{"id":145,"date":"2023-11-10T22:16:07","date_gmt":"2023-11-10T22:16:07","guid":{"rendered":"https:\/\/dataenvelopment.com\/gams\/?p=145"},"modified":"2023-11-10T22:16:56","modified_gmt":"2023-11-10T22:16:56","slug":"chapter-5-fig-5-06","status":"publish","type":"post","link":"https:\/\/dataenvelopment.com\/gams\/chapter-5-fig-5-06\/","title":{"rendered":"Chapter 5 (Fig. 5.06) – The mathematical formulation for Technical and Revenue Efficiency"},"content":{"rendered":"\n
$Title Chapter 5 (Fig. 5.6)\r\n$Title Mathematical formulation for Technical and Revenue Efficiency 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 \/Prodc, Trn, Inv, SatDem, Quantity\/\r\n        i(g)  Inputs \/Prodc, Trn, Inv\/\r\n        r(g) Outputs \/SatDem, Quantity\/;\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        Prodc        Trn        Inv      SatDem   Quantity\r\nDMU1        10        100       61        20        100\r\nDMU2        52        125       100        6        150\r\nDMU3        24        54        56        17        50\r\nDMU4        45        91        14        2         510\r\nDMU5        51        10        67        19        400\r\nDMU6        52        26        56        17        60\r\nDMU7        22        35        34        17        250\r\nDMU8        91        56        101       10        35\r\nDMU9        43        72        55         9        90\r\nDMU10       34        39        16         8        650;\r\n\r\n\r\n\r\nTable Price(j,r) Cost Data for inputs\r\n\r\n        SatDem      Quantity\r\nDMU1        2        2.64\r\nDMU2        3        5.29\r\nDMU3        10       2.43\r\nDMU4        5        8.99\r\nDMU5        1        2.94\r\nDMU6        3        0.75\r\nDMU7        7        6.36\r\nDMU8        8        7.2\r\nDMU9        3        2.16\r\nDMU10       9        7.3;\r\n\r\n\r\n\r\nVariables efficiency objective function\r\n          rev_efficiency revenue efficiency for input DEA model\r\n          Phi     efficiency (Phi values);\r\n\r\nNonnegative variables\r\n          l(j) dual weights (Lambda values)\r\n          y_t(r) auxilliary variable for p*phi;\r\n\r\nParameters DMU_data(g) slice of data\r\n           prs(r) slice of price data\r\n           eff(j) efficiency\r\n           tech_eff(j) technical efficiency\r\n           rev_eff(j) revenue efficiency\r\n           lamres(j,j) peers for each DMU;\r\n\r\nEquations OBJ_OUT objective function for output VRS model\r\n          OBJ_REV objective function for revenue efficiency model\r\n          CON1_REV(r) inputs for revenue efficiency model\r\n          CON1_OUT(i) input duals for output VRS model\r\n          CON2_OUT(r) output dual for output VRS model\r\n          CON3 VRS orientation;\r\n\r\nOBJ_OUT..       efficiency=E=Phi;\r\n\r\nCON1_OUT(i)..  SUM(j, l(j)*Data(j,i))=L=DMU_data(i);\r\n\r\nCON2_OUT(r)..  SUM(j, l(j)*Data(j,r))=G=Phi*DMU_data(r);\r\n\r\nCON3..         SUM(j, l(j))=E=1;\r\n\r\nOBJ_REV..       rev_efficiency=E=SUM(r,prs(r)*y_t(r));\r\n\r\nCON1_REV(r)..   SUM(j, l(j)*Data(j,r))=G=y_t(r);\r\n\r\nmodel OUTPUT_DEA_VRS input oriented DEA VRS \/ OBJ_OUT, CON1_OUT, CON2_OUT, CON3\/;\r\nmodel REV_DEA_VRS input oriented DEA VRS \/ OBJ_REV, CON1_OUT, CON1_REV, CON3\/;\r\n\r\n\r\nloop(jj,\r\n   DMU_data(g) = Data(jj,g);\r\n   prs(r) = Price(jj,r);\r\n   solve OUTPUT_DEA_VRS using LP maximizing Phi;\r\n   solve REV_DEA_VRS using LP maximizing rev_efficiency;\r\n   rev_eff(jj) = SUM(r,prs(r)*DMU_data(r))\/SUM(r,prs(r)*y_t.l(r));\r\n   eff(jj)=Phi.l;\r\n   tech_eff(jj)= 1\/eff(jj);\r\n   loop(k,\r\n      Lamres(jj,k)=l.l(k);\r\n    );\r\n);\r\n\r\ndisplay  eff,  tech_eff, rev_eff;\r\n\r\nexecute_unload<\/pre>\n","protected":false},"excerpt":{"rendered":"
$Title Chapter 5 (Fig. 5.6) $Title Mathematical formulation for Technical and Revenue Efficiency 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\/145"}],"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=145"}],"version-history":[{"count":1,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/posts\/145\/revisions"}],"predecessor-version":[{"id":146,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/posts\/145\/revisions\/146"}],"wp:attachment":[{"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/media?parent=145"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/categories?post=145"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/tags?post=145"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}