{"id":148,"date":"2023-11-10T22:19:00","date_gmt":"2023-11-10T22:19:00","guid":{"rendered":"https:\/\/dataenvelopment.com\/gams\/?p=148"},"modified":"2023-11-10T22:19:00","modified_gmt":"2023-11-10T22:19:00","slug":"chapter-5-fig-5-07-the-mathematical-formulation-for-profit-efficiency","status":"publish","type":"post","link":"https:\/\/dataenvelopment.com\/gams\/chapter-5-fig-5-07-the-mathematical-formulation-for-profit-efficiency\/","title":{"rendered":"Chapter 5 (Fig. 5.07) – The mathematical formulation for profit efficiency"},"content":{"rendered":"\n
$Title Chapter 5 (Fig. 5.7)\r\n$Title Mathematical formulation for profit 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\nTable Cost(j,i) Cost Data for inputs\r\n\r\n            Prodc         Trn          Inv\r\nDMU1        0.255        0.161        0.373\r\nDMU2        0.98         0.248        0.606\r\nDMU3        0.507        0.937        0.749\r\nDMU4        0.305        0.249        0.841\r\nDMU5        0.659        0.248        0.979\r\nDMU6        0.568        0.508        0.919\r\nDMU7        0.583        0.628        0.732\r\nDMU8        0.627        0.675        0.738\r\nDMU9        0.772        0.657        0.486\r\nDMU10       0.917        0.639        0.234;\r\n\r\nTable Price(j,r) Price Data for outputs\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          profit_efficiency profit efficiency;\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          x_t(i) auxilliary variable for c*theta;\r\n\r\nParameters DMU_data(g) slice of data\r\n           prs(r) slice of price data\r\n           cst(i) slice of cost data\r\n           profit_eff(j) revenue efficiency\r\n           lamres(j,j) peers for each DMU;\r\n\r\nEquations OBJ_PROFIT Profit efficiency objective function\r\n          CON1_COST(i) Constraint for cost\r\n          CON1_REV(r) Constraint for profit\r\n          CON3 VRS orientation;\r\n\r\nOBJ_PROFIT..    profit_efficiency=E=SUM(r,prs(r)*y_t(r))-SUM(i,cst(i)*x_t(i));\r\nCON1_COST(i)..  SUM(j, l(j)*Data(j,i))=L=x_t(i);\r\nCON1_REV(r)..   SUM(j, l(j)*Data(j,r))=G=y_t(r);\r\nCON3..          SUM(j, l(j))=E=1;\r\n\r\nmodel PROFIT_DEA_VRS profit efficiency \/ALL\/;\r\n\r\n\r\nloop(jj,\r\n   DMU_data(g) = Data(jj,g);\r\n   prs(r) = Price(jj,r);\r\n   cst(i) = Cost(jj,i);\r\n   solve PROFIT_DEA_VRS using LP maximizing profit_efficiency;\r\n   profit_eff(jj) = (SUM(r,prs(r)*DMU_data(r))-SUM(i,cst(i)*DMU_data(i)))\/(SUM(r,prs(r)*y_t.l(r))-SUM(i,cst(i)*x_t.l(i)));\r\n   loop(k,\r\n      Lamres(jj,k)=l.l(k);\r\n    );\r\n);\r\n\r\ndisplay profit_eff, lamres;\r\n\r\nexecute_unload<\/pre>\n","protected":false},"excerpt":{"rendered":"
$Title Chapter 5 (Fig. 5.7) $Title Mathematical formulation for profit 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 j DMUs […]<\/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\/148"}],"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=148"}],"version-history":[{"count":1,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/posts\/148\/revisions"}],"predecessor-version":[{"id":149,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/posts\/148\/revisions\/149"}],"wp:attachment":[{"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/media?parent=148"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/categories?post=148"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/tags?post=148"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}