Multiple Criteria Decision Making

1
???? ??? ??????? ?????? ???? ??? ?????
2
??????

• ??? ??? ??????? ?????? ???????
• ?????? ?? ? ??????? ??? ??? ??? ??? ?????
• ????? ????? ???? ?? ??? ??? ??? ?????

3
????? ???? ?? ??? ??? ???????

• ?? ????? ?????? ???????? ?????? ?????.
• ?????? ?????????????????????? ???????? ? ?????
• ????? ???????
• ????? ??????? ?????
• ????? ????? ?? ????? ????? ???? ?????
• ??????? ????? ??????? ?????
• ????? ?? ?? ???? ????? (????) ????? ???.
• ?????? ?? ???? ?????? ???????? ??????? ???????
  ?????? ?...

4
???? 1

• ??? ??? ??????? ?????? ???????

5
??? ??? ????? ???? ??? ??????

• ?? ???? ????? ? ??? ?? ???? ??? ?? ?????? ?? ????
  ?? ????? ????? ?? ????????? ?? ??? ??? ?????? ??
  ????????? ??? ?? ?????? ?? ????.
• ???????? ?? ???? ??? ?? ????? ???? ?? ????? ????
  ??? ????? ???.
• ?? ???????? ?????? ??? ??? ??????? ?? ?????? ?
  ????? ???? ?????? ??????? ?? ????? ??? ??? ?????
  ?? ????? ???? ?????? ??????.

6
??? ??? ????? ???? ??? ??????
????? ???? ??? ?????? Multiple Criteria Decision
Making
????? ???? ??? ???? Multiple Objective Decision
Making ?????? ???? ???????????? ???? ? ...
????? ???? ??? ????? Multiple Attribute Decision
Making SAW,AHP,TOPSIS,
?? ??? ????? ? ????? ???? ??? ??? ????? ????
??????????? ?????? ??? ???? ?? ??? ?? ?? ???????.
7
????? ?????? ????? ??????AHP

• ???? ??? ??? ????? ???? ?? ??? ????? ????? ??
  ???? ?? ????? ? ????? ????? ?? ??????.
• AHP ????? ?????? ?? ???? ?? ???? ????? ?????? ?
  ?????? ?????? ?? ????? ??? ?????? ? ?????? ??
  ????? ?????.
• ??????? ??????? ?? ???? ??????? ???? ? ?????? ???
  ???? ????? ?? ????? ?? ??????? ? ????? ?? ?? ????
  ????? ??????(???? ????? ??????? ?? ?? ?? ??
  ?????? ?????? ?? ???????? ???? ?? ????? ?? ??
  ???? ?? ???? ????????? ?? ?? ?? ?????? ??????
  ??.)

8
?????? ???? ?????
???
?????
???? ?? ????
????? ??? ?????
????? ?????
??????
???????
????
???? ?????
???? ??????
???? ??????
?????
9
????
Kite Flying Inc. has two Job openings for an
aerospace engineer.The company has received nine
applications and resumes from qualified
applicants, and has reviewed each of the
applicants.Kite Flying desires a consistent
method of selecting their employees based on
criteria determined by management. Management
criteria and their weights are as
follows. Education .25 Bachelors 20 0 yrs
0 Excellent 50 Experience .50 Masters 30 1
yr. 20 Good 30 Interview .25 Doctorate
50 2 yrs 30 Fair 20 3 yrs 50 a) Draw
the AHP Hierarchy
10
(No Transcript)
11
?????...

• The following is a list of the candidates and the
  results of their screening
• Employee Education Yrs. Experience Interview
• 1 Bachelors 0 Excellent
• 2 Doctorate 2 Excellent
• 3 Masters 3 Fair
• 4 Bachelors 0 Poor
• 5 Bachelors 3 Excellent
• 6 Masters 2 Excellent
• 7 Masters 1 Poor
• 8 Doctorate 1 Fair
• 9 Masters 0 Good
• Assuming the company wants to hire the employees
  with the greatest education and
• experience and the highest interview results, use
  AHP to determine the two employees to
• whom the job offers should be extended

12
Solution Part b
13
??? ????? ???? ????Simple Additive Weighted(SAW)

• ??? ?? ???? ???? ??? ??? ????? ???? ????????.
• ?? ?????? ????? ???? ?? ?? ???? ?? ????? ?? ???
  ??? ??????? ????.
• ???? ?????? ????? ???? ?? ?? ???? ?? ??? AHP ????
  ???.
• ?????? ???? ?? ?? ?? ????? ???? ??????.
• ????? ???? ?? ?? ?? ?????? ?? ????? ??? ???
  ??????.
• ????? ?? ?????? ?????????? ???????? ?? ??????
  ????? ???? ?? ???.

