{"id":87,"date":"2023-11-10T21:48:48","date_gmt":"2023-11-10T21:48:48","guid":{"rendered":"https:\/\/dataenvelopment.com\/gams\/?p=87"},"modified":"2023-11-10T21:49:41","modified_gmt":"2023-11-10T21:49:41","slug":"chapter-4-fig-4-01","status":"publish","type":"post","link":"https:\/\/dataenvelopment.com\/gams\/chapter-4-fig-4-01\/","title":{"rendered":"Chapter 4 (Fig. 4.01) – The mathematical formulation of the non-radial VRS DEA model"},"content":{"rendered":"\n
$Title Chapter 4 (Fig. 4.1)\r\n$Title Mathematical formulation of the non-radial VRS DEA model 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(k,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 for radial model\r\n          efficiency_nr objective function for non-radial model\r\n          Theta(i)     efficiency (Theta values) for second stage\r\n          Lambda(j) dual weights (Lambda values)\r\n          splus(r) slacks assigned to inputs;\r\n\r\nNonnegative variables\r\n          Lambda(j)\r\n          sminus(i)\r\n          splus(r);\r\n\r\nParameters DMU_data(g) slice of data\r\n           eff(j,i) Optimal values for Theta(i) for each DMU\r\n           slice_theta(i) slice of efficiency for second stage of non-radial model\r\n           lamres(j,j) peers for each DMU\r\n           slacks(j,g) slacks for inputs and outputs\r\n           m ;\r\n           m=CARD(i);\r\n\r\nEquations OBJ objective function\r\n          CON1(i) input duals\r\n          CON2(r) output dual\r\n          CON3(i) Theta less than 1\r\n          CON4 VRS orientation\r\n          OBJ_nr objective function of input slack non-radial model\r\n          CON1_nr(i) input duals non-radial model\r\n          CON2_nr(r) output duals non-radial model;\r\n\r\nOBJ..       efficiency=E=1\/m*{SUM(i,Theta(i))-1E-6*SUM(r,splus(r))};\r\n\r\nCON1(i)..  SUM(j, Lambda(j)*Data(j,i))=E=Theta(i)*DMU_data(i);\r\n\r\nCON2(r)..  SUM(j, Lambda(j)*Data(j,r))-splus(r)=E=DMU_data(r);\r\n\r\nCON3(i)..  Theta(i)=L=1;\r\n\r\nCON4..     SUM(j, Lambda(j))=E=1;\r\n\r\nOBJ_nr..       efficiency_nr=E=SUM(r,splus(r));\r\n\r\nCON1_nr(i)..  SUM(j, Lambda(j)*Data(j,i))=E=Theta(i)*DMU_data(i);\r\n\r\nCON2_nr(r)..  SUM(j, Lambda(j)*Data(j,r))-splus(r)=E=DMU_data(r);\r\n\r\nmodel DEA_radial_VRS input oriented for radial\r\n         \/ OBJ, CON1, CON2, CON3, CON4\/;\r\n\r\nmodel DEA_non_radial_VRS input slack for non-radial\r\n         \/ OBJ_nr, CON1_nr, CON2_nr, CON4\/;\r\n\r\nloop(jj,\r\n   DMU_data(g) = Data(jj,g);\r\n   solve DEA_radial_VRS using LP minimizing Efficiency;\r\n   eff(jj,i)=Theta.l(i);\r\n   loop(k,\r\n      Lamres(jj,k)=Lambda.l(k);\r\n    );\r\n);\r\n\r\nloop(jj,\r\n   DMU_data(g) = Data(jj,g);\r\n   slice_theta(i)=eff(jj,i);\r\n   solve DEA_non_radial_VRS using LP maximizing Efficiency_nr ;\r\n   slacks(jj,r)=splus.l(r);\r\n   loop(kk,\r\n      Lamres(jj,k)=Lambda.l(k);\r\n    );\r\n);\r\n\r\nExecute_unload<\/pre>\n","protected":false},"excerpt":{"rendered":"
$Title Chapter 4 (Fig. 4.1) $Title Mathematical formulation of the non-radial VRS DEA model 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: https:\/\/dataenvelopment.com\/GAMS\/ $offText […]<\/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\/87"}],"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=87"}],"version-history":[{"count":1,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/posts\/87\/revisions"}],"predecessor-version":[{"id":137,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/posts\/87\/revisions\/137"}],"wp:attachment":[{"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/media?parent=87"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/categories?post=87"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/tags?post=87"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}