$Title Chapter 2 (Fig. 2.21) $Title Mathematical formulation of the multiplier CRS DEA model with Assurance Region (AR) constraints 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 Sets j DMUs /DMU1*DMU10/ g Inputs and Outputs /ProdCost, TrnCost, HoldInv, SatDem, Rev/ i(g) Inputs /ProdCost, TrnCost, HoldInv/ r(g) Outputs /SatDem, Rev/; alias(j,jj); Table Data(j,g) Data for inputs and outputs ProdCost TrnCost HoldInv SatDem Rev DMU1 0.255 0.161 0.373 20 2.64 DMU2 0.98 0.248 0.606 6 5.29 DMU3 0.507 0.937 0.749 17 2.43 DMU4 0.305 0.249 0.841 2 8.99 DMU5 0.659 0.248 0.979 19 2.94 DMU6 0.568 0.508 0.919 17 0.75 DMU7 0.583 0.628 0.732 17 6.36 DMU8 0.627 0.675 0.738 10 7.2 DMU9 0.772 0.657 0.486 9 2.16 DMU10 0.917 0.639 0.234 8 7.3; Variables efficiency objective function mu v(i) dual input u(r) dual output; Nonnegative variables v(i) dual input u(r) dual output; Parameters DMU_data(g) slice of data eff(j) efficiency report res_v(j,i) results for dual input res_u(j,r) results for dual output sm(j); Equations OBJ objective function CON1(j) CON2 CON3 CON4 CON5 CON6 CON7 CON8; OBJ.. efficiency=E=SUM(r,u(r)*DMU_data(r)); CON1(j).. SUM(r,u(r)*Data(j,r))-SUM(i,v(i)*Data(j,i))=L=0; CON2.. SUM(i,v(i)*DMU_data(i))=E=1; CON3.. v('TrnCost')=G=0.5*v('ProdCost'); CON4.. v('TrnCost')=L=4*v('ProdCost'); CON5.. v('HoldInv')=G=2*v('ProdCost'); CON6.. v('HoldInv')=L=6*v('ProdCost'); CON7.. u('SatDem')=G=3*u('Rev'); CON8.. u('SatDem')=L=5*u('Rev'); model multiplier_DEA_CRS_AR input oriented DEA CRS / OBJ, CON1, CON2, CON3, CON4, CON5, CON6, CON7, CON8/; loop(jj, DMU_data(i) = Data(jj,i); DMU_data(r) = Data(jj,r); solve multiplier_DEA_CRS_AR using LP Maximizing efficiency; eff(jj)=efficiency.l; res_v(jj,i)=v.l(i); res_u(jj,r)=u.l(r); sm(j)=multiplier_DEA_CRS_AR.modelstat; ); Display eff, res_v, res_u; execute_unload