{"id":82,"date":"2023-11-10T22:09:41","date_gmt":"2023-11-10T22:09:41","guid":{"rendered":"https:\/\/dataenvelopment.com\/gams\/?p=82"},"modified":"2023-11-10T22:11:16","modified_gmt":"2023-11-10T22:11:16","slug":"chapter-4-fig-4-21","status":"publish","type":"post","link":"https:\/\/dataenvelopment.com\/gams\/chapter-4-fig-4-21\/","title":{"rendered":"Chapter 4 (Fig. 4.21) &#8211; The mathematical formulation of the SORM model"},"content":{"rendered":"\n<pre class=\"wp-block-preformatted\">$Title Chapter 4 (Fig. 4.21)\r\n$Title Mathematical formulation of the SORM model 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        k(g) Negative Outputs \/Rev\/\r\n        r(g) Outputs \/SatDem\/;\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\ndmu_data(g), res_eff(j), Y1(j,k), Y2(j,k), lamres(j,j), y1_s(k), y2_s(k), stat(j);\r\n\r\n\r\nloop(jj,\r\n     y1(jj,k)$(data(jj,k)>=0)=data(jj,k);\r\n     y1(jj,k)$(data(jj,k)&lt;0)=0;\r\n     y2(jj,k)$(data(jj,k)>=0)=0;\r\n     y2(jj,k)$(data(jj,k)&lt;0)=-data(jj,k);\r\n);\r\n\r\n\r\nvariables h efficiency measure;\r\nnonnegative variables l(j) peers of DMU j;\r\n\r\nEQUATIONS\r\n\r\n\r\nCON1(i) Inputs constraint\r\nCON2(r) Positive Outputs constraint\r\nCON3(k) Negative output constraint Y1\r\nCON4(k) Negative output constraint Y2\r\nCON5 VRS;\r\n\r\n\r\nCON1(i).. SUM(j,l(j)*Data(j,i))=L=dmu_data(i)*h;\r\nCON2(r).. SUM(j,l(j)*Data(j,r))=G=dmu_data(r);\r\nCON3(k).. SUM(j,l(j)*y1(j,k))=G=y1_s(k);\r\nCON4(k).. SUM(j,l(j)*y2(j,k))=L=y2_s(k);\r\nCON5..    SUM(j,l(j))=E=1;\r\n\r\nModel SORM\/All\/\r\n\r\nloop(jj,\r\n    dmu_data(g) = Data(jj,g);\r\n    y1_s(k)=y1(jj,k);\r\n    y2_s(k)=y2(jj,k);\r\n    Solve SORM min h using LP;\r\n    res_eff(jj) = h.l;\r\n    stat(jj) = SORM.modelstat;\r\n    loop(kk,\r\n      Lamres(jj,kk)=l.l(kk);\r\n    );\r\n );\r\n\r\ndisplay res_eff, lamres;\r\n\r\nexecute_unload<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>$Title Chapter 4 (Fig. 4.21) $Title Mathematical formulation of the SORM model 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. &#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; Website: https:\/\/dataenvelopment.com\/GAMS\/ $offText Sets j [&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\/82"}],"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=82"}],"version-history":[{"count":1,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/posts\/82\/revisions"}],"predecessor-version":[{"id":142,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/posts\/82\/revisions\/142"}],"wp:attachment":[{"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/media?parent=82"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/categories?post=82"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/dataenvelopment.com\/gams\/wp-json\/wp\/v2\/tags?post=82"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}