$Title Chapter 5 (Fig. 5.1) $Title Mathematical formulation for Allocative and Cost Efficiency 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 /Prodc, Trn, Inv, SatDem, Rev/ i(g) Inputs /Prodc, Trn, Inv/ r(g) Outputs /SatDem, Rev/; alias(jj,j); alias(k,jj); Table Data(j,g) Data for inputs and outputs Prodc Trn Inv SatDem Rev DMU1 10 100 61 20 2.64 DMU2 52 125 100 6 5.29 DMU3 24 54 56 17 2.43 DMU4 45 91 14 2 8.99 DMU5 51 10 67 19 2.94 DMU6 52 26 56 17 0.75 DMU7 22 35 34 17 6.36 DMU8 91 56 101 10 7.2 DMU9 43 72 55 9 2.16 DMU10 34 39 16 8 7.3; Table Cost(j,i) Cost Data for inputs Prodc Trn Inv DMU1 0.255 0.161 0.373 DMU2 0.98 0.248 0.606 DMU3 0.507 0.937 0.749 DMU4 0.305 0.249 0.841 DMU5 0.659 0.248 0.979 DMU6 0.568 0.508 0.919 DMU7 0.583 0.628 0.732 DMU8 0.627 0.675 0.738 DMU9 0.772 0.657 0.486 DMU10 0.917 0.639 0.234; Variables efficiency objective function cost_efficiency cost efficiency Theta efficiency (Theta values); Nonnegative variables l(j) dual weights (Lambda values) x_t(i) auxilliary variable for c*theta; Parameters DMU_data(g) slice of data cst(i) slice of cost data eff(j) efficiency tech_eff(j) technical efficiency cost_eff(j) cost efficiency alloc_eff(j) allocative efficiency lamres(j,j) peers for each DMU; Equations OBJ_INP objective function for input VRS model OBJ_COST objective function for cost efficiency model CON1_COST(i) inputs for cost efficiency model CON1_INP(i) input duals for input VRS model CON2_INP(r) output dual for input VRS model CON3 VRS orientation; OBJ_INP.. efficiency=E=Theta; CON1_INP(i).. SUM(j, l(j)*Data(j,i))=L=Theta*DMU_data(i); CON2_INP(r).. SUM(j, l(j)*Data(j,r))=G=DMU_data(r); CON3.. SUM(j, l(j))=E=1; OBJ_COST.. cost_efficiency=E=SUM(i,cst(i)*x_t(i)); CON1_COST(i).. SUM(j, l(j)*Data(j,i))=L=x_t(i); model INPUT_DEA_VRS input oriented DEA CRS / OBJ_INP, CON1_INP, CON2_INP, CON3/; model COST_DEA_VRS input oriented DEA CRS / OBJ_COST, CON1_COST, CON2_INP, CON3/; loop(jj, DMU_data(g) = Data(jj,g); cst(i) = Cost(jj,i); solve INPUT_DEA_VRS using LP minimizing Theta; solve COST_DEA_VRS using LP minimizing cost_efficiency; cost_eff(jj) = SUM(i,cst(i)*x_t.l(i))/SUM(i,cst(i)*DMU_data(i)); eff(jj)=Theta.l; tech_eff(jj)= eff(jj); alloc_eff(jj) = cost_eff(jj)/tech_eff(jj); loop(k, Lamres(jj,k)=l.l(k); ); ); display eff, lamres, tech_eff, cost_eff, alloc_eff; execute_unload