND"</span>=ifelse(ccr.in<span style="color: rgb(71, 115, 115); ">$</span>eff <span style="color: rgb(189, 68, 147); ">==</span> bcc.in<span style="color: rgb(71, 115, 115); ">$</span>eff <span style="color: rgb(189, 68, 147); ">|</span> bcc.in<span style="color: rgb(71, 115, 115); ">$</span>eff <span style="color: rgb(189, 68, 147); ">==</span> bcc.in.irs<span style="color: rgb(71, 115, 115); ">$</span>eff <span style="color: rgb(189, 68, 147); ">&</span> bcc.in<span style="color: rgb(71, 115, 115); ">$</span>eff <span style="color: rgb(189, 68, 147); ">==</span> bcc.in.drs<span style="color: rgb(71, 115, 115); ">$</span>eff, </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; "><span class="Apple-tab-span" style="white-space: pre; "> </span><span style="color: rgb(92, 70, 193); ">"constante"</span>, ifelse(bcc.in<span style="color: rgb(71, 115, 115); ">$</span>eff <span style="color: rgb(189, 68, 147); ">==</span> bcc.in.drs<span style="color: rgb(71, 115, 115); ">$</span>eff <span style="color: rgb(189, 68, 147); ">&</span> bcc.in<span style="color: rgb(71, 115, 115); ">$</span>eff <span style="color: rgb(189, 68, 147); ">!=</span> bcc.in.irs<span style="color: rgb(71, 115, 115); ">$</span>eff, <span style="color: rgb(92, 70, 193); ">"decrescen"</span>, </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(92, 70, 193); "><span style="color: rgb(0, 0, 0); "><span class="Apple-tab-span" style="white-space: pre; "> </span></span>"crescente"<span style="color: rgb(0, 0, 0); ">)))</span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># de modo equivalente pode-se fazer</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">data.frame(<span style="color: rgb(92, 70, 193); ">"CRS"</span>=ccr.in<span style="color: rgb(71, 115, 115); ">$</span>eff,<span style="color: rgb(92, 70, 193); ">"VRS"</span>=bcc.in<span style="color: rgb(71, 115, 115); ">$</span>eff, <span style="color: rgb(92, 70, 193); ">"IRS"</span>=bcc.in.irs<span style="color: rgb(71, 115, 115); ">$</span>eff, <span style="color: rgb(92, 70, 193); ">"DRS"</span>=bcc.in.drs<span style="color: rgb(71, 115, 115); ">$</span>eff, <span style="color: rgb(92, 70, 193); ">"E_ESC"</span>=ccr.in<span style="color: rgb(71, 115, 115); ">$</span>eff<span style="color: rgb(189, 68, 147); ">/</span>bcc.in<span style="color: rgb(71, 115, 115); ">$</span>eff,</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; "><span class="Apple-tab-span" style="white-space: pre; "> </span><span style="color: rgb(92, 70, 193); ">"REND"</span>=ifelse(ccr.in<span style="color: rgb(71, 115, 115); ">$</span>eff <span style="color: rgb(189, 68, 147); ">==</span> bcc.in<span style="color: rgb(71, 115, 115); ">$</span>eff <span style="color: rgb(189, 68, 147); ">|</span> bcc.in<span style="color: rgb(71, 115, 115); ">$</span>eff <span style="color: rgb(189, 68, 147); ">==</span> bcc.in.irs<span style="color: rgb(71, 115, 115); ">$</span>eff <span style="color: rgb(189, 68, 147); ">&</span> bcc.in<span style="color: rgb(71, 115, 115); ">$</span>eff <span style="color: rgb(189, 68, 147); ">==</span> bcc.in.drs<span style="color: rgb(71, 115, 115); ">$</span>eff, </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; "><span class="Apple-tab-span" style="white-space: pre; "> </span><span style="color: rgb(92, 70, 193); ">"constante"</span>, ifelse(bcc.in<span style="color: rgb(71, 115, 115); ">$</span>eff <span style="color: rgb(189, 68, 147); ">==</span> bcc.in.irs<span style="color: rgb(71, 115, 115); ">$</span>eff <span style="color: rgb(189, 68, 147); ">&</span> bcc.in<span style="color: rgb(71, 115, 115); ">$</span>eff <span style="color: rgb(189, 68, 147); ">!