14
????
????? ???? ??????? ?? ???? ??? ?? ??? ?????????
??? ???? ?????? ??????????? ????? ??????????
?????? ? ????? ????? ????? ?? ?????? ????? ???.??
???? ?? ?????????? ??? ??? ????? ???? ?? ??????
??????.
????
????? ?????
????? ???????
??????
????? ?????
?????
300,5
9000
48
3,274,159
20
??????
89.5
1100
9
1,152,773
5
??????
5
79
1500
8
1,554,391
15
?? ????? ???? ???? ??
??? ???? ?? ???? ???? ???????? ?? ????? ?? ??
??????? ????? ????? ?? ???? ????? ?? ????. ???
?????? ????
????
????? ?????
????? ???????
??????
????? ?????
?????
1
1
1
1
1
??????
0.3
0.12
0.19
0.35
0.25
??????
0.25
0.27
0.17
0.17
0.47
16
?????...

• ?? ??????? ?? ?????? ????? ????? ??????(AHP)? ?
  ?? ????? ???? ????? ???? ???? ???????????????? ?
  ??????? ???? ??? ????? ??? ???? ?????? ?? ????
  ??? ??? ?? ????.
• ????0.55
• ????? ????? 0.02
• ????? ???????0.05
• ????? ??????0.35
• ????? ????? ?????0.03
• ???? ?????? ?? ??? ?????? ??? ?? ????? ????? 1
  ????.

17
??? ?????? ????? ???? ?? ????? ???? ?????? ????
?? ?? ?? ?????? ?? ????? ??? ??? ?? ??????.???
???? ???? ?? ?????? ???? ?? ????? ?? ????

• ?????

1 X.55
1 X.02
1 X.05
1 X.35
1 X.03
1

• ??????

0.3 X.55
0.12 X.02
0.19 X.05
0.35 X.35
0.25 X.03
0.3

• ??????

0.27 X.55
0.17 X.02
0.17 X.05
0.47 X.35
0.25 X.03
0.33
?????gt??????gt??????
18
????? ????? ???? ??Data Envelopment Analysis

• ???? ????? ?? ?????? ???? ??? ??? ?????? ??????
  ???? ??????? ?????? ?? ????? ????? ?? ????? ??
  ????.
• ???? ??? ????????
• ?? ????? ????? ?? ? ????? ?? ??? ?? ???
• ???? ???? ????? ???? ? ??????
• ?????? ??????????
• ???? ???? ????? ?????? ????? ??????

19
????? ????? ? ????? ?? DEA

• ?????? ???? ???? ? ????? ?????? ? ??????? ?????
  ???????? ? ????? ???? ? ... ?? ???? ????? ??????
  ???? ???? ???? ?? ????? ????? ???? ??????? ????
  ?? ?????? ???? ?? ?? ????? ?????? ?? ???? ??
  ????? ???????? ?? ?? ????? ????? ??? ?? ?? ?????
  ?? ?? ???? ???? ???? ???? ?????? ?????? ?? ????
  ?? ???? ?????? ? ???? ??? ???? ????? ??? ???.
• ????? ?? ???? ? ????? ????? ??????? ????? ? ?????
  ?????? ?? ??????? ?? ??? ??? ??????? ????? ??
  ????. ?? ????? ????????? ?? ????? ?? ?? ???? ????
  ???? ???? ?????? ?????? ?? ?? ?????? ????? ????
  ????? ??? ???? ????.

20
???? ??? ??????? ???? ???

• ????? ??? ????? ? ????????
• ????? ?????? ?? ????? ?????
• ????? ????? ?????
• ????? ????
• ????? ?????
• ???? ?? ????
• ???? ?? ????
• ??????
• ??????? ????? ??????
• ??? ?????? ?????? ????
• ????? ???????

?????
?????
21
???? ??? ??????? ????? ????

• ???? ? ?????
• ????? ??????(????????? ??? ??? ????)
• ?????? ???? ???(?? ??????)
• ????
• ????? ?????
• ???? ?? ??????
• ??? ?????? ????

