```MODEL: ! Data Envelopment Analysis of Decision Maker Efficiency ; ! Keywords: DEA, Data Envelopment Analysis, Efficiency, Pareto optimal, Benchmarking; SETS: DMU: !The decisionmaking units; SLK, ! Slack variable on SCORE(k) <= 1; SCORE; ! Each decision making unit has a score to be computed; FACTOR: TW; ! There is a set of factors, input & output; DXF( DMU, FACTOR): F, ! F( I, J) = Jth factor of DMU I; W; ! Weights used to compute DMU I's score; ENDSETS DATA: DMU = BL HW NT OP YK EL; ! The schools; ! Inputs are spending/pupil, % not low income; ! Outputs are Writing score and Science score; NINPUTS = 2; ! The first NINPUTS factors are inputs; FACTOR= COST RICH WRIT SCIN; ! The inputs, the outputs; F = 89.39 64.3 25.2 223 ! BL; 86.25 99 28.2 287 ! HW; 108.13 99.6 29.4 317 ! NT; 106.38 96 26.4 291 ! OP; 62.40 96.2 27.2 295 ! YK; 47.19 79.9 25.5 222; ! EL; WGTMIN = .0005; ! Min weight applied to every factor; BIGM = 999999; ! Biggest a weight can be; EPSILON = .000001; ! Zero tolerance; ENDDATA !----------------------------------------------------------; SUBMODEL DEA: ! The Model; ! IU = DMU we are currently considering; ! Try to make the score of DMU IU as high as possible; MAX = TSCORE; TSCORE = @SUM( FACTOR(J)|J #GT# NINPUTS: F(INOW, J)* TW( J)); ! Sum of inputs(denominator) = 1; [SUM21] @SUM( FACTOR( J)| J #LE# NINPUTS: F( INOW, J)* TW( J)) = 1; ! Using DMU IU's weights, no DMU can score better than 1 Note, Numer/Denom <= 1 implies Numer <= Denom; @FOR( DMU( K): [LE1] @SUM( FACTOR( J)| J #GT# NINPUTS: F( K, J) * TW( J)) + SLK(K)= @SUM( FACTOR( J)| J #LE# NINPUTS: F( K, J) * TW( J)) ); ! The weights, TW( ), must be greater than zero; @FOR( FACTOR( j): @BND( WGTMIN, TW(j), BIGM)); ENDSUBMODEL CALC: @SET( 'TERSEO', 2); !Minimal output; !Write out a solution report; @WRITE( @NEWLINE( 2), 32*' ','Factor Weight:', @NEWLINE( 1), ' DMU Score' ); @FOR( FACTOR( I): @WRITE( ' ', FACTOR( I))); @WRITE(' Dominated by some combination of...'); @WRITE( @NEWLINE( 1)); ! Solve the DEA model for each DMU D; @FOR( DMU( D): INOW = D; @SOLVE( DEA); ! Solve the model above; @WRITE( ' ', DMU( D), ' ', @FORMAT( TSCORE, '6.3f'), ' '); @FOR( FACTOR( I): @WRITE( @FORMAT( TW(I), '8.4f'), ' ') ); @IFC( TSCORE #LT# 1 - EPSILON: ! Does D get a score < 1? ; @FOR( DMU(k) | k #NE# D: ! Yes, find those k that get a score of 1, ; @IFC( SLK(k) #LE# EPSILON: ! using D's weights. These k dominate D; @WRITE( ' ', DMU(k)); ); ); ); @WRITE( @NEWLINE( 1)); ); ENDCALC END ```