=</span> bcc.in.drs<span style="color: rgb(71, 115, 115); ">$</span>eff, <span style="color: rgb(92, 70, 193); ">"crescente"</span>, </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(92, 70, 193); "><span style="color: rgb(0, 0, 0); "><span class="Apple-tab-span" style="white-space: pre; "> </span></span>"decrescen"<span style="color: rgb(0, 0, 0); ">)))</span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># no problema dual do modelo BCC (vrs) insumos orientado [maximização] é expressa na forma multiplicada, onde os </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># lambdas são substituidos pelos peso insumo (u) e peso produto (v). ver notação pág 117 Ferreira e Gomes (2009)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">bcc.in.dual <- dea.dual(insumos, produtos, RTS=<span style="color: rgb(92, 70, 193); ">"vrs"</span>, ORIENTATION=<span style="color: rgb(92, 70, 193); ">"in"</span>)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">names(bcc.in.dual)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">print(cbind(<span style="color: rgb(92, 70, 193); ">"eff"</span>=bcc.in.dual<span style="color: rgb(71, 115, 115); ">$</span>eff, bcc.in.dual<span style="color: rgb(71, 115, 115); ">$</span>u, bcc.in.dual<span style="color: rgb(71, 115, 115); ">$</span>v), digits=<span style="color: rgb(36, 0, 150); ">3</span>)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); ">######## BCC Output Orientado #######</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># Em benchmarking modelo BCC (vrs) output orientado, o problema primal é a maximização do produto dada a</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># quantidade de insumos. Modelo envoltório (que usa lambda), ver notação página 118 Ferreira e Gomes (2009)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">bcc.out <- dea(insumos, produtos, RTS=<span style="color: rgb(92, 70, 193); ">"vrs"</span>, ORIENTATION=<span style="color: rgb(92, 70, 193); ">"out"</span>, SLACK=<span style="color: rgb(162, 0, 149); ">TRUE</span>)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">summary(bcc.out)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">lambda(bcc.out)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">lambda(bcc.out, KEEPREF = <span style="color: rgb(162, 0, 149); ">TRUE</span>)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">print(<span style="color: rgb(36, 0, 150); ">1</span><span style="color: rgb(189, 68, 147); ">/</span>bcc.out<span style="color: rgb(71, 115, 115); ">$</span>eff, digits=<span style="color: rgb(36, 0, 150); ">2</span>)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">which(<span style="color: rgb(36, 0, 150); ">1</span><span style="color: rgb(189, 68, 147); ">/</span>bcc.out<span style="color: rgb(71, 115, 115); ">$</span>eff <span style="color: rgb(189, 68, 147); ">==</span> <span style="color: rgb(36, 0, 150); ">1</span> <span style="color: rgb(189, 68, 147); ">&</span> <span style="color: rgb(189, 68, 147); ">!</span>bcc.out<span style="color: rgb(71, 115, 115); ">$</span>slack)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">data.frame(<span style="color: rgb(92, 70, 193); ">"eff"</span>=<span style="color: rgb(36, 0, 150); ">1</span><span style="color: rgb(189, 68, 147); ">/</span>bcc.out<span style="color: rgb(71, 115, 115); ">$</span>eff, <span style="color: rgb(92, 70, 193); ">"ins"</span>=insumos, <span style="color: rgb(92, 70, 193); ">"rad"</span>=(<span style="color: rgb(36, 0, 150); ">1</span><span style="color: rgb(189, 68, 147); ">/</span>bcc.out<span style="color: rgb(71, 115, 115); ">$</span>eff) <span style="color: rgb(189, 68, 147); ">*</span> insumos,<span style="color: rgb(92, 70, 193); ">"fol"</span>=bcc.out<span style="color: rgb(71, 115, 115); ">$</span>sx, </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; "><span class="Apple-tab-span" style="white-space: pre; "> </span><span style="color: rgb(92, 70, 193); ">"alv"</span>=insumos <span style="color: rgb(189, 68, 147); ">-</span> bcc.in<span style="color: rgb(71, 115, 115); ">$</span>sx)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">data.frame(<span style="color: rgb(92, 70, 193); ">"eff"</span>=<span style="color: rgb(36, 0, 150); ">1</span><span