{"id":85,"date":"2023-11-10T21:57:31","date_gmt":"2023-11-10T21:57:31","guid":{"rendered":"https:\/\/dataenvelopment.com\/gams\/?p=85"},"modified":"2023-11-10T21:59:45","modified_gmt":"2023-11-10T21:59:45","slug":"chapter-4-fig-4-09","status":"publish","type":"post","link":"https:\/\/dataenvelopment.com\/gams\/chapter-4-fig-4-09\/","title":{"rendered":"Chapter 4 (Fig. 4.09) – The mathematical formulation of the dual RAM model"},"content":{"rendered":"\n
$Title Chapter 4 (Fig. 4.9)\r\n$Title Mathematical formulation of the dual RAM 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 RAM model\r\n          v(i) input dual\r\n          mu(r) output dual\r\n          u0 constraint dual;\r\n\r\nNonnegative variables\r\n          v(i) input dual\r\n          mu(r) output dual;\r\n\r\nParameters DMU_data(g) slice of data\r\n           eff(j) optimal values objective function\r\n           Rminus(i) range for inputs i\r\n           Rplus(r) range for outputs r\r\n           m cardinal of set of inputs\r\n           s cardinal of set of outputs\r\n           res_v(j,i) results of v(i)\r\n           res_mu(j,r) results of mu(r);\r\n\r\nRminus(i)=smax(j,Data(j,i))- smin(j,Data(j,i));\r\nRplus(r)=smax(j,Data(j,r))- smin(j,Data(j,r));\r\n\r\nm=CARD(i);\r\ns=CARD(r);\r\n\r\n\r\n\r\nEquations OBJ objective function\r\n          CON1(j)\r\n          CON2(i) upper bound for input dual\r\n          CON3(r) upper bound for output dual;\r\n\r\n\r\nOBJ..       efficiency=E=SUM(i,v(i)*DMU_data(i))-SUM(r,mu(r)*DMU_data(r))-u0;\r\n\r\nCON1(j)..  SUM(i,v(i)*Data(j,i))-SUM(r,mu(r)*Data(j,r))-u0=G=0;\r\n\r\nCON2(i)..  v(i)=G=1\/Rminus(i);\r\n\r\nCON3(r)..  mu(r)=G=1\/Rplus(r);\r\n\r\n\r\nmodel Dual_RAM Dual Range Adjusted Measure model\r\n         \/ OBJ, CON1, CON2, CON3\/;\r\n\r\nloop(jj,\r\n   DMU_data(g) = Data(jj,g);\r\n   solve Dual_RAM using LP minimizing efficiency;\r\n   eff(jj)=1-efficiency.l;\r\n   res_v(jj,i)=v.l(i);\r\n   res_mu(jj,r)=mu.l(r);\r\n   );\r\n\r\nDisplay res_v, res_mu, eff\r\nExecute_unload<\/pre>\n","protected":false},"excerpt":{"rendered":"
$Title Chapter 4 (Fig. 4.9) $Title Mathematical formulation of the dual RAM 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 Sets […]<\/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\/85"}],"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=85"}],"version-history":[{"count":1,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/posts\/85\/revisions"}],"predecessor-version":[{"id":139,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/posts\/85\/revisions\/139"}],"wp:attachment":[{"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/media?parent=85"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/categories?post=85"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/tags?post=85"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}