{"id":89,"date":"2023-11-10T21:33:13","date_gmt":"2023-11-10T21:33:13","guid":{"rendered":"https:\/\/dataenvelopment.com\/gams\/?p=89"},"modified":"2023-11-10T21:34:06","modified_gmt":"2023-11-10T21:34:06","slug":"chapter-3-fig-3-17","status":"publish","type":"post","link":"https:\/\/dataenvelopment.com\/gams\/chapter-3-fig-3-17\/","title":{"rendered":"Chapter 3 (Fig. 3.17) &#8211; The mathematical formulation of categorical variables in DEA under the VRS technol-ogy with the corresponding GAMS formulation"},"content":{"rendered":"\n<pre class=\"wp-block-preformatted\">$Title Chapter 3 (Fig. 3.17)\r\n$Title Mathematical formulation of categorical variables in DEA under the VRS technol-ogy with 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           l categorical orientations \/Or1*Or4\/;\r\n           alias(jj,j);\r\n           alias(kk,jj);\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\nTable w(j,l) Descriptor service vector\r\n\r\n           Or1      Or2      Or3      Or4\r\nDMU1        1        1        1        0\r\nDMU2        0        1        1        1\r\nDMU3        0        0        0        1\r\nDMU4        1        1        1        0\r\nDMU5        1        0        1        0\r\nDMU6        1        1        1        0\r\nDMU7        1        1        1        1\r\nDMU8        1        0        0        0\r\nDMU9        0        0        0        0\r\nDMU10       0        0        0        0;\r\n\r\n\r\n\r\n  Variables objective    objective function for model\r\n            Lambda(j)      dual weights (Lambda values);\r\n\r\n  Nonnegative variables\r\n            Lambda(j)      dual weights (Lambda values)\r\n\r\n  Binary variables\r\n            t(l)           Binary auxiliary variables;\r\n\r\n  Parameters DMU_data(g)     slice of data\r\n             Lamres_s(j,j)   peers for each DMU for strong disposability model\r\n             slice_w(l)      slice of descriptor service vector\r\n             res_t(j,l)      parameter for binary variables;\r\n\r\n\r\n  Equations OBJ objective function\r\n            CON1(i) input constraint\r\n            CON2(r) output constraint\r\n            CON3(l) service orientation\r\n            CON4(l) sequential improvememt constraint\r\n            VRS    VRS constraint;\r\n\r\nOBJ..      objective=E=SUM(l$(ORD(l)&lt;=(CARD(l)-1)),t(l));\r\n\r\nCON1(i)..  SUM(j, Lambda(j)*Data(j,i))=L=DMU_data(i);\r\n\r\nCON2(r)..  SUM(j, Lambda(j)*Data(j,r))=G=DMU_data(r);\r\n\r\nCON3(l)$(ORD(l)&lt;=(CARD(l)-1))..  SUM(j, Lambda(j)*w(j,l))-t(l)=E=slice_w(l);\r\n\r\nCON4(l)$(ORD(l)>=2 AND ORD(l)&lt;=(CARD(l)-1))..  t(l-1)=G=t(l);\r\n\r\nVRS..      SUM(j,Lambda(j))=E=1;\r\n\r\n\r\n  model DEA_categorical MIP model with categorical variables \/OBJ, CON1, CON2, CON3, CON4, VRS\/;\r\n\r\n  loop(jj,\r\n      DMU_data(g) = Data(jj,g);\r\n      slice_w(l)= w(jj,l);\r\n      solve DEA_categorical maximizing objective using MIP ;\r\n      res_t(jj,l)=t.l(l);\r\n);\r\n\r\n    Display res_t;\r\n\r\n    execute_unload<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>$Title Chapter 3 (Fig. 3.17) $Title Mathematical formulation of categorical variables in DEA under the VRS technol-ogy with and the corresponding GAMS code $onText If using this code, please cite: &#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212; 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. [&hellip;]<\/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\/89"}],"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=89"}],"version-history":[{"count":1,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/posts\/89\/revisions"}],"predecessor-version":[{"id":134,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/posts\/89\/revisions\/134"}],"wp:attachment":[{"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/media?parent=89"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/categories?post=89"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/tags?post=89"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}