{"id":91,"date":"2023-11-10T21:25:59","date_gmt":"2023-11-10T21:25:59","guid":{"rendered":"https:\/\/dataenvelopment.com\/gams\/?p=91"},"modified":"2023-11-10T21:26:42","modified_gmt":"2023-11-10T21:26:42","slug":"chapter-3-fig-3-12","status":"publish","type":"post","link":"https:\/\/dataenvelopment.com\/gams\/chapter-3-fig-3-12\/","title":{"rendered":"Chapter 3 (Fig. 3.12) &#8211; The mathematical formulation of the input-oriented DEA model under strong and weak disposability and congestion index calculation with corresponding GAMS formulation"},"content":{"rendered":"\n<pre class=\"wp-block-preformatted\">$Title Chapter 3 (Fig. 3.12)\r\n$Title Mathematical formulation of the input-oriented DEA model under strong and weak disposability and congestion index calculation 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           g Inputs and Outputs \/ProdCost, TrnCost, HoldInv, SatDem, Rev\/\r\n           i(g)  Inputs \/ProdCost, TrnCost,HoldInv\/\r\n           r(g) Outputs \/SatDem, Rev\/;\r\n           alias(jj,j);\r\n           alias(kk,jj);\r\n\r\n\r\nTable Data(j,g) Data for inputs and outputs\r\n\r\n           ProdCost     TrnCost      HoldInv     SatDem      Rev\r\nDMU1        0.255        0.161        0.373        20        2.64\r\nDMU2        0.98         0.248        0.606        6         5.29\r\nDMU3        0.507        0.937        0.749        17        2.43\r\nDMU4        0.305        0.249        0.841        2         8.99\r\nDMU5        0.659        0.248        0.979        19        2.94\r\nDMU6        0.568        0.508        0.919        17        0.75\r\nDMU7        0.583        0.628        0.732        17        6.36\r\nDMU8        0.627        0.675        0.738        10        7.2\r\nDMU9        0.772        0.657        0.486        9         2.16\r\nDMU10       0.917        0.639        0.234        8         7.3;\r\n\r\n\r\n\r\n  Variables efficiency    objective function for model 1\r\n            efficiency1   objective function for model 2\r\n            Theta          Strong disposability efficiency\r\n            Theta_tilde    Weak disposability efficiency\r\n            Lambda(j)      dual weights (Lambda values);\r\n\r\n  Nonnegative variables\r\n            Lambda(j)      dual weights (Lambda values)\r\n\r\n\r\n  Parameters DMU_data(g) slice of data\r\n             eff_Theta(j)   Strong disposability efficiency values\r\n             eff_Theta_tilde(j)  Weak disposability efficiency values\r\n             Congestion(j) Congestion for each DMU\r\n             Lamres_s(j,j) peers for each DMU for strong disposability model\r\n             Lamres_w(j,j) peers for each DMU for weak disposability model;\r\n\r\n  Equations OBJ_s objective function for strong disposability\r\n            CON1_s(i) input constraint for strong disposability\r\n            CON2_s(r) output constraint for strong disposability\r\n            OBJ_w objective function for weak disposability\r\n            CON1_w(i) input constraint for weak disposability\r\n            CON2_w(r) output constraint for weak disposability\r\n            VRS    VRS constraint;\r\n\r\n  OBJ_s..       efficiency=E=Theta;\r\n\r\n  CON1_s(i)..  SUM(j, Lambda(j)*Data(j,i))=L=Theta*DMU_data(i);\r\n  CON2_s(r)..  SUM(j, Lambda(j)*Data(j,r))=G=DMU_data(r);\r\n\r\n\r\n  OBJ_w..       efficiency1=E=Theta_tilde;\r\n\r\n  CON1_w(i)..  SUM(j, Lambda(j)*Data(j,i))=E=Theta_tilde*DMU_data(i);\r\n  CON2_w(r)..  SUM(j, Lambda(j)*Data(j,r))=G=DMU_data(r);\r\n\r\n  VRS..        SUM(j, Lambda(j))=E=1;\r\n\r\n  model Input_DEA_strong_disposability Input oriented DEA model for strong disposability \/OBJ_s, CON1_s, CON2_s, VRS\/;\r\n  model Input_DEA_weak_disposability  Input oriented DEA model for weak disposability \/OBJ_w, CON1_w, CON2_w, VRS\/;\r\n\r\n  loop(jj,\r\n      DMU_data(g) = Data(jj,g);\r\n       solve Input_DEA_strong_disposability using LP minimizing Theta;\r\n       eff_Theta(jj)=Theta.l;\r\n\r\n       solve Input_DEA_weak_disposability using LP minimizing Theta_tilde;\r\n       eff_Theta_tilde(jj)=Theta_tilde.l;\r\n\r\n       Congestion(jj)=eff_Theta(jj)\/eff_Theta_tilde(jj);\r\n\r\n      );\r\n\r\n    Display eff_Theta, eff_Theta_tilde, congestion;\r\n\r\n    execute_unload<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>$Title Chapter 3 (Fig. 3.12) $Title Mathematical formulation of the input-oriented DEA model under strong and weak disposability and congestion index calculation 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 [&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\/91"}],"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=91"}],"version-history":[{"count":1,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/posts\/91\/revisions"}],"predecessor-version":[{"id":132,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/posts\/91\/revisions\/132"}],"wp:attachment":[{"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/media?parent=91"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/categories?post=91"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/tags?post=91"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}