{"id":86,"date":"2023-11-10T21:51:17","date_gmt":"2023-11-10T21:51:17","guid":{"rendered":"https:\/\/dataenvelopment.com\/gams\/?p=86"},"modified":"2023-11-10T21:52:36","modified_gmt":"2023-11-10T21:52:36","slug":"chapter-4-fig-4-06","status":"publish","type":"post","link":"https:\/\/dataenvelopment.com\/gams\/chapter-4-fig-4-06\/","title":{"rendered":"Chapter 4 (Fig. 4.06) – (The mathematical formulation of the RAM model"},"content":{"rendered":"\n
$Title Chapter 4 (Fig. 4.6)\r\n$Title Mathematical formulation of the 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          Lambda(j) dual weights (Lambda values)\r\n          sminus(i) slacks assigned to inputs\r\n          splus(r) slacks assigned to outputs;\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) optimal values objective function\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           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\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(i) input duals\r\n          CON2(r) output dual\r\n          CON3(i) upper bound for input slack\r\n          CON4(r) upper bound for output slack\r\n          CON5 VRS;\r\n\r\n\r\nOBJ..       efficiency=E=1-1\/(m+s)*{SUM(i,sminus(i)\/Rminus(i))+SUM(r,splus(r)\/Rplus(r))};\r\n\r\nCON1(i)..  SUM(j, Lambda(j)*Data(j,i))+sminus(i)=E=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)..  sminus(i)=L=Rminus(i);\r\n\r\nCON4(r)..  splus(r)=L=Rplus(r);\r\n\r\nCON5..     SUM(j, Lambda(j))=E=1;\r\n\r\n\r\nmodel RAM Range Adjusted Measure model\r\n         \/ OBJ, CON1, CON2, CON3, CON4, CON5\/;\r\n\r\nloop(jj,\r\n   DMU_data(g) = Data(jj,g);\r\n   solve RAM using LP maximizing efficiency;\r\n   eff(jj)=efficiency.l;\r\n   loop(k,\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. 4.6) $Title Mathematical formulation of the 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 j […]<\/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\/86"}],"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=86"}],"version-history":[{"count":1,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/posts\/86\/revisions"}],"predecessor-version":[{"id":138,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/posts\/86\/revisions\/138"}],"wp:attachment":[{"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/media?parent=86"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/categories?post=86"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/tags?post=86"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}