?????
?????
22
?????? ????
?????? ?????
???????????
???? ????? ???? DMU
?????
??????
?????
???? ?? ?? ???
????? ???? ??? ???
??????
????? ????? ???
23
?????... ??? ????? ?? ?????
?????
?????
????? ?????
???? ????? ???? DMU
???
????? ????
??????
24
?????... ??? ????? ??? ?????
???
????? ?????
???? ????? ???? DMU
????? ?????
????? ????
????? ????
??????
25
????? ?? ?? ??? ???????????? ?? ? ????? ?????
??????????? ?? ? ????? ??? ?????? ???? ????? ????
???? ????? ?????? ??????????? ????? ????? ?? ????
????? ????
26
????? ????? ???? ???? ?????? ???? ??????? ??????
?? ???? ???? ?? ?????? ??? ???????
u1??? ???? ??? ?? ????? 1 O1k ????? ????? 1 ??
????k
V1k??? ???? ??? ?? ???? 1 O1k ????? ???? 1 ??
????k
27
????? ???? ??? ?? ?? ???? ?? ???? ??? ???? ?? ??
??? CCR ????? ???
Max Ek U1O1k U2O2k............... UmOmk
  Subject to   V1I1k V2I2k
.............. VnInk 1   (U1O1k
U2O2k............... UmOmk ) - 1(V1I1k
V2I2k .............. VnInk ) lt 0     where
Uj j1,2,3, , m and Vj gt 0
j1,2,3, , n  
28
Efficient Frontier
OUTPUT
F
E
D
A
C
B
INPUT
OUTPUT
INPUT
NUMBER OF DATA REQUIRED ATLEAST TWICE AS MANY
VARIABLES(INPUTS)
29
???? 2

• ??????? ?? ? ??????? ??? ??? ??? ???????
• ?????

30
??????? ??? ??? AHP

• ?????? ??? ???? ? ???? ???? ?? ???????
• ????? ??????? ??? ?????? ? ?????? ????? ?? ?????
  ????
• ??????? ?? ?? ?? ??? ???? ?????? ? ????? ??? ??
  ??? ???? ?? ?????
• ????? ????? ?????? ???? ???? ??? ???

31
??????? ??? ??? AHP

• AHP ???? ????? ???? ????? ???? ?? ??? ??? ????
  ????? ???? ?? ?????? ???? ????? ???? ? ??? ??
  ???? ?????? ????? ????? ??????.
• ????? ?????? ?? ?????? AHP ?? ??? ????? ???????
  ???? ????? ????? ????.
• ???? ??? ??????? ???? ????? ?????? ??????
  ?????.(?? ???? ?? ???????? ? ????? ?????? ????)

32
?????? ??? ??? SAW

• ????? ? ????? ???????
• ????? ???? ???? ????? ??????????? ? ?? ????????
  ??
• ??????? ??? ?? ???? ?? ???? ????? ?? ???????
  ????? ?? ???? ?? ???? ?? ??? ??? ? ???? ???? ??
  ???? ?? ??? ??? ???? ??????? ????

33
??????? ??? ??? SAW

• ??? ???????? ??? ??? ?? ??????? ?????? ? ????
  ???? ???? ???? ?? ?? ?????? ???.
• ??? ????? ???? ??? ???? ??? ?? ????? ????? ?????
  ? ??? ?? ?????? ???? ???.
• ??? ???? ? ?? ????? ???? ???? ??

34
?????? ??? DEA ?? ?????? ?? ???? ??? ??

• ??????? ???? ?????? ??? ??? ?? ???? ??? ???
  ???????
• ??? ???? ?? ???? ??????
• ??????? ???? ?????? ?? ?? ?????
• ????? ?????? ???? ??? ??? DEA
• ????? ??????? ???? ? ??????
• ????? ????????? ????? ??????

35
??????? ??? ??? DEA

• ??? ??????? ?? ?????? ????? ????? ?????? ??????
  ????
• ????? ????? ?? ??? ?? ???? ???
• ????? ???? ?????? ???? ??? ??????? ????
  ??????????????????? ? ?? ????? ??? ?? ???? ???
  ????? ???? ???.
• ??? ???? ????? ?? ???? ? ??? ??? ???? ?????? ????
  ???? ?? ? ????? ?? ?? ????? ???????? ????? ??
  ???? ?? ?? ??? ????.

