{"id":96,"date":"2023-11-10T21:18:05","date_gmt":"2023-11-10T21:18:05","guid":{"rendered":"https:\/\/dataenvelopment.com\/gams\/?p=96"},"modified":"2023-11-10T21:19:09","modified_gmt":"2023-11-10T21:19:09","slug":"chapter-3-fig-3-05","status":"publish","type":"post","link":"https:\/\/dataenvelopment.com\/gams\/chapter-3-fig-3-05\/","title":{"rendered":"Chapter 3 (Fig. 3.05) – The mathematical formulation of the VRS-DEA model with exogenously fixed inputs and the corresponding GAMS formulation"},"content":{"rendered":"\n
$Title Chapter 3 (Fig. 3.5)\r\n$Title Mathematical formulation of the VRS-DEA model with exogenously fixed inputs 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        d(g)  Inputs \/ProdCost, TrnCost\/\r\n        k(g)  Exogenously fixed inputs \/HoldInv\/\r\n        r(g) Outputs \/SatDem, Rev\/;\r\n        alias(jj,j);\r\n        alias(kk,jj);\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\nVariables efficiency objective function\r\n          Theta     efficiency (Theta values)\r\n          Lambda(j) dual weights (Lambda values)\r\n          sminus_nf(d) slacks assigned to inputs under managerial control\r\n          sminus_f(k)  slacks assigned to exogenously fixed inputs\r\n          splus(r) slacks assigned to inputs;\r\n\r\nNonnegative variables\r\n          Lambda(j)\r\n          sminus_nf(d)\r\n          sminus_f(k)\r\n          splus(r);\r\n\r\nParameters DMU_data(g) slice of data\r\n           eff(j) efficiency report\r\n           Lamres(j,j) peers for each DMU\r\n           slacks(j,g) slacks for inputs and outputs;\r\n\r\nEquations OBJ objective function\r\n          CON1(d) input constraint for inputs under managerial control\r\n          CON2(k) input constraint for exogenously fixed inputs\r\n          CON3(r) output dual\r\n          CON4    VRS constraint;\r\n\r\nOBJ..       efficiency=E=Theta-1E-6*(SUM(d,sminus_nf(d))+SUM(r,splus(r)));\r\n\r\nCON1(d)..  SUM(j, Lambda(j)*Data(j,d))+sminus_nf(d)=E=Theta*DMU_data(d);\r\nCON2(k)..  SUM(j, Lambda(j)*Data(j,k))+sminus_f(k)=E=DMU_data(k);\r\nCON3(r)..  SUM(j, Lambda(j)*Data(j,r))-splus(r)=E=DMU_data(r);\r\nCON4..     SUM(j, Lambda(j))=E=1;\r\nmodel Exogenous_input_DEA_VRS Exogenously input oriented DEA model \/OBJ, CON1, CON2, CON3, CON4\/;\r\n\r\n\r\n\r\nloop(jj,\r\n   DMU_data(g) = Data(jj,g);\r\n   solve Exogenous_input_DEA_VRS using LP minimizing Efficiency ;\r\n   eff(jj)=Theta.l;\r\n   slacks(jj,d)=sminus_nf.l(d);\r\n   slacks(jj,k)=sminus_f.l(k);\r\n   slacks(jj,r)=splus.l(r);\r\n   loop(kk,\r\n      Lamres(jj,kk)=Lambda.l(kk);\r\n    );\r\n);\r\n\r\nDisplay eff, Lamres, slacks;\r\n\r\nexecute_unload<\/pre>\n","protected":false},"excerpt":{"rendered":"
$Title Chapter 3 (Fig. 3.5) $Title Mathematical formulation of the VRS-DEA model with exogenously fixed inputs and the corresponding GAMS code $onText If using this code, please cite: ——————————————————————————— 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. ——————————————————————————— Website: […]<\/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\/96"}],"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=96"}],"version-history":[{"count":1,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/posts\/96\/revisions"}],"predecessor-version":[{"id":130,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/posts\/96\/revisions\/130"}],"wp:attachment":[{"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/media?parent=96"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/categories?post=96"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/tags?post=96"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}