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 EJOR04.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:\COURSES\UGRADS\INDR\INDR471\SHARE\Labs\lab3-DLP-A-so.xls
• Also open the power point file:
F:\COURSES\UGRADS\INDR\INDR471\SHARE\labs\DEA-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: qA =0.93333
Reference set: RA={ lambda E }
Employee (n1, s1-)
Area (n2, s2-) Sales (u1, s1+)
Profits (u2 , s2+)
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 u1 of A, and its effect on the
efficiency of A. How about u2 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 u1 and u2 of A, and the
corresponding slacks, s1+ and s2+, 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 n1 of A, and its effect on the efficiency
of A. Note that a change in the employee input, n1, changes
the constraint (unlike a change in the outputs).
N
v I
i 1
i ie
1
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)/(1v(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:\COURSES\UGRADS\INDR\INDR471\SHARE\labs\LAB3-Ex1DEAsolver-data.xls,
– F:\COURSES\UGRADS\INDR\INDR471\SHARE\labs\LAB3-Ex2DEAsolver-data.xls
– F:\COURSES\UGRADS\INDR\INDR471\SHARE\software helps\DEASolver-LV.xls.
– F:\COURSES\UGRADS\INDR\INDR471\SHARE\reading material\DEA
SOLVER USER MANUAL.doc.
• Open the file “DEA-Solver-LV.xls”
• Click here to start  OK  CCR-I  OK  OK  Choose Ex1DEAsolver-data.xls  Run  Save as Ex1-DEAsolver-CCR-I.xls
-Example 1DEA Solver output: Weights
Model Name = CCR-I
Workbook Name = D:\DEA\LAB2-PART1-results.xls
No.
DMU
Score
V( 1)
V( 2)
1A
0.857143
0.1429
0.1429
2B
0.631579
0.0526
0.2105
3C
1
0.0833
0.3333
4D
1
0.1667
0.1667
5E
1
0.2143
0.1429
6F
1
0.0000
1.0000
7G
0.666667
0.3333
0.0000
U( 1)
0.8571
0.6316
1.0000
1.0000
1.0000
1.0000
0.6667
DEA Solver output
for Example 1
Model Name = CCR-I
Workbook Name = D:\DEA\LAB2-PART1-results.xls
Excess
Excess
Shortage
No.
DMU
Score
Input 1
Input 2
Output
S-( 1)
S-( 2)
S+( 1)
1A
0.857143
0
0
0
2B
0.631579
0
0
0
3C
1
0
0
0
4D
1
0
0
0
5E
1
0
0
0
6F
1
2
0
0
7G
0.666667
0 0.666667
0
DEA solver
• Open the file “DEA-Solver-LV.xls”
• Click here to start  OK  CCR-O  OK  OK 
Choose Ex1-DEAsolver-data.xls  Run  Save as
Ex1-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  OK 
Choose Ex1-DEAsolver-data.xls  Run  Save as
Ex1-DEAsolver- BCC-I.xls
DEA solver
• Open the file “DEA-Solver-LV.xls”
• Click here to start  OK  BCC-O  OK  OK 
Choose Ex1-DEAsolver-data.xls  Run  Save as
Ex1-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…