1. Schedule Reading material for DEA: F:\COURSES\UGRADS\INDR\INDR471\SHARE\reading material Homework 1 is due to tomorrow 17:00 (27-02-2009). Homework 2 will be placed today and it will be due to next Friday (06-03-2009).

2. Fractional Program (FP): Linear Program (LP):

3. Dual of the Linear Program (DLP-I):

4. Modified Dual of the Linear Program (DLP-II):

5. Today We will write and solve the corresponding DLP I and II to analyze a simple DEA problem. Here is our data set: DMUABCDEFG Input I1I1 47842103 I2I2 3312417 OutputO1111111

6. Graphically...

7. Obtain file(s): Copy and paste the excel file to your own accounts: F:\COURSES\UGRADS\INDR\INDR471\SHARE\Labs\lab1-DLP-raw.xls Also open the power point file: F:\COURSES\UGRADS\INDR\INDR471\SHARE\labs\DEA-Lab-26-02-09.ppt

8. 1 Solve the DLP for DMU A in Excel. Keep the sensitivity report.

9. 1.a What are the efficiencies of DMU A? Is it purely technical (or ratio)? It is only ratio inefficient because 1.Efficiency is 0.8571<1 2.lagrange multipliers lar weights’dir.values are positive (not mixed inefficient)

10. 1.b What are the values of k ’s? Observe the correspondence between these values and the shadow prices of the LP in part 1. They are in the solution.

11. 1.c Use the values of k ’s to determine the reference set for DMU A, and to compute the level of input for each DMU to be ratio (or purely technical) efficient? Compare your new computations with the levels you found in part 1.b of last week’s lecture. What can you say about the output levels? I1a=I 1a *efficiency=lambda D *Id+lambda E *Ie

12. 1.d What are the shadow prices of the constraints? Observe the correspondence between these values and the optimal weights of the LP solved last week. Lagrange multipliers

13. 1.e Consider DMU A. Construct the hypothetical composite unit (HCU) of A using DLP I, call this unit as DMU Q. I 1a,I 2a are the hypothetical composite unit Solve the DLP I for DMU Q. Verify that DMU Q is efficient. YOU TRY THIS LATER AT HOME…

14. 1 – Repeat for F Solve the DLP for DMU F in Excel. Keep the sensitivity report.

15. 1.a What are the efficiencies of DMU F? Is it purely technical (or ratio)? Mixed inefficiency because efficiency=1 and one of the lagrange multipliers are equal to zero So we have to solve the dual II and find how mixed ineff. is this.

16. 1.b What are the values of k ’s? Observe the correspondence between these values and the shadow prices of the LP in part 1.

17. 1.c Use the values of k ’s to determine the reference set for DMU F, and to compute the level of input for each DMU to be ratio (or purely technical) efficient?

18. 2.d What are the shadow prices of the constraints?

19. DLP- II Given the value of  * from Phase I, construct and solve the following LP:

20. 2 Let  e * be the efficiency of DMU e that is computed in part 2 for e=F. Use the value of  e * to solve the above LP for DMU F. Keep the sensitivity report.

21. 2.a What are the values of k ’s? Are they different from those you found in part 1? Why?

22. 2.b What are the values of the slack variables for DMU F? Using this information with the solution of DLP I, identify the DMUs as efficient, ratio inefficient, mix inefficient and both ratio and mix inefficient.

23. 2.c Compute the level of input for each DMU to be CCR-efficient. Compare these with your answers of part 1.c.

24. Hypothetical composite unit (HCU) and target setting for inefficient for DMU e HCU is always CCR-efficient. Input targets: Output targets: CCR projections.

25. 3.a. Discuss the meaning of v 1 of A, and its effect on the efficiency of the corresponding DMUs. How about v 2 ? Compute the efficiency of A if the corresponding input is decreased by one unit.

26. 3.b. How can you interpret the relation between the weights v 1 and v 2 of A, and the corresponding slacks, s 1 - and s 2 -, using the complementary slackness condition?