36
??????????Benchmarking

• ?????? ?????????? ? ?????? ?? ?????? ???? ?????
  ????????????? ? ???? ??? ?????? ?? ?????? ??
  ?????? ??? ???? ? ??????? ?? ???? ??????? ????
  ???????
• ?????????? ???????? ???? ???? ???? ????? ??
  ?????? ?????? ???? ???? ?? ??? ????

37
????? ...

• 2.?????????? ??????? ???? ?? ?????? ?? ?? ?????
  ???? ?????????? ???? ?? ???.?? ????? ????? ????
  ?? ?????? ?? ????? ?????????? ???? ??????? ??
  ????? ????? ????? ??????? ?????? ?? ?????????
  ?????
• 3.?????????? ????????????? ????????? ?? ??????
  ?? ????? ????? ?? ??????.????? ?? ??? ??? ???????
  ???? ?? ????? ??? ??? ? ?? ???? ? ???? ??????.

Benchmarking
38
???? 3

• ???????? ????? ?? ??? ??? ???????
• ?????

39
???????? ????? ??? AHP

• ??? ?? ????? ???? ??? ??? ????? ???? ???????? ??
  ????? ?????? ????? ????
• ??? ?? ??? ??? ????? ?? ?????? ????? ???? ?? ????
  ???? ???? ????? ????? ?????? ? ?? ?????? ?????
  ???? ???.
• ??? ?? ??? ??? ?? ????? ?? ??????? ???? ????
  ????? ?? ????? .

40
????? ????? ??? SAW

• ?????? ????? ? ?????? ?? ???????? ?? ????????
  ????? ??????? ?? ?????? ?? ????? ????.?? ???
  ????? ???? ?? ?? ??? ?????? ??? ????? ??????
  ?????.

41
????? ??? ????? ??? DEA

• ????? ?????? ???? ??????? ?????? ?? ?????? ?????
  ?? ????? ?? ????.
• ??????? ??????? ???? ? ??????
• ???? ?????? ??????? ?????? ? ????? ????? ???????
  ??????
• ????? ???? ?????? ???? ?????? ???? ?????
  ?????????????????? ?? ?? ????? ??????????? ???
  ????????????? ???????? ??? ?????? ?? ? ...