style="color: rgb(189, 68, 147); ">/</span>bcc.out<span style="color: rgb(71, 115, 115); ">$</span>eff, <span style="color: rgb(92, 70, 193); ">"pro"</span>=produtos, <span style="color: rgb(92, 70, 193); ">"rad"</span>=<span style="color: rgb(36, 0, 150); ">1</span><span style="color: rgb(189, 68, 147); ">/</span>bcc.out<span style="color: rgb(71, 115, 115); ">$</span>eff <span style="color: rgb(189, 68, 147); ">*</span> produtos,<span style="color: rgb(92, 70, 193); ">"fol"</span>=bcc.out<span style="color: rgb(71, 115, 115); ">$</span>sy,</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; "><span class="Apple-tab-span" style="white-space: pre; "> </span><span style="color: rgb(92, 70, 193); ">"alv"</span>=produtos <span style="color: rgb(189, 68, 147); ">+</span> bcc.out<span style="color: rgb(71, 115, 115); ">$</span>sy)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">bcc.out.irs <- dea(insumos, produtos, RTS=<span style="color: rgb(92, 70, 193); ">"irs"</span>, ORIENTATION=<span style="color: rgb(92, 70, 193); ">"out"</span>, SLACK=<span style="color: rgb(162, 0, 149); ">TRUE</span>) <span style="color: rgb(48, 149, 95); "># eff BCC out orientado rend crescentes</span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">bcc.out.drs <- dea(insumos, produtos, RTS=<span style="color: rgb(92, 70, 193); ">"drs"</span>, ORIENTATION=<span style="color: rgb(92, 70, 193); ">"out"</span>, SLACK=<span style="color: rgb(162, 0, 149); ">TRUE</span>) <span style="color: rgb(48, 149, 95); "># eff BCC out orientado rend decrescentes</span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">data.frame(<span style="color: rgb(92, 70, 193); ">"CRS"</span>=ccr.out<span style="color: rgb(71, 115, 115); ">$</span>eff,<span style="color: rgb(92, 70, 193); ">"VRS"</span>=bcc.out<span style="color: rgb(71, 115, 115); ">$</span>eff, <span style="color: rgb(92, 70, 193); ">"IRS"</span>=bcc.out.irs<span style="color: rgb(71, 115, 115); ">$</span>eff, <span style="color: rgb(92, 70, 193); ">"DRS"</span>=bcc.out.drs<span style="color: rgb(71, 115, 115); ">$</span>eff,</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; "><span class="Apple-tab-span" style="white-space: pre; "> </span><span style="color: rgb(92, 70, 193); ">"E_ESC"</span>=ccr.out<span style="color: rgb(71, 115, 115); ">$</span>eff<span style="color: rgb(189, 68, 147); ">/</span>bcc.out<span style="color: rgb(71, 115, 115); ">$</span>eff, </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; "><span class="Apple-tab-span" style="white-space: pre; "> </span><span style="color: rgb(92, 70, 193); ">"REND"</span>=ifelse(ccr.out<span style="color: rgb(71, 115, 115); ">$</span>eff <span style="color: rgb(189, 68, 147); ">==</span> bcc.out<span style="color: rgb(71, 115, 115); ">$</span>eff <span style="color: rgb(189, 68, 147); ">|</span> bcc.out<span style="color: rgb(71, 115, 115); ">$</span>eff <span style="color: rgb(189, 68, 147); ">==</span> bcc.out.irs<span style="color: rgb(71, 115, 115); ">$</span>eff <span style="color: rgb(189, 68, 147); ">&</span> bcc.out<span style="color: rgb(71, 115, 115); ">$</span>eff <span style="color: rgb(189, 68, 147); ">==</span> bcc.out.drs<span style="color: rgb(71, 115, 115); ">$</span>eff, </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; "><span class="Apple-tab-span" style="white-space: pre; "> </span><span style="color: rgb(92, 70, 193); ">"constante"</span>, ifelse(bcc.out<span style="color: rgb(71, 115, 115); ">$</span>eff <span style="color: rgb(189, 68, 147); ">==</span> bcc.out.irs<span style="color: rgb(71, 115, 115); ">$</span>eff <span style="color: rgb(189, 68, 147); ">&</span> bcc.out<span style="color: rgb(71, 115, 115); ">$</span>eff <span style="color: rgb(189, 68, 147); ">!