P Cube - A Data Envelopment
Analysis Based Solution for
Business Process Intelligence
Evaluating the effectiveness of any process is one of the
most challenging tasks faced by managers today,
especially when there are multiple inputs and outputs of
the process. The difficulty is further compounded when
the relationships between the inputs and the outputs
are complex and involve unknown tradeoffs. The
challenge is in terms of comparing the performance of a
process at different locations of the organization, or
evaluating how the process has been performing at a
particular location over consecutive periods of time
(also called window analysis).
The P Cube tool developed by TCS is targeted towards
solving such managerial problems, and can be applied
to both macro-level and micro-level processes, thereby
providing an effective performance measurement and
monitoring framework for Business Process Intelligence
(BPI). It caters to the performance evaluation needs of
both top management as well as different functional
managers within an organization. The tool can
seamlessly integrate with an organization’s information
management system to provide insightful dashboards
for monitoring processes and identifying benchmark
groups, so as to ensure continual improvement of
processes. Various strategic, tactical, and operational
decisions can be taken based on the insights provided.
P Cube - A Data Envelopment Analysis Based Solution for Business Process Intelligence
About the Author
Prakash Chandra Sah
Prakash Chandra Sah is a Consultant in the Business Intelligence
and Performance Management (BIPM) Service at Tata Consultancy
Services (TCS). He is a B. Tech from IIT Kharagpur and MBA from IIM
Calcutta with professional experience of more than 16 years. He
brings his rich domain expertise into analytical computing.
1
P Cube - A Data Envelopment Analysis Based Solution for Business Process Intelligence
Table of Contents
1. Performance Evaluation: Brief Introduction...................................... 3
2. Data Envelopment Analysis: An overview......................................... 5
3. P Cube - A TCS Solution........................................................................... 6
4. Different application scenarios of P Cube........................................ 10
5. Conclusion................................................................................................... 11
6. Acknowledgements................................................................................. 12
2
P Cube - A Data Envelopment Analysis Based Solution for Business Process Intelligence
Performance Evaluation: Brief Introduction
Performance Evaluation
It is difficult to evaluate the performance of a process when there are multiple inputs and multiple outputs. This point
is illustrated below with a macro example of an organization having operations across multiple locations:
Performance evaluation
of DMUs that are
heterogeneous in nature
CEO
DMUs spread across geographies operating at different levels and different market scenarious
A Decision Making Unit (DMU), as depicted below, is a separate entity/unit, with multiple inputs and outputs. The
efficiency of the unit depends on how best the unit leverages the inputs to maximize the outputs.
Inputs
Outputs
Decision making Unit (DMU)
Efficiency, in its most elementary form can be written as:
Efficiency =
Output
Input
When there are multiple inputs and outputs, the best way of coming up with a single efficiency measure is as below:
Efficiency =
where,
(w1* O1) + (w2* O2) +……. + (wm*Om)
-------------------------------------------------(u1* I1) + (u2* I2) + ……. + (un* In)
for m outputs and n inputs
Oi = Output i
Ij = Input j
wi = weight applied to output i
uj = weight applied to input j
3
P Cube - A Data Envelopment Analysis Based Solution for Business Process Intelligence
Key Challenges
In the above definition of efficiency, there is always a big debate on how to arrive at a set of weights for inputs and
outputs that would be fair to all DMUs, since DMUs differ in terms of:
l
Mix of customers served
l
Availability and cost of inputs
l
Facility configuration
l
Processes/practices used
and so on……
It may also not always be fair to use the same set of weights for all the DMUs, because of the points mentioned above.
Different DMUs may wish to give varying degree of importance to different outputs, because of the local market
conditions and their own operating strategy. In such a scenario, the key challenges for top management are:
l
How to compare efficiency of a diverse set of units serving diverse set of markets?
l
What are the best practices?
l
What is the trade-offs among inputs and outputs?
l
Which are the poorly performing units?
l
Where are the various improvement opportunities and how big are they?
Traditional Approaches for Performance Evaluation
Some traditional approaches employed by many organizations are given below:
1. Output Focus: Focus only on outputs. There are two approaches adopted here – one, focus on only a single
output measure like profit; two, use a weighted sum of output measures with some pre-defined weights.
2. Operating Ratios: Use of operating ratios such as Labor-hrs/transaction, $sales/sq. ft., etc. Although these are
good for highly standardized operations, they do not reflect varying mix of inputs and outputs found in more
diverse operations.