42
Problem 1 The lower Merion Board of Education
wants to evaluate the efficiency of the countrys
4 elementary schools. The three outputs of the
school are defined to be Output 1 average
reading score Output 2 average mathematics
score Output 3 average self esteem score The
three inputs to the school are defined to
one Input 1 average educational level of
mothers( defined by highest grade completed 12
high school graduate 16 college graduate,
and so on) Input 2 number of parent visits to
school (per child) Input 3 teacher to student
ratio Inputs
Outputs
School 1 2 3 1 2 3 1 13 4 .05 9 7 6
2 14 5 .05 10 8 7 3 11 6 .06 11 7 8
4 15 8 .08 9 9 9 The relevant information
for the four schools is given in the Table
above. Determine which (if any) schools are
inefficient.For any inefficient school determine
how it can be inefficient.
43
(No Transcript)
44
(No Transcript)
45
SCHOOL 1 MAX 9U17U26U3 S.T. 9U17U26U3-13V1-4
V2-0.05V3lt0 10U18U27U3-14V1-5V2-0.05V3lt0 11U17U
28U3-11V1-6V2-0.06V3lt0 13V14V20.05V31 9U19U2
9U3-15V1-8V2-0.08V3lt0 U1gt0.001
U2gt0.001 U3gt0.001 V1gt0.001 V2gt0.001 V3gt0.001
 Lindo Output LP OPTIMUM FOUND AT STEP
6   OBJECTIVE FUNCTION VALUE   1)
1.000000   VARIABLE VALUE
REDUCED COST U1 0.030464
0.000000 U2 0.102832
0.000000 U3 0.001000
0.000000 V1 0.051418
0.000000 V2 0.082878
0.000000 V3 0.001000
0.000000     ROW SLACK OR SURPLUS
DUAL PRICES 2) 0.000000
1.000000 3) 0.000000
0.000000 4) 0.000000
0.000000 5) 0.000000
1.000000 6) 0.225713
0.000000 7) 0.029464
0.000000 8) 0.101832
0.000000 9) 0.000000
0.000000 10) 0.050418
0.000000 11) 0.081878
0.000000 12) 0.000000
0.000000   NO. ITERATIONS 6     RANGES
IN WHICH THE BASIS IS UNCHANGED  
OBJ COEFFICIENT RANGES VARIABLE
CURRENT ALLOWABLE ALLOWABLE
COEF INCREASE
DECREASE U1 9.000000
0.000000 0.000000 U2
7.000000 0.000000 0.000000
U3 6.000000 0.000000
INFINITY V1 0.000000
2.694444 0.000000 V2
0.000000 0.000000 0.829060
V3 0.000000 0.000000
INFINITY
46
LINDO OUTPUT LP OPTIMUM FOUND AT STEP 6
OBJECTIVE FUNCTION VALUE 1)
1.000000 VARIABLE VALUE REDUCED
COST U1 0.001000
0.000000 U2 0.122875
0.000000 U3 0.001000
0.000000 V1 0.055323
0.000000 V2 0.001000
0.000000 V3 4.409483
0.000000 ROW SLACK OR SURPLUS DUAL
PRICES 2) 0.068552
0.000000 3) 0.000000
1.000000 4) 0.000000
0.000000 5) 0.000000
1.000000 6) 0.066733
0.000000 7) 0.000000
0.000000 8) 0.121875
0.000000 9) 0.000000
0.000000 10) 0.054323
0.000000 11) 0.000000
0.000000 12) 4.408483
0.000000 NO. ITERATIONS 6 RANGES IN
WHICH THE BASIS IS UNCHANGED
OBJ COEFFICIENT RANGES VARIABLE
CURRENT ALLOWABLE ALLOWABLE
COEF INCREASE
DECREASE U1
10.000000 0.000000
INFINITY U2
8.000000 INFINITY
0.000000 U3
7.000000 0.000000
INFINITY V1
0.000000 6.628572
0.000000 V2
0.000000 0.000000
INFINITY V3
0.000000 0.000000
0.000000
SCHOOL 2 MAX 10U18U27U3 S.T. 9U17U26U3-13V1
-4V2-0.05V3lt0 10U18U27U3-14V1-5V2-0.05V3lt0 11U1
7U28U3-11V1-6V2-0.06V3lt0 14V15V20.05V31 9U19U
29U3-15V1-8V2-0.08V3lt0 U1gt0.001
U2gt0.001 U3gt0.001 V1gt0.001 V2gt0.001 V3gt0.001
47
LP OPTIMUM FOUND AT STEP 6
OBJECTIVE FUNCTION VALUE 1)
1.000000 VARIABLE VALUE
REDUCED COST U1 0.001000
0.000000 U2 0.001000
0.000000 U3 0.122750
0.000000 V1 0.090358
0.000000 V2 0.001000
0.000000 V3 0.001000
0.000000 ROW SLACK OR SURPLUS DUAL
PRICES 2) 0.426206
0.000000 3) 0.392815
