{"id":182,"date":"2024-03-25T12:05:22","date_gmt":"2024-03-25T12:05:22","guid":{"rendered":"https:\/\/dataenvelopment.com\/gams\/?p=182"},"modified":"2024-03-25T12:10:24","modified_gmt":"2024-03-25T12:10:24","slug":"chapter-3-fig-3-19-2","status":"publish","type":"post","link":"https:\/\/dataenvelopment.com\/gams\/chapter-3-fig-3-19-2\/","title":{"rendered":"Chapter 3 (Fig. 3.19) – The Mathematical formulation of stochastic (Chance constraints) efficiency models and the corresponding GAMS code"},"content":{"rendered":"\n
$Title Chapter 3 (Fig. 3.19)\n$Title Mathematical formulation of stochastic (Chance constraints) efficiency models and the corresponding GAMS code\n\n$onText\n\nIf using this code, please cite:\n\n---------------------------------------------------------------------------------\nEmrouznejad, A., P. Petridis, and V. Charles (2023). Data Envelopment Analysis\nwith GAMS: A Handbook on Productivity Analysis, and Performance Measurement,\nSpringer, ISBN: 978-3-031-30700-3.\n---------------------------------------------------------------------------------\n\nWebsite: https:\/\/dataenvelopment.com\/GAMS\/\n\n$offText\n\nOption NLP=KNITRO;\n\n Sets    j DMUs \/DMU1*DMU10\/\n           g Inputs and Outputs \/ProdCost,TrnCost, HoldInv, SatDem, Rev\/\n           i(g)  Inputs \/ProdCost, TrnCost, HoldInv\/\n           r(g) Outputs \/SatDem, Rev\/\n           alias(jj,j);\n\n\nTable Data(j,g) Data for inputs and outputs\n\n           ProdCost     TrnCost      HoldInv     SatDem      Rev\nDMU1        0.255        0.161        0.373        20        2.64\nDMU2        0.98         0.248        0.606        6         5.29\nDMU3        0.507        0.937        0.749        17        2.43\nDMU4        0.305        0.249        0.841        2         8.99\nDMU5        0.659        0.248        0.979        19        2.94\nDMU6        0.568        0.508        0.919        17        0.75\nDMU7        0.583        0.628        0.732        17        6.36\nDMU8        0.627        0.675        0.738        10        7.2\nDMU9        0.772        0.657        0.486        9         2.16\nDMU10       0.917        0.639        0.234        8         7.3;\n\n\nParameters var_in(i) variance for inputs,\n           var_out(r) Variance for outputs,\n           mux(i) average of inputs,\n           muy(r) average of outputs,\n           Data_DMU(g),\n           cc1,\n           sigma_out(r),\n           sigma_in(i),\n           DMU_data_stoch_form(g),\n           res_stat(j);\n\n\n     mux(i)=(1\/CARD(j))*SUM(j,Data(j,i));\n     muy(r)=(1\/CARD(j))*SUM(j,Data(j,r));\n\n******************Output parameters****************************************************************\n    var_out(r)= (1\/(CARD(j)-1))*SUM(j,power((Data(j,r)-muy(r)),2));\n    sigma_out(r) = sqrt(var_out(r));\n***************************************************************************************************\n\n******************Input parameters*****************************************************************\n    var_in(i)= (1\/(CARD(j)-1))*SUM(j,power((Data(j,i)-mux(i)),2));\n    sigma_in(i) = sqrt(var_in(i));\n***************************************************************************************************\n\n\n Scalar Alpha \/0.5\/;\n Parameter FF frictional function;\n FF=errorf(Alpha);\n\n  Variables objective      objective function for model\n            Lambda(j)      dual weights (Lambda values)\n            Phi            Output efficiency scores;\n\n  Nonnegative variables\n            Lambda(j)      dual weights (Lambda values)\n            sminus(i)      input slack variable\n            splus(r)       output slack variable;\n\n  Parameters DMU_data(g)     slice of data\n             Lamres(j,j)     peers for each DMU\n             res_Phi(j)      output efficiency results;\n\n\n  Equations OBJ objective function\n            CON1(r) output constraint\n            CON2(i) input constraint\n            VRS     VRS constraint;\n\n\nOBJ..      objective=E=Phi+1E-3*(SUM(i,sminus(i))+SUM(r,splus(r)));\n\nCON1(r)..  Phi*DMU_data_stoch_form(r)-SUM(j$(ord(j)<>cc1), Lambda(j)*Data(j,r))+splus(r)=E=0;\n\nCON2(i)..  SUM(j$(ord(j)<>cc1), Lambda(j)*Data(j,i))+sminus(i)=E=DMU_data_stoch_form(i);\n\nVRS..      SUM(j,Lambda(j))=E=1;\n\nmodel Chance_DEA_constraints \/OBJ, CON1, CON2, VRS\/;\n\n  loop(jj,\n      DMU_data(g) = Data(jj,g);\n      DMU_data_stoch_form(r) = DMU_data(r) - FF*sigma_out(r);\n      DMU_data_stoch_form(i) = DMU_data(i) + FF*sigma_in(i);\n      cc1 = ord(jj);\n      solve Chance_DEA_constraints max objective using LP;\n      res_Phi(jj)=Phi.l;\n      res_stat(jj)=Chance_DEA_constraints.modelstat;\n);\n\ndisplay res_Phi;\n\n    execute_unload<\/pre>\n","protected":false},"excerpt":{"rendered":"
$Title Chapter 3 (Fig. 3.19) $Title Mathematical formulation of stochastic (Chance constraints) efficiency models 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\/182"}],"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=182"}],"version-history":[{"count":3,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/posts\/182\/revisions"}],"predecessor-version":[{"id":186,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/posts\/182\/revisions\/186"}],"wp:attachment":[{"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/media?parent=182"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/categories?post=182"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/tags?post=182"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}