3. Financial approach: Convert everything to Dollar.
$Inputs
$Outputs
The problems with this approach are:
l
Some inputs/outputs cannot be valued in $ (non-profit)
l
A single ratio like Return on Investment (ROI) is not holistic
P Cube – a TCS Solution: Brief Introduction
P Cube is a multiple-measure performance evaluation and benchmarking tool. With this solution, the focus of
performance evaluation and benchmarking is shifted from characterizing performance in terms of single measures
to evaluating performance from a multidimensional systems perspective. It has the advantage of dynamically
adjusting weights. P Cube has been designed based on Data Envelopment Analysis, a linear programming model,
which is explained in the next section. P Cube is explained in greater detail later in this paper.
4
P Cube - A Data Envelopment Analysis Based Solution for Business Process Intelligence
P Cube stands for
l
Performance Evaluation,
l
Productivity Measurement, and
l
Profitability Analysis,
which are the areas that the solution analyzes.
Data Envelopment Analysis: An Overview
What is Data Envelopment Analysis
Data Envelopment Analysis (DEA) is a non-parametric, linear programming-based method of analysis to evaluate the
performance of multi-input and multi-output processes. DEA requires neither an explicit formulation of the
underlying functional relationship nor pre-assigned weights for outputs and inputs in evaluating performance
relative to peer group. The main advantage of using DEA is its ability to explicitly take into account the use of multiple
inputs (resources) to indicate multiple outputs (services). DEA also helps to minimize the complexity of analysis by
simultaneously evaluating the attributes of interest and presenting a single, composite score, referred to as
"efficiency."
DEA is a relatively new “data oriented” approach for evaluating the performance of a set of peer entities (or processes)
called Decision Making Units (DMUs) which convert multiple inputs into multiple outputs. The definition of a DMU
is generic and flexible. Recent years have seen a great variety of applications of DEA for use in evaluating the
performances of multiple entities engaged in various activities in different contexts in several countries.
DEA is a methodology directed to frontiers rather than central tendencies. The following sentences explain this
statement. Instead of trying to fit a regression plane through the center of data as in statistical regression, for example,
one ‘floats’ a piecewise linear surface to rest on top of the observations. Because of this perspective, DEA proves
particularly adept at uncovering relationships that remain hidden from other methodologies. For instance, consider
what one wants to mean by “efficiency”, or more generally, what one wants to mean by saying that one DMU is more
efficient than another DMU. This is accomplished in a straightforward manner by DEA without requiring explicitly
formulated assumptions and variations with various types of models such as in linear and nonlinear regression
models.
This frontier analysis concept is illustrated on the next page for a very simplistic case of single input, two outputs, and
6 DMUs (DMUs A to F) scenario.
Mkt. share/Capital employed
Frontier Analysis
5
(C)
(B)
4
3
ncy
ficie
f
E
tive
Rela
(E)
2
1
0
0
(A)
(D)
(F)
1
2
Sales / Capital employed
Figure 1: Frontier Analysis
5
3
P Cube - A Data Envelopment Analysis Based Solution for Business Process Intelligence
Input
Outputs
Axes
Input 1
Output 1
Output 2
X-axis
Y-axis
Capital employed
Sales
Market share
Sales / Capital employed
Market share / Capital employed
Table 1: Input/Output Parameters & Axes for the Frontier Analysis Example
The frontier is drawn by enveloping a convex surface (line in this case) over the points lying farthest away from the
origin. The points lying on the surface can be said to be 100% efficient relatively (In the above example, DMUs B, C and
D can be said to be 100% efficient), while other DMUs can be evaluated for their efficiency by calculating the ratio of
their distance from origin to that of the distance of the nearest frontier to the origin. The graph above depicts relative
efficiency of DMU A, as ratio of distance of A from origin to that of the frontier from the origin. Such analysis also gives
insight on the shortest path the DMUs can take for reaching the frontier i.e. to become more efficient.
The above diagram is a lot easier to understand, make sense of, and generate insight from, than the list of traditional
ratios talked about earlier. This method of looking at data in a different way is an important practical issue. Many
managers are happy with ratios but showing them that their ratios can be viewed differently and used to obtain new
information is often an eye-opener to them.
Extending to More Inputs/Outputs
In the simple example there was just one input and two outputs. This can be ideal for a simple graphical analysis. If
there are more inputs or outputs, drawing a simple graph is not possible. However it is still possible to carry out
EXACTLY the same analysis as above by using mathematics rather than pictures. This is where DEA is used. DEA can be
used for evaluating any number of DMU's, with any number of inputs and outputs. It can be formulated as a nonlinear optimization problem which, at first sight, is difficult to solve numerically. However it can be converted into a
linear programming problem and solved, which is what TCS’ P Cube solution does.
