Question

The Eastern Washington County School Corporation is interested in comparing educational performance at four elementary schools and has hired you to prepare a DEA model to do so. After detailed conversations with the corporation administrative staff and the building principals, you have isolated the following input and output measurements: Input Measures Output Measures Average classroom size Percent of children in remedial classes Percent of students on reduced-price lunch Average first-grade score on the standard test The average number of parent volunteer hours per week Average fifth-grade score on the standard test Data is collected for each school on each measure                                    School Archer Hayes Ralston Creekside Inputs    Classroom size 21 28 32 20    % reduced lunch 10 8 25 2    Avg. vol. hours 30 46 15 64 Outputs    % remediation 15 12 19 3    1st grade score 83 84 62 85    5th grade score 76 72 53 79 Develop the DEA model that would evaluate the efficiency of Ralston Elementary School.

1. Define the decision variables.
2. Define the objective function.
3. Define the constraints.
4. Determine an optimal solution.

Answer 1

Let         A = the weight applied to inputs and outputs for Archer Elementary

H = the weight applied to inputs and outputs for Hayes Elementary

R = the weight applied to inputs and outputs for Ralston Elementary

C = the weight applied to inputs and outputs for Creekside Elementary

            E = input contribution to composite from Ralston

      Min E

     

      s.t. A + H + R + C = 1

            .15A + .12H + .19R + .03C > .19

            83A + 84H + 62R + 85C > 62

            76A + 72H + 53R + 79C > 53

            -32E +21A + 28H + 32R + 20C < 0

            -.25E+ .10A + .08H + .25R + .02C < 0

            -15E + 30A + 46H + 15R + 64C < 0

All variables >= 0