=</span> bcc.out.drs<span style="color: rgb(71, 115, 115); ">$</span>eff,<span style="color: rgb(92, 70, 193); ">"crescente"</span>,<span style="color: rgb(92, 70, 193); ">"decrescen"</span>)))</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># de modo equivalente pode-se escrever</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">data.frame(<span style="color: rgb(92, 70, 193); ">"CRS"</span>=ccr.out<span style="color: rgb(71, 115, 115); ">$</span>eff,<span style="color: rgb(92, 70, 193); ">"VRS"</span>=bcc.out<span style="color: rgb(71, 115, 115); ">$</span>eff, <span style="color: rgb(92, 70, 193); ">"IRS"</span>=bcc.out.irs<span style="color: rgb(71, 115, 115); ">$</span>eff, <span style="color: rgb(92, 70, 193); ">"DRS"</span>=bcc.out.drs<span style="color: rgb(71, 115, 115); ">$</span>eff,</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; "><span class="Apple-tab-span" style="white-space: pre; "> </span><span style="color: rgb(92, 70, 193); ">"E_ESC"</span>=ccr.out<span style="color: rgb(71, 115, 115); ">$</span>eff<span style="color: rgb(189, 68, 147); ">/</span>bcc.out<span style="color: rgb(71, 115, 115); ">$</span>eff, </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; "><span class="Apple-tab-span" style="white-space: pre; "> </span><span style="color: rgb(92, 70, 193); ">"REND"</span>=ifelse(ccr.out<span style="color: rgb(71, 115, 115); ">$</span>eff <span style="color: rgb(189, 68, 147); ">==</span> bcc.out<span style="color: rgb(71, 115, 115); ">$</span>eff <span style="color: rgb(189, 68, 147); ">|</span> bcc.out<span style="color: rgb(71, 115, 115); ">$</span>eff <span style="color: rgb(189, 68, 147); ">==</span> bcc.out.irs<span style="color: rgb(71, 115, 115); ">$</span>eff <span style="color: rgb(189, 68, 147); ">&</span> bcc.out<span style="color: rgb(71, 115, 115); ">$</span>eff <span style="color: rgb(189, 68, 147); ">==</span> bcc.out.drs<span style="color: rgb(71, 115, 115); ">$</span>eff, </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; "><span class="Apple-tab-span" style="white-space: pre; "> </span><span style="color: rgb(92, 70, 193); ">"constante"</span>, ifelse(bcc.out<span style="color: rgb(71, 115, 115); ">$</span>eff <span style="color: rgb(189, 68, 147); ">==</span> bcc.out.drs<span style="color: rgb(71, 115, 115); ">$</span>eff,<span style="color: rgb(92, 70, 193); ">"decrescen"</span>,<span style="color: rgb(92, 70, 193); ">"crescente"</span>)))</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); ">### CUIDADO!! quando exite diferença entre as variáves selecionadas, considerando muitas casa </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); ">### decimais, pode ocorrer equívocuo na análise de rendimentos de escala. para evitar esse erro é necessário </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); ">### limitar o número de casa decinais com a função round(x, digits=n)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">print(cbind(<span style="color: rgb(92, 70, 193); ">"CRS"</span>=ccr.out<span style="color: rgb(71, 115, 115); ">$</span>eff, <span style="color: rgb(92, 70, 193); ">"VRS"</span>=bcc.out<span style="color: rgb(71, 115, 115); ">$</span>eff, <span style="color: rgb(92, 70, 193); ">"IRS"</span>=bcc.out.irs<span style="color: rgb(71, 115, 115); ">$</span>eff,<span style="color: rgb(92, 70, 193); ">"DRS"</span>=bcc.out.drs<span style="color: rgb(71, 115, 115); ">$</span>eff), digits=<span style="color: rgb(36, 0, 150); ">18</span>)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">ee <- data.frame(round((cbind(<span style="color: rgb(92, 70, 193); ">"CRS"</span>=ccr.out<span style="color: rgb(71, 115, 115); ">$</span>eff, <span style="color: rgb(92, 70, 193); ">"VRS"</span>=bcc.out<span style="color: rgb(71, 115, 115); ">$</span>eff, <span style="color: rgb(92, 70, 193); ">"IRS"</span>=bcc.out.irs<span style="color: rgb(71, 115, 115); ">$</span>eff,<span style="color: rgb(92, 70, 193); ">"DRS"</span>=bcc.out.drs<span style="color: rgb(71, 115, 115); ">$</span>eff)), </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; "><span class="Apple-tab-span" style="white-space: