Schedule Homeworks Homework 3 due to 23 March2009

Schedule • Homeworks: – Homework 3, due to 23 -March-2009 17: 00 – Homework 4, due to 30 -March-2009 17: 00 • Reading homework – Golf (golfers by fried-lambrinos-tyler in EJOR 04. pdf): Next Tuesday (17 -03 -09) due to class time. – Oral and Yolalan (oralyolalan. pdf): due to class time on Thursday, 19 -03 -09. – Modell’s DEA (modell. pdf): due to class time on Thursday, 19 -03 -09.

Obtain file(s): • Copy and paste the excel file to your own accounts: F: COURSESUGRADSINDR 471SHARELabslab 3 -DLP-A-so. xls • Also open the power point file: F: COURSESUGRADSINDR 471SHARElabsDEA-Lab-12 -03 -09. ppt

Example: Data Store Employee Area Sales Profits A 10 20 70 6 B 15 15 100 3 C 20 30 80 5 D 25 15 100 2 E 12 9 90 8

Example: Results for A Efficiency of A: q. A =0. 93333 Reference set: RA={ lambda E } Employee (n 1, s 1 -) Area (n 2, s 2 -) Sales (u 1, s 1+) Profits (u 2 , s 2+) Optimal weights 0. 1 0 0. 013333 0 Slacks 0 11. 66667 0 0. 2222 Slacks DLP II-da formullerin icinde, optimal weights DLP I sensitivity shadow prices.

3. a. Discuss the meaning of u 1 of A, and its effect on the efficiency of A. How about u 2 of A? Compute the efficiency of A if the corresponding output is increased by one unit. How can you interpret the relation between the weights u 1 and u 2 of A, and the corresponding slacks, s 1+ and s 2+, using the complementary slackness condition? – if you increse the outputs by one the efficiency increses by the weights. Complementary slackness=S(i)*u(i)

3. b. Discuss the meaning of n 1 of A, and its effect on the efficiency of A. Note that a change in the employee input, n 1, changes the constraint (unlike a change in the outputs). Compute the efficiency of A if the Number of employees is decreased by one unit. – if you increse the inputs by epsilone E(new)=E(old)/(1 v(i)*epsilone)

Now: Make sure that in Excel: • Tools*Macro*Security: – Security Level “Medium” should be changed to “Low” • Tools*Options*International: – Decimal separators “. ” – Thousands separator “ , ”

The easy way … DEA solver • Copy the files into your own accounts: – F: COURSESUGRADSINDR 471SHARElabsLAB 3 -Ex 1 DEAsolver-data. xls, – F: COURSESUGRADSINDR 471SHARElabsLAB 3 -Ex 2 DEAsolver-data. xls – F: COURSESUGRADSINDR 471SHAREsoftware helpsDEASolver-LV. xls. – F: COURSESUGRADSINDR 471SHAREreading materialDEA SOLVER USER MANUAL. doc. • Open the file “DEA-Solver-LV. xls” • Click here to start OK CCR-I OK Choose Ex 1 DEAsolver-data. xls Run Save as Ex 1 -DEAsolver-CCR-I. xls

-Example 1 DEA Solver output: Weights

DEA Solver output for Example 1

DEA solver • Open the file “DEA-Solver-LV. xls” • Click here to start OK CCR-O OK Choose Ex 1 -DEAsolver-data. xls Run Save as Ex 1 -DEAsolver-CCR-O. xls

Questions - 1 • What are the efficiencies of the DMUs? Which DMUs have purely technical (or ratio) inefficiencies? • Relation between CCR-I (q*, v*, u*) and CCR-O (h *, p*, q*) ? – h* =1/ q* – m*= l*/q* – t-*=s-*/ q* , t+*=s+*/ q* – p* =v*/ q* , q* =u*/q*

Questions - 2 • What are the values of the slack variables for each of the DMUs? Identify the DMUs as efficient, ratio inefficient, mix inefficient and both ratio and mix inefficient. • Relation between CCR-I (q*, v*, u*) and CCR-O (h*, p*, q*) ? – h* =1/ q* – m*= l*/q* – t-*=s-*/ q* , t+*=s+*/ q* – p* =v*/ q* , q* =u*/q*

Questions - 3 • What are the values of lk’s? What are the level of inputs for each DMU to be efficient in CCR-I? • What are the values of mk’s? What are the level of outputs for each DMU to be efficient in CCR-O? • Relation between CCR-I (q*, v*, u*) and CCR-O (h*, p*, q*) ? – h* =1/ q* – m*= l*/q* – t-*=s-*/ q* , t+*=s+*/ q* – p* =v*/ q* , q* =u*/q*

DEA solver • Open the file “DEA-Solver-LV. xls” • Click here to start OK BCC-I OK Choose Ex 1 -DEAsolver-data. xls Run Save as Ex 1 -DEAsolver- BCC-I. xls

DEA solver • Open the file “DEA-Solver-LV. xls” • Click here to start OK BCC-O OK Choose Ex 1 -DEAsolver-data. xls Run Save as Ex 1 -DEAsolver- BCC-O. xls

Questions - 1 • What are the efficiencies of the DMUs? Which DMUs have purely technical (or ratio) inefficiencies?

Questions - 2 • What are the values of the slack variables for each of the DMUs? Identify the DMUs as efficient, ratio inefficient, mix inefficient and both ratio and mix inefficient.

Questions - 3 • What are the values of lk’s? What are the level of inputs for each DMU to be efficient in BCC-I? • What are the values of mk’s? What are the level of outputs for each DMU to be efficient in BCC-O?

Questions - 4 • What are the returns-to-scale (RTS) of DMUS in BCC-I and in BCC-O?

DEA Solver for Example 2… • For CCR-I, CCR-O, BCC-I, BCC-O … • Let’s answer the above questions for this one as well…