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Reference
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Outline
Deterministic Stochastic DEA
Introduction for DEA
Deterministic Model
Case Study on Deterministic Model
Drawbacks for Deterministic Model
Stochastic Model
Illustration
Case Study
Conclusion
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Deterministic Stochastic DEA o
????DEA?????????????DEA??????,??Deterministic
DEA?????????????DEA??????,??????????,???Stochastic
DEA
o ??, ???, Toshiyuki Sueyoshi ?????? -???????,
???????? (2003) 97
5
Introduction for DEA1
In the simplest case where a unit has a single
input and a single output, efficiency is defined
simply as
output
Efficiency
input
1 A. Boussofiane, R. G. Dyson, E. Thanassoulis,
Applied data envelopment analysis, European
Journal of Operations Research (1991) 1-15
6
Introduction for DEA2
More typically organizational units have multiple
inputs and outputs, defining the efficiency as
weighted sum of output
Efficiency
weighted sum of input
2 A. Boussofiane, R. G. Dyson, E. Thanassoulis,
Applied data envelopment analysis, European
Journal of Operations Research (1991) 1-15
7
Deterministic Model 3
where
n the number of units
s the number of outputs
m the number of inputs
subject to
ur the weight given to output r
vi the weight given to input i
yrj amount of output r from unit j
xij amount of input i from unit j
ur, vi
e r1, 2, , s i1, 2, , m
j1, 2, , n
3 A. Charnes, W. W. Cooper, E. Rhodes, Measuring
the efficiency of decision making, European
Journal of Operations Research (1978) 429-444
8
Deterministic Model 4
where
n the number of units
subject to
s the number of outputs
m the number of inputs
ur the weight given to output r
vi the weight given to input i
yrj amount of output r from unit j
xij amount of input i from unit j
ur, vi
e r1, 2, , s i1, 2, , m
j1, 2, , n
4 CS Sarrico, RG DysonUsing DEA for planning in
UK university, Journal of the Operations
Research Society (2000) 789-800
9
Case study5 on deterministic model
Input
Output
??? ???
?? ??
?? ??
?? ??
??
??
??
67.55 85.78 80.33 205.92 51.28 82.09 123.02 71.77
61.95 25.83 27.87 72.60 84.83
82.83 123.98 104.65 183.49 117.51 104.94 82.44 88.
16 99.77 105.80 107.60 132.73 104.28
44.37 55.13 53.30 144.16 32.07 46.51 87.35 69.19 3
3.00 9.51 14.00 44.67 159.12
60.85 108.46 79.06 59.66 84.50 127.28 98.80 123.14
86.37 227.20 146.43 173.48 171.11
26.04 43.51 27.28 14.09 46.20 44.87 43.33 44.83 45
.43 19.40 25.47 5.55 11.53
85.00 173.93 132.49 196.29 144.99 108.53 125.84 74
.54 79.60 120.09 131.79 135.65 110.22
23.95 6.45 42.67 16.15 0.00 0.00 404.69 6.14 1252.
62 0.00 0.00 24.13 49.09
?? ?? ?? ??? ?? ?? ?? ?? ?? ?? ?? ?? ??
????19781988????????
5 Chiang Kao, Yong Chi Yang, Reorganization of
forest districts via efficiency measurement,
European Journal of Operations Research (1992)
356-362
10
Drawbacks for Deterministic Model
??DEA????????????DEA?????,????????,???????????????
????????????????,??????????,????????????,?????????
????
11
Case Study 6
??????????????????
2004? (?????)
2003? (??)
????? ???
??
???(???)
???(?/?)
????
???
????
(???)
1720000
3350
7780
Seven-Eleven
1658500
1777
6531
Family Mart
?
346295
322
664
HOTSPAR
2800
22
54
Apple Mart
6000
85
102
Everyone
7150
36
67
Caramel Mart
4000
162
866
Coco Store
? ? ?
6 ??, ???, Toshiyuki Sueyoshi ?????? -???????,
???????? (2003) 112-117
12
Case Study 6
??????????????????
2004? (?????)
2003? (??)
????? ???
??
???(???)
???(?/?)
???
???
????
(???)
