Process Benchmarking with Data Envelopment Analysis

Chapter 11

Business Process Modeling, Simulation and Design 1

Overview

• DEA: Tool for Benchmarking • Relative Efficiency – Important Concepts – Black-box model • Graphical Analysis – Efficiency calculations • Linear Programming – Formulation – Using the Excel Add-in 2

DEA: Tool for Benchmarking

• Successfully applied to assess the efficiency of various organizations and/or processes.

– Process = Decision Making Unit (DMU) – The efficiency of a process is only relative to the performance of other processes in the set • Considers process as a black box and analyzes the relationships between its inputs and outputs 3

Process as Black Box

Input Output Process Figure 11.1 Black box model of a process Output Efficiency = Input • However, with multiple inputs and outputs, it becomes more difficult to evaluate the process efficiency.

4

Calculating Efficiency Process

A B

Labor Cost

($/week) 2,000 1,500

Throughput

(jobs/week) 1,500 1,100

Efficiency

(jobs/$) 0.750

0.733

• Clearly, process A is more efficient than process B, but...

Process

A B

Office Area

(ft 2 ) 10,000 6,900

Throughput

(jobs/week) 1,500 1,100

Efficiency

(jobs/ft 2 ) 0.15

0.16

• A new assessment based on office space shows that process B is more efficient than process A, so… 5

Calculating Efficiency

• DEA offers a variety of models that use multiple inputs and outputs to compare the efficiency of two or more processes.

• The

ratio model

is based on the following definition of efficiency: Weighted Sum of Outputs Efficiency = Weighted Sum of Inputs 6

Graphical Analysis

• Suppose we have the following input and output data:

Process

A B C D E F

Labor Cost

10 15 12 22 14 18

Throughput

10 30 36 25 31 27

Customer Rating

10 12 6 16 8 7 • We label the independent efficiency ratios

x

and

y

:

Process

A B C D E F

Throughput Labor (x)

1 2 3 1.136

2.214

1.5

Rating Labor (y)

1 0.8

0.5

0.727

0.571

0.389

7

Graphical Analysis

• Then, we plot the relative position of each process:

rating/labor

1.2

1 0.8

0.6

0.4

0.2

0 0 0.5

A D F Efficient frontier B 1 1.5

2

throughput/labor

E 2.5

3 C 3.5

8

Efficiency Calculations

• Relatively efficient processes are those on the efficient frontier: – Considered to have 100% efficiency.

– What is the efficiency of the relatively inefficient processes?

P1 (x 1 ,y 1 ) (x

v

,y

v

) P2 (x 2 ,y 2 ) P0 (x 0 ,y 0 ) x = output1/input Projection of a relatively inefficient process 9

Efficiency Calculations

• P1 and P2 are relatively efficient  P0’s

peer group

.

P1 (x 1 ,y 1 ) P0 (x 0 ,y 0 ) (x

v

,y

v

) P2 (x 2 ,y 2 ) x = output1/input Projection of a relatively inefficient process

Define a and b such that:

a



y

2 

x

2 

y x

1 1

b



x

2

y

1 

x

2 

x

1

x

1

y

2

Then, we get the efficient virtual process corresponding to

x v and y v :

x v



b y

0

x

0 

a y v



a x v



b

The efficiency of process P0 is:

E

0 

x

2 0 

x v

2 

y

0 2

y v

2 10

Linear Programming

• The ratio model measures the efficiency of a process by comparing to a hypothetical process that is a weighted linear combination of other processes.

• Individual processes might value inputs and outputs differently.

• Therefore, each process is allowed to adopt a set of weights to show it in the most favorable light.

• Formulated as a sequence of linear programs (one for each process) to: -Maximize the efficiency of one process -Subject to the efficiency of all processes  100% 11

Linear Programming

• The variables are the weights assigned to each input and output:

wout(j), win(i)

• An LP formulation for a given process Maximize

j q

  1

out

(

j

,

p

) *

wout

(

j

)

p

is: Subject to

i m

  1

in

(

i

,

k

) *

win

(

i

)  1

j q

  1

out

(

j

,

k

) *

wout

(

j

) 

i m

  1

in

(

i

,

k

) *

win

(

i

) 

wout(j)

 0.0001

win(i)

 0.0001 0 for

k

= 1, … , n for

j

= 1, … , q for

i

= 1, … , m 12

Using the Excel Add-in

NOTE: We recommend presenting/explaining the DEA Add-in, available on the CD that comes with the textbook, by running it directly in Excel.

However, for your convenience, we have attached a selection of the figures/screenshots from Chapter 11 of the book as the basis for an in class presentation without access to a computer with the Excel Add-in installed.

13

Using the Excel Add-in

Creating a new DEA model 14

Using the Excel Add-in

New model dialog window 15

Using the Excel Add-in

Completed Example.Output worksheet 16

Using the Excel Add-in

Efficiency worksheet 17

Using the Excel Add-in

Best Practice worksheet 18

Using the Excel Add-in

Targets worksheet 19

Using the Excel Add-in

Virtual Output worksheet 20

Using the Excel Add-in

Virtual Output chart 21