0.000000 4) 0.000000
1.000000 5) 0.000000
1.000000 6) 0.240703
0.000000 7) 0.000000
0.000000 8) 0.000000
0.000000 9) 0.121750
0.000000 10) 0.089358
0.000000 11) 0.000000
0.000000 12) 0.000000
0.000000 NO. ITERATIONS 6 RANGES IN
WHICH THE BASIS IS UNCHANGED
OBJ COEFFICIENT RANGES VARIABLE
CURRENT ALLOWABLE ALLOWABLE
COEF INCREASE
DECREASE U1 11.000000
0.000000 INFINITY U2
7.000000 0.000000 INFINITY
U3 8.000000 INFINITY
0.000000 V1 0.000000
INFINITY 0.000000 V2
0.000000 0.000000 INFINITY
V3 0.000000 0.000000
INFINITY
SCHOOL 3 MAX 11U17U28U3 S.T. 9U17U26U3-13V1
-4V2-0.05V3lt0 10U18U27U3-14V1-5V2-0.05V3lt0 11U1
7U28U3-11V1-6V2-0.06V3lt0 11V16V20.06V31 9U19U
29U3-15V1-8V2-0.08V3lt0 U1gt0.001
U2gt0.001 U3gt0.001 V1gt0.001 V2gt0.001 V3gt0.001
48
SOLUTION LP OPTIMUM FOUND AT STEP 0
OBJECTIVE FUNCTION VALUE 1)
0.9429709 VARIABLE VALUE
REDUCED COST U1 0.001000
0.000000 U2 0.102775
0.000000 U3 0.001000
0.000000 V1 0.046313
0.000000 V2 0.001000
0.000000 V3 3.716364
0.000000 ROW SLACK OR SURPLUS DUAL
PRICES 2) 0.057462
0.000000 3) 0.000000
0.065455 4) 0.000000
1.210909 5) 0.057029
0.000000 6) 0.000000
0.949091 7) 0.000000
-4.974545 8) 0.101775
0.000000 9) 0.000000
-1.145455 10) 0.045313
0.000000 11) 0.000000
0.000000 12) 3.715364
0.000000 NO. ITERATIONS 0 RANGES IN
WHICH THE BASIS IS UNCHANGED
OBJ COEFFICIENT RANGES VARIABLE
CURRENT ALLOWABLE ALLOWABLE
COEF INCREASE
DECREASE U1 9.000000
4.974545 INFINITY U2
9.000000 INFINITY 1.016129
U3 9.000000 1.145455
INFINITY V1 0.000000
0.321429 2.625000 V2
0.000000 0.000000 INFINITY
V3 0.000000 0.014000
0.000000
SCHOOL 4 MAX 9U19U29U3 S.T. 9U17U26U3-13V1-4V
2-0.05V3lt0 10U18U27U3-14V1-5V2-0.05V3lt0 11U17U2
8U3-11V1-6V2-0.06V3lt0 9U19U29U3-15V1-8V2-0.08V3
lt0 15V18V20.08V31 U1gt0.001 U2gt0.001 U3gt0.001 V
1gt0.001 V2gt0.001 V3gt0.001
NOT 1
49
How to make School 4 Efficient Modified School
4 Output Output of School 2 Output of School
3 10 11 13.96
0.065 8 1.21 7
9 7 8 10.13 Dual Price
from Constraint Related to School 2
Efficiency Dual Price from
Constraint Related to School 2 Efficiency
14 11 14.22 0.065
5 1.21 6
7.59 0.05 0.06 0.08
Modified school 4 Input
Input of School 2
Input of School 3
50
LP OPTIMUM FOUND AT STEP 6  
OBJECTIVE FUNCTION VALUE   1)
1.000000   VARIABLE VALUE
REDUCED COST U1 0.001000
0.000000 U2 0.108434
0.000000 U3 0.001000
0.000000 V1 0.051718
0.000000 V2 0.034848
0.000000 V3 0.001000
0.000000     ROW SLACK OR SURPLUS
DUAL PRICES 2) 0.037730
0.000000 3) 0.013861
0.000000 4) 0.000000
0.000000 5) 0.000000
1.000000 6) 0.000000
1.000000 7) 0.000000
0.000000 8) 0.107434
0.000000 9) 0.000000
0.000000 10) 0.050718
0.000000 11) 0.033848
0.000000 12) 0.000000
0.000000   NO. ITERATIONS 6     RANGES
IN WHICH THE BASIS IS UNCHANGED  
OBJ COEFFICIENT RANGES VARIABLE
CURRENT ALLOWABLE ALLOWABLE
COEF INCREASE
DECREASE U1 13.960000
0.000000 INFINITY
U2 9.000000 INFINITY
0.000000 U3 10.130000
0.000000 INFINITY V1
0.000000 0.309994
0.000000 V2 0.000000
0.000000 0.165461 V3
0.000000 0.000000
INFINITY    
School 4 Modified MAX 13.96U19U210.13U3 S.T. 9U
17U26U3-13V1-4V2-0.05V3lt0 10U18U27U3-14V1-5V2-
0.05V3lt0 11U17U28U3-11V1-6V2-0.06V3lt0 13.96U19U
210.13U3-14.22V1-7.59V2-0.08V3lt0 14.22V17.59V20
.08V31 U1gt0.001 U2gt0.001 U3gt0.001 V1gt0.001 V2gt0.0
01 V3gt0.001
51