This paper does not go into the details of the mathematical formulation. The purpose of the paper is to illustrate the
benefits of using the model and explore its various application scenarios, rather than getting into the nitty-gritty of
the mathematical formulation. In the next section, using an illustration of a multi-site organization, the P Cube model
has been explained in detail.
P Cube - A TCS Solution
Solution description
With the DEA background, based on which the P Cube solution is built, some key characteristics of the solution are
listed below:
l
Multiple-input, multiple-output efficiency measurement tool
l
Uses a multi-dimensional efficient frontier to define multiple Input/Output productivity
l
Relative distance to the frontier shows the Relative Efficiency
l
Every DMU is shown in the best-possible light to provide level playing field to all the DMUs
l
Allows the management to specify minimum or maximum weights that can be attached to the various inputs
and outputs (This is optional and is in addition to the optimization model built in the tool)
l
Has provision for Scenario analysis with weight changes to avoid error in managerial decision making as far as
weight restriction (as described in the previous point) is concerned
6
P Cube - A Data Envelopment Analysis Based Solution for Business Process Intelligence
The following diagram illustrates the solution framework at high level, as applied to multi-site/unit performance
evaluation scenario:
Identity DMUs
and I/O
Parameters
Get the Relative
Efficiencies of
the DMUs
Find benchmarks
& best practices
Decision Support
l
Who are the best
performers?
P Cube- TCS'
Analytical
Engine based
on Data
Envelopment
Analysis
Benchmarking
& Scenario
Analysis
l
Which units to close down?
l
Which units have the
potential to improve?
l
What should be the new
benchmarks?
l
How to devise incentive
scheme?
Figure 2: Solution framework
The various steps followed by the solution are displayed below:
Plan Phase
Identify the
Strategic Inputs
and outputs
and get data
Identify the
Decision making
units (DMUs) to
be compared
Weight restriction
preferences
Data Envelopment Analysis Phase
Scenario
Analysis
Arrive at
optimal solution
Relative
efficiencies
Liner
Programming
model
Benchmarking Phase
Profitability Efficiency Matrix
identify best performers
Effective
Decision making
Figure 3: Solution steps
The following example explains the working of the solution.
7
P Cube - A Data Envelopment Analysis Based Solution for Business Process Intelligence
An Illustration
The tool was tested with a hypothetical example of an organization having operations at 30 sites (called DMUs). The
top management of the organization wants to evaluate how these 30 sites have been performing. Investments in
these sites in terms of capital and number of employees vary widely (these are the two key inputs, considered critical
from performance perspective). Also, there is more than one parameter (like profit) which is important for the
organization from long-term perspective. The top Management has decided that there are three important
parameters based on which the sites should be evaluated. These are profit, revenue growth, and customer
satisfaction index. The challenges for top management are:
l
How to come up with a single measure of operating efficiency for these sites
l
What weights should be applied to the various inputs and outputs
l
How benchmarking should be done
l
How decisions such as closure of some units should can be taken
Let’s see how P Cube helps the top management of the organization to address these challenges. The following is the
data of the identified inputs and outputs for all the 30 DMUs for a particular period of time, for which evaluation has to
be done:
DMUs and their input/output values
Capital
Invested
(Million USD)
Total Annual
Wages
(Million USD)
Profit
(Million
USD)
Revenue
Growth (%)
Customer
Satisfaction
Index
DMU 1
1080
235
204
106
7
DMU2
1000
225
208
32
6
DMU3
500
123
131
138
4
DMU4
180
56
114
103
6
DMU29
800
183
170
57
9
DMU30
166
57
38
60
9
.........
Table 2: Sample data used
Additionally, the top management feels that some minimum weights (as shown in the table below) should be applied
to each of the parameters. The model allows this optional feature.
Top Management weight restrictions (Optional)
Restriction
type
Capital
Invested
(Million USD)
Total Annual
Wages
(Million USD)
Profit
(Million
USD)
Revenue
Growth (%)
Customer
Satisfaction
Index
At least (%)
30
30
20
30
10
At most (%)
100
100
100
100
100
Table 3: Sample data used
8
P Cube - A Data Envelopment Analysis Based Solution for Business Process Intelligence
With these inputs P Cube does analysis based on DEA (discussed earlier) and provides the following insights to the
top management:
l
Relative efficiency of the various DMUs
l
Trend of relative efficiency values over consecutive periods of time (of course for this data for past periods is also
required)
l
Best practices group (for benchmarking purpose)
l
Profitability-Efficiency Matrix
All these are illustrated in the Efficiency Dashboard on the next page.
