Data Envelopment Analysis (DEA) was developed to help compare the relative performance of decision-making units. DEA generates an efficiency score between 0 and 1 for each of the units, indicating how effectively they are managing their resources. A compelling feature of DEA is it develops a unique rating system for each unit designed to make them look their best, which should facilitate acceptance of DEA within an organization. For more information on DEA, see Schrage (2001).

MODEL:

! Data Envelope Analysis of Decision Maker Efficiency;

SETS:

 DMU/BL HW NT OP YK EL/: ! Six schools;

    SCORE; ! Each decision making unit has a;

           ! score to be computed;

 FACTOR/COST RICH WRIT SCIN/;

! There is a set of factors, input & output;

  DXF( DMU, FACTOR):  F; ! F( I, J) = Jth factor

                          of DMU I;

ENDSETS

 

DATA:

! Inputs are spending/pupil, % not low income;

! Outputs are Writing score and Science score;

 NINPUTS = 2;  ! The first NINPUTS factors are

                 inputs;

!      The inputs,    the outputs;

   F  =  8939  64.3     25.2   223

         8625  99       28.2   287

        10813  99.6     29.4   317

        10638  96       26.4   291

         6240  96.2     27.2   295

         4719  79.9     25.5   222;

ENDDATA

 

SETS:

  ! Weights used to compute DMU I's score;

  DXFXD(DMU,FACTOR) : W;

ENDSETS

 

! Try to make everyone's score as high as possible;

  MAX = @SUM( DMU: SCORE);

 

! The LP for each DMU to get its score;

  @FOR( DMU( I):

   SCORE( I) = @SUM( FACTOR(J)|J #GT# NINPUTS:

    F(I, J)* W(I, J));

 

! Sum of inputs(denominator) = 1;

   @SUM( FACTOR( J)| J #LE# NINPUTS:

    F( I, J)* W( I, J)) = 1;

! Using DMU I's weights, no DMU can score

 better than 1;

   @FOR( DMU( K):

    @SUM( FACTOR( J)| J #GT# NINPUTS:

     F( K, J) * W( I, J))

      <= @SUM( FACTOR( J)| J #LE# NINPUTS:

       F( K, J) * W( I, J))

   )

  );

 

! The weights must be greater than zero;

  @FOR( DXFXD( I, J): @BND( .00001, X, 100000));

END

Model: DEAMOD