• The Philadelphia 76ers have 12 players in their
  roster.The players salary and performance
  statistics are shown below.
• NO PLAYER INPUT OUTPUT
• SALARY() FG FT
  R A
• Barros 937,000 50.1
  89.5 3.2 7.4
• Weatherspoon 1,800,000 42.9
  76.3 7.0 3.0
• Burton 1,200,000 42.4
  81.7 3.4 2.0
• Wright 600,000 45.3
  66.3 5.7 0.4
• Bradley 5,520,000 45.7
  68.3 6.7 0.5
• Grayer 350,000
  38.2 82.4 2.6 1.6
• Williams 1,500,000 50.7
  74.4 7.0 1.0
• Graham 350,000 41.9 71.1
  1.1 1.1
• Alston 650,000 44.9
  46.9 3.0 0.5
• Tyler 850,000 37.8
  62.2 0.0 3.0
• Perry 1,900,000 38.0 60.0
  1.0 0.2
• Malone 2,500,000 50.8 86.2
  2.6 1.5
• (FG Field Goal Percentage FT Free Throw
  Percentage R Rebounds A Assisits
• Give a Data envelopment analysis(DEA)model to
  evaluate the performance of Weatherspoon.

52
LP OPTIMUM FOUND AT STEP 4
OBJECTIVE FUNCTION VALUE 1)
0.3772690 VARIABLE VALUE
REDUCED COST FG 0.000000
44.611881 FT 0.000000
22.657431 R 0.084571
0.000000 A 0.044864
0.000000 S 0.000001
0.000000 ROW SLACK OR SURPLUS DUAL
PRICES 2) 0.178214
0.000000 3) 0.773412
0.000000 4) 0.622731
0.000000 5) 0.000000
0.029703 6) 4.010942
0.000000 7) 0.000000
1.242574 8) 0.613139
0.000000 9) 0.149288
0.000000 10) 0.265522
0.000000 11) 0.573742
0.000000 12) 1.489790
0.000000 13) 1.796153
0.000000 14) 0.000000
0.377269 15) -0.000001
0.000000 16) -0.000001
0.000000 17) 0.084570
0.000000 18) 0.044863
0.000000 19) 0.000000
0.000000 NO. ITERATIONS 4
Problem 3 MAX 4.2FG81.7FT3.4R2A S.T. 50.1FG
89.5FT3.2R7.4A-937000Slt0 42.9FG76.3FT7R3A-18
00000Slt0 42.4FG81.7FT3.4R2.0A-1200000Slt0 45.3
FG66.3FT5.7R0.4A-600000Slt0 45.7FG68.3FT6.7R
0.5A-5520000Slt0 38.2FG82.4FT2.6R1.6A-350000Slt
0 50.7FG74.4FT7.0R1A-1500000Slt0 41.9FG71.1FT
1.1R1.1A-350000Slt0 44.9FG46.9FT3R0.5A-650000S
lt0 37.8FG62.2FT0R3.0A-850000Slt0 38.0FG60.0FT
1.0R0.2A-1900000Slt0 50.8FG86.2FT2.6R1.5A-250
0000Slt0 1200000S1 FGgt0.000001 FTgt0.000001 Rgt0.00
0001 Agt0.000001 Sgt0.000001
53
SOLUTION MAX 42.9FG76.3FT7R3A S.T. 50.1FG89
.5FT3.2R7.4A-937000Slt0 42.9FG76.3FT7R3A-1800
000Slt0 42.4FG81.7FT3.4R2.0A-1200000Slt0 45.3FG
66.3FT5.7R0.4A-600000Slt0 45.7FG68.3FT6.7R0.
5A-5520000Slt0 38.2FG82.4FT2.6R1.6A-350000Slt0
50.7FG74.4FT7.0R1A-1500000Slt0 41.9FG71.1FT1.
1R1.1A-350000Slt0 44.9FG46.9FT3R0.5A-650000Slt
0 37.8FG62.2FT0R3.0A-850000Slt0 38.0FG60.0FT1
.0R0.2A-1900000Slt0 50.8FG86.2FT2.6R1.5A-25000
00Slt0 1800000S1 FGgt0.000001,FTgt0.000001,Rgt0.0000
01,Agt0.000001,Sgt0.000001 (B) We can conclude
that Burton is not efficient, because as you see
from the computer output, The OBJECTIVE FUNCTION
VALUE IS 0.3772690 MODIFIED BURTON OUTPUT
38.2 45.3
48.8 1.2425
82.4 0.029 66.3
104.4 2.6
5.7 3.4
1.6
0.4 2.00 Modified
Burton Salary(input) 1.2425(350000)
0.029(600000) 452723
54
?????

• ????????????????? ???? ????? ?? ???????????????
  ??????? ?????
• ????????????????? ?????? ??????? ?????????????
  ?????? ?????
• ????????????????? ?????? ?????? ????????????
  ?????? ?????
• ?????????????????? ?????? ?????? ????? ??? ????
  ??? ????? ????? ???? ?????? ??????? ?? ???
  DEA????? ??????????? ???? ???????? ???? ??????
  ??????
• www.expertchoice.com