{"id":84,"date":"2023-11-10T22:04:58","date_gmt":"2023-11-10T22:04:58","guid":{"rendered":"https:\/\/dataenvelopment.com\/gams\/?p=84"},"modified":"2023-11-10T22:06:46","modified_gmt":"2023-11-10T22:06:46","slug":"chapter-4-fig-4-18","status":"publish","type":"post","link":"https:\/\/dataenvelopment.com\/gams\/chapter-4-fig-4-18\/","title":{"rendered":"Chapter 4 (Fig. 4.18) – The mathematical formulation of MSBM for negative data (inputs\/outputs)"},"content":{"rendered":"\n
$Title Chapter 4 (Fig. 4.18)\r\n$Title Mathematical formulation of MSBM for negative data (inputs\/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\/\r\n        i(g)  Inputs \/ProdCost, TrnCost, HoldInv\/\r\n        r(g) Outputs \/SatDem, Rev\/;\r\n        alias(jj,j);\r\n        alias(jj,kk);\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\nParameters\r\n\r\nRplus(j,r), Rminus(j,i), max_y(r), min_x(i), dmu_data(g), Rmin(i), Rpl(r), res_eff(j), Lamres(j,j), stat(j);\r\n\r\nmax_y(r) = smax(j,Data(j,r));\r\nmin_x(i) = smax(j,Data(j,i));\r\n\r\nloop(jj,\r\n   Rplus(jj,r) =  max_y(r) - Data(jj,r);\r\n   Rminus(jj,i) =  Data(jj,i) - min_x(i);\r\n   );\r\n\r\nRplus(jj,r)$(Rplus(jj,r)=0)=10**3;\r\nRminus(jj,i)$(Rminus(jj,i)=0)=10**3;\r\n\r\nparameters w(i), v(r);\r\n\r\nw(i) = 1\/CARD(i);\r\nv(r) = 1\/CARD(r);\r\n\r\nvariables tau efficiency measure;\r\nnonnegative variables lambda(j) peers of DMU j,\r\n                      t auxiliary variable,\r\n                      sminus(i) slack variable for inputs,\r\n                      splus(r) slack variable for outputs;\r\n\r\nEQUATIONS\r\n\r\n\r\nOBJ  Objective function\r\nCON1(i) Inputs constraint\r\nCON2(r) Outputs constraint\r\nCON3\r\nCON4;\r\n\r\n\r\nOBJ..    tau =E=t-SUM(i,(sminus(i)*w(i))\/Rmin(i));\r\nCON1(i).. SUM(j,lambda(j)*Data(j,i))+sminus(i)=E=dmu_data(i)*t;\r\nCON2(r).. SUM(j,lambda(j)*Data(j,r))-splus(r)=E=dmu_data(r)*t;\r\nCON3..    SUM(r,(v(r)*splus(r))\/Rpl(r))+t=E=1;\r\nCON4..    SUM(j,lambda(j))=E=t;\r\n\r\nModel MSBM\/All\/\r\n\r\nloop(jj,\r\n    dmu_data(g) = Data(jj,g);\r\n    Rmin(i) = Rminus(jj,i);\r\n    Rpl(r) =  Rplus(jj,r);\r\n    Solve MSBM min tau using LP;\r\n    res_eff(jj) = tau.l;\r\n    stat(jj) = MSBM.modelstat;\r\n   loop(kk,\r\n      Lamres(jj,kk)=Lambda.l(kk);\r\n    );\r\n );\r\n\r\ndisplay res_eff, lamres;\r\n\r\nexecute_unload<\/pre>\n","protected":false},"excerpt":{"rendered":"
$Title Chapter 4 (Fig. 4.18) $Title Mathematical formulation of MSBM for negative data (inputs\/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\/ $offText […]<\/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\/84"}],"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=84"}],"version-history":[{"count":1,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/posts\/84\/revisions"}],"predecessor-version":[{"id":141,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/posts\/84\/revisions\/141"}],"wp:attachment":[{"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/media?parent=84"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/categories?post=84"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/tags?post=84"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}