pre; "> </span>digits=<span style="color: rgb(36, 0, 150); ">6</span>))</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">data.frame(ee, <span style="color: rgb(92, 70, 193); ">"E_ESC"</span>=ee<span style="color: rgb(71, 115, 115); ">$</span>CRS<span style="color: rgb(189, 68, 147); ">/</span>ee<span style="color: rgb(71, 115, 115); ">$</span>VRS,<span style="color: rgb(92, 70, 193); ">"REND"</span>=ifelse(ee<span style="color: rgb(71, 115, 115); ">$</span>CRS <span style="color: rgb(189, 68, 147); ">==</span> ee<span style="color: rgb(71, 115, 115); ">$</span>VRS <span style="color: rgb(189, 68, 147); ">|</span> ee<span style="color: rgb(71, 115, 115); ">$</span>VRS <span style="color: rgb(189, 68, 147); ">==</span> ee<span style="color: rgb(71, 115, 115); ">$</span>IRS <span style="color: rgb(189, 68, 147); ">&</span> ee<span style="color: rgb(71, 115, 115); ">$</span>VRS <span style="color: rgb(189, 68, 147); ">==</span> ee<span style="color: rgb(71, 115, 115); ">$</span>DRS, </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; "><span class="Apple-tab-span" style="white-space: pre; "> </span><span style="color: rgb(92, 70, 193); ">"constante"</span>, ifelse(ee<span style="color: rgb(71, 115, 115); ">$</span>VRS <span style="color: rgb(189, 68, 147); ">==</span> ee<span style="color: rgb(71, 115, 115); ">$</span>IRS <span style="color: rgb(189, 68, 147); ">&</span> ee<span style="color: rgb(71, 115, 115); ">$</span>VRS <span style="color: rgb(189, 68, 147); ">!=</span> ee<span style="color: rgb(71, 115, 115); ">$</span>DRS,<span style="color: rgb(92, 70, 193); ">"crescente"</span>,<span style="color: rgb(92, 70, 193); ">"decrescen"</span>)))</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># o problema dual BCC (vrs) output orientado é de minimização, na forma multiplicada que considera os pesos dos </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># insumos (u) e produtos (v)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">bcc.out.dual <- dea.dual(insumos, produtos, RTS=<span style="color: rgb(92, 70, 193); ">"vrs"</span>, ORIENTATION=<span style="color: rgb(92, 70, 193); ">"out"</span>) <span style="color: rgb(48, 149, 95); "># problema dual</span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">names(bcc.out.dual)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">print(cbind(<span style="color: rgb(92, 70, 193); ">"eff"</span>=bcc.out.dual<span style="color: rgb(71, 115, 115); ">$</span>eff, bcc.out.dual<span style="color: rgb(71, 115, 115); ">$</span>u, bcc.out.dual<span style="color: rgb(71, 115, 115); ">$</span>v), digits=<span style="color: rgb(36, 0, 150); ">5</span>)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); ">######## Análise de Supereficiência #######</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># ver Coll e Blasco (2006) capítulo 4 página 135</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># ver Ferreira e Gomes (2009) capítulo 4 página 136</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">s.ccr.in <- sdea(insumos, produtos, RTS=<span style="color: rgb(92, 70, 193); ">"crs"</span>, ORIENTATION=<span style="color: rgb(92, 70, 193); ">"in"</span>)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">data.frame(<span style="color: rgb(92, 70, 193); ">"CRS"</span>=ccr.in<span style="color: rgb(71, 115, 115); ">$</span>eff, <span style="color: rgb(92, 70, 193); ">"CCR_SUPER"</span>=s.ccr.in<span style="color: rgb(71, 115, 115); ">$</span>eff)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">s.ccr.out <- sdea(insumos, produtos, RTS=<span style="color: rgb(92, 70, 193); ">"crs"</span>, ORIENTATION=<span style="color: rgb(92, 70, 193); ">"out"</span>)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">data.frame(<span style="color: rgb(92, 70, 193); ">"CCR"</span>=<span style="color: rgb(36, 0, 150); ">1</span><span style="color: rgb(189, 68, 147); ">/</span>ccr.out<span style="color: rgb(71, 