{"id":164,"date":"2024-03-25T11:44:12","date_gmt":"2024-03-25T11:44:12","guid":{"rendered":"https:\/\/dataenvelopment.com\/gams\/?p=164"},"modified":"2024-03-25T11:44:59","modified_gmt":"2024-03-25T11:44:59","slug":"chapter-6-fig-6-04","status":"publish","type":"post","link":"https:\/\/dataenvelopment.com\/gams\/chapter-6-fig-6-04\/","title":{"rendered":"Chapter 6 (Fig. 6.04) &#8211; The Mathematical formulation for the Modified MOLP DEA model for output values and the corresponding GAMS code"},"content":{"rendered":"\n<pre class=\"wp-block-preformatted\">$Title Chapter 6 (Fig. 6.4)\r\n$Title Mathematical formulation for the Modified MOLP DEA model for output values and the corresponding GAMS code\r\n\r\n$onText\r\n\r\nIf using this code, please cite:\r\n\r\n---------------------------------------------------------------------------------\r\nEmrouznejad, A., P. Petridis, and V. Charles (2023). Data Envelopment Analysis\r\nwith GAMS: A Handbook on Productivity Analysis, and Performance Measurement,\r\nSpringer, ISBN: 978-3-031-30700-3.\r\n---------------------------------------------------------------------------------\r\n\r\nWebsite: https:\/\/dataenvelopment.com\/GAMS\/\r\n\r\n$offText\r\n\r\nSets    j DMUs \/DMU1*DMU10\/\r\n        sc scenarios \/SC1*SC100\/\r\n        g Inputs and Outputs \/Prodc, Trn, Inv, SatDem, Rev\/\r\n        i(g)  Inputs \/Prodc, Trn, Inv\/\r\n        r(g) Outputs \/SatDem, Rev\/;\r\n        alias(jj,j);\r\n        alias(k,jj);\r\n\r\nTable Data(j,g) Data for inputs and outputs\r\n\r\n            Prodc     Trn      Inv         SatDem        Rev\r\nDMU1        10        100       61           20         2.64\r\nDMU2        52        125       100          6          5.29\r\nDMU3        24         54       56           17         2.43\r\nDMU4        45         91       14            2         8.99\r\nDMU5        51         10       67           19         2.94\r\nDMU6        52         26       56           17         0.75\r\nDMU7        22         35       34           17         6.36\r\nDMU8        91         56       101          10         7.2\r\nDMU9        43         72       55            9         2.16\r\nDMU10       34         39       16            8         7.3;\r\n\r\n\r\nParameter w(sc) weights on outputs for scenario s\r\n\r\nloop(sc,\r\n   w(sc)=ORD(sc)\/100;\r\n   );\r\n\r\n\r\nVariables efficiency objective function\r\n          sigma(r)  \u00ef\u00bf\u00bd*y;\r\n\r\nNonnegative variables\r\n          l(j) dual weights (Lambda values);\r\n\r\nParameters DMU_data(g) slice of data\r\n           lamres(j,j) peers for each DMU\r\n           res_sigma(r,sc) results for sigma for each scenario s\r\n           ww slice of res_sigma;\r\n\r\n\r\nEquations  OBJ Objective function of the MOLP model\r\n           CON1(i) Input constraints for MOLP model\r\n           CON2(r) Output constraints for MOLP model;\r\n\r\nOBJ..       efficiency=E=sigma('SatDem')*ww*DMU_data('SatDem')+sigma('Rev')*(1-ww)*DMU_data('Rev');\r\n\r\nCON1(i)..  SUM(j, l(j)*Data(j,i))=L=DMU_data(i);\r\n\r\nCON2(r)..  SUM(j, l(j)*Data(j,r))=E=sigma(r)*DMU_data(r);\r\n\r\nmodel MOLP_DEA Multi Objective LP DEA \/All\/;\r\n\r\nloop(sc,\r\n ww = w(sc);\r\n loop(jj,\r\n   DMU_data(g) = Data(jj,g);\r\n   solve MOLP_DEA using LP maximizing efficiency;\r\n   loop(k,\r\n      Lamres(jj,k)=l.l(k);\r\n    );\r\n    res_sigma(r,sc)= sigma.l(r);\r\n );\r\n);\r\n\r\n\r\ndisplay  res_sigma;\r\n\r\nexecute_unload<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>$Title Chapter 6 (Fig. 6.4) $Title Mathematical formulation for the Modified MOLP DEA model for output values and the corresponding GAMS code $onText If using this code, please cite: &#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212; Emrouznejad, A., P. Petridis, and V. Charles (2023). Data Envelopment Analysis with GAMS: A Handbook on Productivity Analysis, and Performance Measurement, Springer, ISBN: 978-3-031-30700-3. &#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212; [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[2],"tags":[],"_links":{"self":[{"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/posts\/164"}],"collection":[{"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/comments?post=164"}],"version-history":[{"count":2,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/posts\/164\/revisions"}],"predecessor-version":[{"id":166,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/posts\/164\/revisions\/166"}],"wp:attachment":[{"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/media?parent=164"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/categories?post=164"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/tags?post=164"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}