1

DEA Based Approaches and Their Applications in Supply

Chain Management

Dr. Sri Talluri Professor of Supply Chain Management

Short Course at Aalto University

2

Course Outline

Introduction to Data Envelopment Analysis (DEA)

DEA Models and Approaches

Application Papers in Supply Chain Management

3

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

5

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.

6

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.

7

CCR Ratio Model (Output-Oriented): Dual Form

i

kyy

jxxts

i

kpkii

i

jpjii

i

0

.

max

Efficiency = 1

8

Graphical Depiction of DEA

O1/I

O2/I

A

F

E

DC

B Efficient Frontier

B1

9

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

10

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

11

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

12

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)

13

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

14

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

15

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.

16

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

17

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

18

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

19

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