115, 115); ">$</span>eff, <span style="color: rgb(92, 70, 193); ">"CCR_SUPER"</span>=<span style="color: rgb(36, 0, 150); ">1</span><span style="color: rgb(189, 68, 147); ">/</span>s.ccr.out<span style="color: rgb(71, 115, 115); ">$</span>eff)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); ">######## Modelo FHD #######</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># ver Ferreira e Gomes (2009) capítulo 4 página 143</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">bcc.in.fhd <- dea(insumos, produtos, RTS=<span style="color: rgb(92, 70, 193); ">"fdh"</span>, ORIENTATION=<span style="color: rgb(92, 70, 193); ">"in"</span>)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">data.frame(<span style="color: rgb(92, 70, 193); ">"CRS"</span>=ccr.in<span style="color: rgb(71, 115, 115); ">$</span>eff,<span style="color: rgb(92, 70, 193); ">"VRS"</span>=bcc.in<span style="color: rgb(71, 115, 115); ">$</span>eff, <span style="color: rgb(92, 70, 193); ">"IRS"</span>=bcc.in.irs<span style="color: rgb(71, 115, 115); ">$</span>eff, <span style="color: rgb(92, 70, 193); ">"DRS"</span>=bcc.in.drs<span style="color: rgb(71, 115, 115); ">$</span>eff, <span style="color: rgb(92, 70, 193); ">"FHD"</span>=bcc.in.fhd<span style="color: rgb(71, 115, 115); ">$</span>eff)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">bcc.out.fhd <- dea(insumos, produtos, RTS=<span style="color: rgb(92, 70, 193); ">"fdh"</span>, ORIENTATION=<span style="color: rgb(92, 70, 193); ">"out"</span>)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">data.frame(<span style="color: rgb(92, 70, 193); ">"CRS"</span>=<span style="color: rgb(36, 0, 150); ">1</span><span style="color: rgb(189, 68, 147); ">/</span>ccr.out<span style="color: rgb(71, 115, 115); ">$</span>eff,<span style="color: rgb(92, 70, 193); ">"VRS"</span>=<span style="color: rgb(36, 0, 150); ">1</span><span style="color: rgb(189, 68, 147); ">/</span>bcc.out<span style="color: rgb(71, 115, 115); ">$</span>eff, <span style="color: rgb(92, 70, 193); ">"IRS"</span>=<span style="color: rgb(36, 0, 150); ">1</span><span style="color: rgb(189, 68, 147); ">/</span>bcc.out.irs<span style="color: rgb(71, 115, 115); ">$</span>eff, <span style="color: rgb(92, 70, 193); ">"DRS"</span>=<span style="color: rgb(36, 0, 150); ">1</span><span style="color: rgb(189, 68, 147); ">/</span>bcc.out.drs<span style="color: rgb(71, 115, 115); ">$</span>eff, </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; "><span class="Apple-tab-span" style="white-space: pre; "> </span><span style="color: rgb(92, 70, 193); ">"FHD"</span>=<span style="color: rgb(36, 0, 150); ">1</span><span style="color: rgb(189, 68, 147); ">/</span>bcc.out.fhd<span style="color: rgb(71, 115, 115); ">$</span>eff)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); ">######## Seleção de variáveis ########</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">cor(coll.blasco, use = <span style="color: rgb(92, 70, 193); ">"all.obs"</span>, method = c(<span style="color: rgb(92, 70, 193); ">"spearman"</span>)) <span style="color: rgb(48, 149, 95); "># teste de correlação de Spearman</span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">cor(coll.blasco, use = <span style="color: rgb(92, 70, 193); ">"all.obs"</span>, method = c(<span style="color: rgb(92, 70, 193); ">"kendall"</span>)) <span style="color: rgb(48, 149, 95); "># teste de correlação de Kendall</span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">cor(coll.blasco, use = <span style="color: rgb(92, 70, 193); ">"all.obs"</span>, method = c(<span style="color: rgb(92, 70, 193); ">"pearson"</span>)) <span style="color: rgb(48, 149, 95); "># teste de correlação de Pearson</span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); ">######## Eficiência custo (econômica), alocativa, receita e lucro #######</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; color: rgb(48, 149, 95); "># ver Ferreira e Gomes (2009) capítulo 