Chapter 2 (Fig. 2.17) – The mathematical formulation of the multiplier VRS DEA model and the corresponding GAMS formulation

$Title Chapter 2 (Fig. 2.17)
$Title Mathematical formulation of the multiplier VRS DEA model and the corresponding GAMS code

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If using this code, please cite:

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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.
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Website: https://dataenvelopment.com/GAMS/

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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(jj,j);
        alias(k,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
           res_mu(j)  results for mu;


Equations OBJ objective function
          CON1(j)
          CON2;

OBJ..       efficiency=E=SUM(r,u(r)*DMU_data(r))+mu;

CON1(j)..   SUM(r,u(r)*Data(j,r))-SUM(i,v(i)*Data(j,i))+mu=L=0;

CON2..      SUM(i,v(i)*DMU_data(i))=E=1;

model DEA_CRS input oriented DEA CRS / OBJ, CON1, CON2 /;



loop(jj,
   DMU_data(g) = Data(jj,g);
   solve DEA_CRS using LP Maximizing efficiency;
   eff(jj)=efficiency.l;
   res_v(jj,i)=v.l(i);
   res_u(jj,r)=u.l(r);
   res_mu(j)=mu.l;
   );

Display eff, res_v, res_u, res_mu;