{"id":95,"date":"2023-11-10T12:28:47","date_gmt":"2023-11-10T12:28:47","guid":{"rendered":"https:\/\/dataenvelopment.com\/gams\/?p=95"},"modified":"2025-02-21T08:13:31","modified_gmt":"2025-02-21T08:13:31","slug":"chapter-2-fig-2-17-2","status":"publish","type":"post","link":"https:\/\/dataenvelopment.com\/gams\/chapter-2-fig-2-17-2\/","title":{"rendered":"Chapter 2 (Fig. 2.17) – The mathematical formulation of the multiplier VRS DEA model and the corresponding GAMS formulation"},"content":{"rendered":"\n
$Title Chapter 2 (Fig. 2.17)\n$Title Mathematical formulation of the multiplier VRS DEA model and the corresponding GAMS code\n\n$onText\n\nIf using this code, please cite:\n\n---------------------------------------------------------------------------------\nEmrouznejad, A., P. Petridis, and V. Charles (2023). Data Envelopment Analysis\nwith GAMS: A Handbook on Productivity Analysis, and Performance Measurement,\nSpringer, ISBN: 978-3-031-30700-3.\n---------------------------------------------------------------------------------\n\nWebsite: https:\/\/dataenvelopment.com\/GAMS\/\n\n$offText\n\nSets    j DMUs \/DMU1*DMU10\/\n        g Inputs and Outputs \/ProdCost, TrnCost, HoldInv, SatDem, Rev\/\n        i(g)  Inputs \/ProdCost, TrnCost, HoldInv\/\n        r(g) Outputs \/SatDem, Rev\/;\n        alias(jj,j);\n        alias(k,jj);\n\nTable Data(j,g) Data for inputs and outputs\n\n           ProdCost     TrnCost      HoldInv     SatDem      Rev\nDMU1        0.255        0.161        0.373        20        2.64\nDMU2        0.98         0.248        0.606        6         5.29\nDMU3        0.507        0.937        0.749        17        2.43\nDMU4        0.305        0.249        0.841        2         8.99\nDMU5        0.659        0.248        0.979        19        2.94\nDMU6        0.568        0.508        0.919        17        0.75\nDMU7        0.583        0.628        0.732        17        6.36\nDMU8        0.627        0.675        0.738        10        7.2\nDMU9        0.772        0.657        0.486        9         2.16\nDMU10       0.917        0.639        0.234        8         7.3;\n\n\nVariables efficiency objective function\n          mu\n          v(i) dual input\n          u(r) dual output;\n\nNonnegative variables\n          v(i) dual input\n          u(r) dual output;\n\nParameters DMU_data(g) slice of data\n           eff(j) efficiency report\n           res_v(j,i) results for dual input\n           res_u(j,r) results for dual output\n           res_mu(j)  results for mu;\n\n\nEquations OBJ objective function\n          CON1(j)\n          CON2;\n\nOBJ..       efficiency=E=SUM(r,u(r)*DMU_data(r))+mu;\n\nCON1(j)..   SUM(r,u(r)*Data(j,r))-SUM(i,v(i)*Data(j,i))+mu=L=0;\n\nCON2..      SUM(i,v(i)*DMU_data(i))=E=1;\n\nmodel DEA_CRS input oriented DEA CRS \/ OBJ, CON1, CON2 \/;\n\n\n\nloop(jj,\n   DMU_data(g) = Data(jj,g);\n   solve DEA_CRS using LP Maximizing efficiency;\n   eff(jj)=efficiency.l;\n   res_v(jj,i)=v.l(i);\n   res_u(jj,r)=u.l(r);\n   res_mu(jj)=mu.l;\n   );\n\nDisplay eff, res_v, res_u, res_mu;<\/pre>\n","protected":false},"excerpt":{"rendered":"
$Title Chapter 2 (Fig. 2.17) $Title Mathematical formulation of the multiplier 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\/95"}],"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=95"}],"version-history":[{"count":4,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/posts\/95\/revisions"}],"predecessor-version":[{"id":237,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/posts\/95\/revisions\/237"}],"wp:attachment":[{"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/media?parent=95"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/categories?post=95"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/tags?post=95"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}