{"id":94,"date":"2023-11-10T21:23:46","date_gmt":"2023-11-10T21:23:46","guid":{"rendered":"https:\/\/dataenvelopment.com\/gams\/?p=94"},"modified":"2023-11-10T21:24:39","modified_gmt":"2023-11-10T21:24:39","slug":"chapter-3-fig-3-09","status":"publish","type":"post","link":"https:\/\/dataenvelopment.com\/gams\/chapter-3-fig-3-09\/","title":{"rendered":"Chapter 3 (Fig. 3.09) – The mathematical formulation of the DEA model with undesirable outputs and the corresponding"},"content":{"rendered":"\n
$Title Chapter 3 (Fig. 3.9)\r\n$Title Mathematical formulation of the DEA model with undesirable outputs 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,CO2\/\r\n           i(g)  Inputs \/ProdCost, TrnCost,HoldInv\/\r\n           d(g) Outputs \/SatDem, Rev\/\r\n           k(g)  Undesirable Output \/CO2\/;\r\n           alias(jj,j);\r\n           alias(kk,jj);\r\n\r\n\r\nTable Data(j,g) Data for inputs and outputs\r\n\r\n           ProdCost     TrnCost      HoldInv     SatDem      Rev        CO2\r\nDMU1        0.255        0.161        0.373        20        2.64       7.3\r\nDMU2        0.98         0.248        0.606        6         5.29       6.63\r\nDMU3        0.507        0.937        0.749        17        2.43       10.3\r\nDMU4        0.305        0.249        0.841        2         8.99       5.4\r\nDMU5        0.659        0.248        0.979        19        2.94       18.9\r\nDMU6        0.568        0.508        0.919        17        0.75       4.51\r\nDMU7        0.583        0.628        0.732        17        6.36       8.91\r\nDMU8        0.627        0.675        0.738        10        7.2        8.2\r\nDMU9        0.772        0.657        0.486        9         2.16       14.2\r\nDMU10       0.917        0.639        0.234        8         7.3        5.1;\r\n\r\n\r\n\r\n  Variables efficiency objective function\r\n            Beta     inefficiency score(Beta values)\r\n            Lambda(j) dual weights (Lambda values);\r\n\r\n  Nonnegative variables\r\n            Lambda(j)\r\n            Beta;\r\n\r\n  Parameters DMU_data(g) slice of data\r\n             eff(j) Beta values\r\n             Lamres(j,j) peers for each DMU\r\n             slacks(j,g) slacks for inputs and outputs;\r\n\r\n  Equations OBJ objective function\r\n            CON1(i) input constraint\r\n            CON2(d) output constraint for desirable outputs\r\n            CON3(k) output dual\r\n            CON4    VRS constraint;\r\n\r\n  OBJ..       efficiency=E=Beta;\r\n\r\n  CON1(i)..  SUM(j, Lambda(j)*Data(j,i))=L=DMU_data(i);\r\n  CON2(d)..  SUM(j, Lambda(j)*Data(j,d))=G=DMU_data(d)+beta*DMU_data(d);\r\n  CON3(k)..  SUM(j, Lambda(j)*Data(j,k))=L=DMU_data(k)-beta*DMU_data(k);\r\n  CON4..     SUM(j, Lambda(j))=E=1;\r\n  model Undesirable_output_DEA Undesirable output DEA model \/OBJ, CON1, CON2, CON3, CON4\/;\r\n\r\n  loop(jj,\r\n      DMU_data(g) = Data(jj,g);\r\n       solve Undesirable_output_DEA using LP maximizing Efficiency ;\r\n       eff(jj)=beta.l;\r\n       loop(kk,\r\n          Lamres(jj,kk)=Lambda.l(kk);\r\n        );\r\n    );\r\n\r\n    Display eff, Lamres;\r\n\r\n    execute_unload<\/pre>\n","protected":false},"excerpt":{"rendered":"
$Title Chapter 3 (Fig. 3.9) $Title Mathematical formulation of the DEA model with undesirable outputs 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\/ […]<\/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\/94"}],"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=94"}],"version-history":[{"count":1,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/posts\/94\/revisions"}],"predecessor-version":[{"id":131,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/posts\/94\/revisions\/131"}],"wp:attachment":[{"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/media?parent=94"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/categories?post=94"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/tags?post=94"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}