OP ML PE
OP ML PE
1720000
3350
7780
Seven-Eleven
20341 19661 18981
411410 329128 246846
1658500
1777
6531
Family Mart
8978 8397 7816
203475 162378 119107
1058 883 708
21866 16839 11310
346295
322
664
HOTSPAR
73 64 55
1866 1409 933
2800
22
54
Apple Mart
235 175 114
5372 4263 3070
6000
85
102
Everyone
110 84 58
1968 1443 944
7150
36
67
Caramel Mart
1399 1288 1177
24245 18221 11673
4000
162
866
Coco Store
? ? ?
OP??????, ML??????, PE??????
6 ??, ???, Toshiyuki Sueyoshi ?????? -???????,
???????? (2003) 112-117
13
Case Study 6
??????,?????????????????????????beta??,????????
6 ??, ???, Toshiyuki Sueyoshi ?????? -???????,
???????? (2003) 112-117
14
Stochastic Model 7
where
n the number of units
s the number of outputs
subject to
m the number of inputs
ur the weight given to output r
vi the weight given to input i
yrj amount of output r from unit j
xij amount of input i from unit j
7 Toshiyuki Sueyoshi, Stochastic DEA for
restructure strategy an application to a
Japanese petroleum company, The International
Journal of Management Science (2000) 385-398
15
Stochastic Model
Assume
16
Stochastic Model 7
where
n the number of units
s the number of outputs
subject to
m the number of inputs
ur the weight given to output r
vi the weight given to input i
yrj amount of output r from unit j
xij amount of input i from unit j
7 Toshiyuki Sueyoshi, Stochastic DEA for
restructure strategy an application to a
Japanese petroleum company, The International
Journal of Management Science (2000) 385-398
17
Illustration
output
output
inputs
y
x1
x2
OP ML PE
2
2
6
1
3
2
U0
U1
2
5
2
1.5
2.5
2
?
? F-1(0.9)1.282
Max hUO 2u
Subject to
2v16v2 1
hU00.06 u 0.03 v1 0.5 v2?0
hU10.22 u 0.11 v1 0 v2?0.2
1.6 v1 4.8 v2-2u 1.282
1.6 v1 - 4 v2 -2u 1.282
u, v1, v2
10-4
18
Case study 8
??2???????,???????,????????????????,??????????????
????????1997?4???????????,??????????????,?????????
1997?????????,???????????
8 Toshiyuki Sueyoshi, Stochastic DEA for
restructure strategy an application to a
Japanese petroleum company, The International
Journal of Management Science (2000) 385-398
19
Case study 8
INPUT (1998)
OUTPUT ESTIMATE (1999)
No of employees
Size of station
Operation cost
Group
Station
Gasoline PE ML OP
Petrol PE ML OP
420 480 530 . . . 500 540 600
170 200 220 . . . 120 140 155
10 . . . 9
958 . . . 1087
5203 . . . 1087
Large
1 . . . 20
Medium
21 . . . 40
5 . . . 7
513 . . . 628
3028 . . . 3634
140 180 210 . . . 230 250 280
45 60 70 . . . 100 115 135
Small
41 . . . 60
75 85 100 . . . 65 80 90
20 30 35 . . . 25 35 40
3 . . . 4
287 . . . 326
1307 . . . 1453
8 Toshiyuki Sueyoshi, Stochastic DEA for
restructure strategy an application to a
Japanese petroleum company, The International
Journal of Management Science (2000) 385-398
20
Case study 8
ß1.0
efficiency
Group
Station
a0.05
a0.1
a0.5
a0.9
a0.95
Large
89.77 . 95.19 87.92 5.30
91.06 . 96.21 89.12 5.32
1 . 20 mean S dev.
95.95 . 100.00 93.63 5.38
101.41 . 104.43 98.69 5.52
103.08 . 105.77 100.21 5.56
94.08 . 100.00 93.71 5.55
Med.
21 . 40 mean S dev.
60.51 . 70.77 67.61 8.60
59.68 . 69.65 66.64 8.45
63.61 . 75.02 71.28 9.17
67.02 . 79.82 75.39 9.85
68.03 . 81.29 76.64 10.05
65.35 . 73.62 70.89 8.90
Small
41 . 60 mean S dev.
62.17 . 53.57 54.40 8.41
63.01 . 54.34 55.21 8.53
66.17 . 57.30 58.31 8.99
69.68 . 60.62 61.80 9.51
70.74 . 61.63 62.87 9.67
69.88 . 61.40 59.61 8.09
8 Toshiyuki Sueyoshi, Stochastic DEA for
restructure strategy an application to a
Japanese petroleum company, The International
Journal of Management Science (2000) 385-398
21
Conclusion

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Thanks for your attention