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DEA Based Approaches and Their Applications in Supply Chain Management. Dr. Sri Talluri Professor of Supply Chain Management Short Course at Aalto University. Course Outline. Introduction to Data Envelopment Analysis (DEA) DEA Models and Approaches - PowerPoint PPT Presentation
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1
DEA Based Approaches and Their Applications in Supply
Chain Management
Dr. Sri Talluri Professor of Supply Chain Management
Short Course at Aalto University
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Course Outline
Introduction to Data Envelopment Analysis (DEA)
DEA Models and Approaches
Application Papers in Supply Chain Management
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Introduction to DEA DEA evaluates relative efficiencies of a homogenous set
of decision making units (DMUs) in the presence of multiple input and output factors
Efficiency is defined as the ratio of weighted sum of outputs to weighted sum of inputs
A DMU is considered efficient if it achieves a score of 1.00
DEA identifies necessary improvements required in making inefficient DMUs efficient
DEA has extensively been applied in a variety of business and decision making environments that include banking, healthcare, transportation, and supply chain management
4
Some DEA Models and Approaches
CCR Model (Primal and Dual) BCC Model Super Efficiency Model DEA Models with Weight Restrictions Cross-Efficiency Models in DEA Benchmarking in DEA DEA Windows Analysis DEA with Ordinal and Cardinal Factors
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CCR Ratio Model: Primal Form
jkuv
ixu
yvts
xu
yv
jk
m
jjij
ki
s
kk
m
jjpj
kp
s
kk
,0,
,1.
max
1
1
1
1
jkuv
ixuyv
xuts
yv
jk
m
jjijki
s
kk
m
jjpj
kp
s
kk
,0,
,0
1.
max
11
1
1
where: p is the unit being evaluated; s represents the number of outputs; m represents the
number of inputs; yki is the amount of output k provided by unit i; xji is the amount of
input j used by unit i; vk and uj are the weights given to output k and input j, respectively.
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CCR Ratio Model (Input-Oriented): Dual Form
i
kyy
jxxts
i
kpkii
i
jpjii
i
0
.
min
where: represents the efficiency score of unit p; s represent the dual variables that
identify the benchmarks for inefficient units.
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CCR Ratio Model (Output-Oriented): Dual Form
i
kyy
jxxts
i
kpkii
i
jpjii
i
0
.
max
Efficiency = 1
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Graphical Depiction of DEA
O1/I
O2/I
A
F
E
DC
B Efficient Frontier
B1
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CCR Model: Illustration
DMU Input 1 Input 2 Output 1 Output 2 Output 3 1 5 14 9 4 16 2 8 15 5 7 10 3 7 12 4 9 13
0,,,,
01271394
01581075
01451649
1145
..
1649
21321
21321
21321
21321
21
321
uuvvv
uuvvv
uuvvv
uuvvv
uu
ts
vvvMaximize
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CCR Model: Illustration Results
DMU 1 and DMU 3 are efficient (efficiency of 1.00 with no slacks)
DMU 2 is inefficient (efficiency < 1.00)
DMU 2 can utilize DMU 1 and DMU 3 as benchmarks for improvement
See EXCEL file: DEA_Example_HUT
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Selection of Inputs, Outputs, and units in DEA
Inputs: resources (examples: workers, machines, operating expenses, budget, etc.)
Outputs: actual number of products produced to a host of performance and activity measures (examples: quality levels, throughput rates, lead-time, etc.)
If there are m inputs and s outputs then potentially ms DMUs can be efficient. Thus, to achieve discrimination we need substantially more units than ms
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BCC Model
CCR model considers constant returns to scale (CRS) whereas the BCC model considers variable returns to scale (VRS)
i
kyy
jxxts
i
ii
kpkii
i
jpjii
i
0
1
.
min
new constraint(convexity)
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Super Efficiency Model
Super efficiency model allows for effective ranking of efficient DMUs
jkuv
pixuyv
xuts
yv
jk
m
jjijki
s
kk
m
jjpj
kp
s
kk
,0,
,0
1.
max
11
1
1
The DMU being evaluatedis removed from the constraintset thereby allowing its efficiencyscore to exceed a value of 1.00
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DEA Model with Weight Restrictions
Unrestricted weight flexibility in DEA can be resolved through weight restrictions
Weight restrictions also allow for the incorporation of managerial input into DEA models
Methods such as AHP and ANP can be utilized for identifying weight restriction constraints in DEA
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DEA Model with Weight Restrictions
0,
,...,3,2,0
,...,3,2,0
,...,3,2,0
,...,3,2,0
0
1.
max
1
1
1
1
11
1
1
jk
kk
kk
jj
jj
m
jjijki
s
kk
jp
m
jj
kp
s
kk
uv
skvvb
skvva
mjuu
mjuu
ixuyv
xuts
yv
vk is the weight given to output k, uj is the weight given to input j, and , , a, b are non-
negative scalars.
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Cross Efficiencies in DEA
Cross efficiency in DEA allows for effective discrimination between niche performers and good overall performers
Cross efficiency score of a DMU represents how well the unit is performing with respect to the optimal weights of another DMU
A DMU that achieves high cross efficiency scores is considered to be a good overall performer
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Cross Efficiency Models: Aggressive and Benevolent Approaches
jkuv
xuyv
pixuyv
xuts
yv
jk
m
jjpjpkp
s
kk
m
jjijki
s
kk
m
j pijij
s
k pikik
,0,
0
,0
1.
min
11
11
1
1
jkuv
xuyv
pixuyv
xuts
yv
jk
m
jjpjpkp
s
kk
m
jjijki
s
kk
m
j pijij
s
k pikik
,0,
0
,0
1.
max
11
11
1
1
Where p is the relative efficiency score of DMU p obtained from the CCR model
Aggressive Benevolent
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Cross Efficiency Matrix
DMU 1 2 3 N 1 Θ11 Θ12 Θ13 Θ1N 2 Θ21 Θ22 Θ23 Θ2N 3 Θ31 Θ32 Θ33 Θ3N N ΘN1 ΘN2 ΘN3 ΘNN
Efficiency score of DMU 2 when evaluatedwith the optimal weights of DMU 1
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Benchmarking in DEA
We discussed traditional DEA benchmarking in the illustrative example Benchmarks may not be inherently similar to
inefficient DMUs
Virtual benchmarks do not exist in practice
Benchmarking can also be performed based on the cross efficiency matrix. Use of cluster analysis on cross efficiencies
20
Windows Analysis in DEA
Evaluating the performance of a DMU over time by treating it as a different entity in each period
A DMU is compared to itself over time
21
Ordinal and Cardinal Factors in DEA
Discuss Model in Class
Sarkis and Talluri (1999)- IJPR
22
Applications in Supply Chain Management
Supplier Evaluation and Rationalization (CCR DEA Model)
System Performance Evaluation (Super Efficiency Model with Weight Restrictions)
Risk Management in Supply Chains (CCR DEA) Service Efficiency (CCR DEA) NPD Project Performance (BCC Model) Buyer-Supplier Negotiations (DEA Based Approach)
23
Questions