5 página 213</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">ins <- data.frame(insumos)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">p.ins <- data.frame(<span style="color: rgb(92, 70, 193); ">"px1"</span>=c(<span style="color: rgb(36, 0, 150); ">2</span>,<span style="color: rgb(36, 0, 150); ">2</span>,<span style="color: rgb(36, 0, 150); ">2</span>,<span style="color: rgb(36, 0, 150); ">2</span>,<span style="color: rgb(36, 0, 150); ">2</span>,<span style="color: rgb(36, 0, 150); ">2</span>), <span style="color: rgb(92, 70, 193); ">"px2"</span>=c(<span style="color: rgb(36, 0, 150); ">6</span>,<span style="color: rgb(36, 0, 150); ">4</span>,<span style="color: rgb(36, 0, 150); ">3</span>,<span style="color: rgb(36, 0, 150); ">4</span>,<span style="color: rgb(36, 0, 150); ">3</span>,<span style="color: rgb(36, 0, 150); ">2</span>))</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">eff.cost <- cost.opt(ins, produtos, p.ins, RTS=<span style="color: rgb(92, 70, 193); ">"vrs"</span>)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">print(cbind(ins,p.ins,</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; "><span class="Apple-tab-span" style="white-space: pre; "> </span><span style="color: rgb(92, 70, 193); ">"custo_min"</span>= eff.cost<span style="color: rgb(71, 115, 115); ">$</span>cost, </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; "><span class="Apple-tab-span" style="white-space: pre; "> </span><span style="color: rgb(92, 70, 193); ">"eff_econ"</span>=eff.cost<span style="color: rgb(71, 115, 115); ">$</span>cost<span style="color: rgb(189, 68, 147); ">/</span> (ins<span style="color: rgb(71, 115, 115); ">$</span>x1 <span style="color: rgb(189, 68, 147); ">*</span> p.ins<span style="color: rgb(71, 115, 115); ">$</span>px1 <span style="color: rgb(189, 68, 147); ">+</span> ins<span style="color: rgb(71, 115, 115); ">$</span>x2 <span style="color: rgb(189, 68, 147); ">*</span> p.ins<span style="color: rgb(71, 115, 115); ">$</span>px2), </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; "><span class="Apple-tab-span" style="white-space: pre; "> </span><span style="color: rgb(92, 70, 193); ">"eff_tec"</span>=bcc.in<span style="color: rgb(71, 115, 115); ">$</span>eff, </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; "><span class="Apple-tab-span" style="white-space: pre; "> </span><span style="color: rgb(92, 70, 193); ">"eff_aloc"</span>=(eff.cost<span style="color: rgb(71, 115, 115); ">$</span>cost<span style="color: rgb(189, 68, 147); ">/</span> (ins<span style="color: rgb(71, 115, 115); ">$</span>x1 <span style="color: rgb(189, 68, 147); ">*</span> p.ins<span style="color: rgb(71, 115, 115); ">$</span>px1 <span style="color: rgb(189, 68, 147); ">+</span> ins<span style="color: rgb(71, 115, 115); ">$</span>x2 <span style="color: rgb(189, 68, 147); ">*</span> p.ins<span style="color: rgb(71, 115, 115); ">$</span>px2))<span style="color: rgb(189, 68, 147); ">/</span>bcc.in<span style="color: rgb(71, 115, 115); ">$</span>eff),digits=<span style="color: rgb(36, 0, 150); ">3</span>)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; min-height: 15px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">pro <- data.frame(produtos)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">p.pro <- matrix(<span style="color: rgb(36, 0, 150); ">1</span>,nrow=dim(pro)<span style="color: rgb(71, 115, 115); ">[</span><span style="color: rgb(36, 0, 150); ">1</span><span style="color: rgb(71, 115, 115); ">]</span>,ncol=<span style="color: rgb(36, 0, 150); ">2</span>)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">eff.renevue <- revenue.opt(ins, pro, p.pro, RTS=<span style="color: rgb(92, 70, 193); ">"vrs"</span>)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 11px/normal Monaco; ">eff.profit <- profit.opt(ins, pro, p.ins, p.ins, RTS=<span style="color: rgb(92, 70, 193); ">"vrs"</span>)</div><div><br></div></div></div></body></html>