Efficiency Score Chart
1
0.9
0.8
0.7
Efficiency
0.6
0.5
l
Score
0.4
l
Frequency
0.3
Chart
l
Window Analysis
0.2
0.1
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Window analysis of DMUs
Efficiency Freq. Chart
1
10
0.9
9
0.8
8
0.7
7
6
DMU 1
DMU 2
DMU 3
DMU 4
0.5
0.4
5
4
0.3
3
0.2
2
0.1
1
0
0
2005
2006
2007
.1
o0
0t
2008
0.2
to
0.1
0.3
to
0.2
0.4
0.8
0.9
0.6
0.5
0.7
to
to
to
to
to
to
0.3
0.7
0.8
0.5
0.4
0.6
1
to
0.9
Figure 4: Efficiency Dashboard
35
Best practice
compansion group
Under-performing
potential leaders
30
Profitability
Efficiencies
0.6
25
Best
Perfomers
Star
Sleeper
Benchmark
Group
20
15
???
Dog
10
5
Under-performing
possibly profitable
0
20
Candidates
for closure
40
60
Efficiency
Figure 5: Efficiency – Profitability Matrix
9
80
100
P Cube - A Data Envelopment Analysis Based Solution for Business Process Intelligence
The Efficiency – Profitability Matrix on the previous page gives some very significant insights. All the four quadrants of
the matrix deserve to be analyzed separately. The analysis the four quadrants of the matrix are presented in the
following table:
Quadrant
Characteristics
Description
Star
High profitability
High Efficiency
The DMUs here are the best practice group and should be used
for benchmarking purpose by the top management
Sleeper
High profitability
Low Efficiency
These DMUs are just “satisfying” the shareholders. They have the
potential to perform better. They could be having high profitability
possibly because of favorable market condition. Low efficiency is
not a good sign from long-term perspective.
Question
Mark
Low profitability
Low Efficiency
These units are under-performing, and have the potential to
increase their operating efficiency. By increasing their efficiency
they can possibly move to the “star” quadrant.
Dog
Low profitability
High Efficiency
This is the most interesting quadrant. The DMUs in this quadrant
are efficient, but are still not profitable. Here the top management
needs to analyze the possible adverse market scenarios. Strategic
decisions such as closure of units in this quadrant can be taken
after further due diligence.
Table 4: Analysis of the Matrix Quadrants
Solution Features
Some of the advantages of the solution are as follows:
l
Scalability in terms of no. of DMUs or no. of inputs/outputs, so that with changes in business scenario or
evaluation methodology, no re-work on the model is required. It can scale up to any number of input, output or
DMU.
l
Adaptability to serve different application scenarios (covered in next section)
l
Flexibility to allow users to do scenario analysis by varying values (input / outputs) / weight restrictions. Can also
provide correlation analysis between inputs and outputs to come up with cause and effect relationships
between certain input and output combination.
l
User-friendliness to understand and analyze the results in simple dashboards to aid decision-making.
Different Application Scenarios of P Cube
Other than the multi-site performance evaluation scenario described earlier, there are a number of other scenarios
where P Cube be used. In fact, as stated earlier, P Cube can be used for performance evaluation of any process having
multiple inputs and outputs. Examples may be found in a variety of industries, both in manufacturing and services
e.g. Ford Motor Company, Emerson Electric, General Electric, GMAC, and Merrill Lynch.
The following diagram illustrates the various application scenarios in different areas of Supply Chain Operations
Reference (SCOR) model (SCOR is a process reference model developed by the management consulting firm PRTM
and AMR Research and endorsed by the Supply-Chain Council as the cross-industry de facto standard diagnostic tool
for supply chain management). P Cube has framework for each of these scenarios, and the solution can be seamlessly
integrated with the information management landscape of an organization.
10
P Cube - A Data Envelopment Analysis Based Solution for Business Process Intelligence
Multi-site
performance evaluation
Plan
Benchmarking of
Manufacturing Cells
Productivity analysis
of retail network
Plan
Plan
Deliver Source Make Deliver
Source
Return
Return
Supplier
Return
Return
Suppliers'
Supplier
Make
Your
Company
Internal or External
Supplier
Evaluation
Deliver
Return
Source Make Deliver Source
Return
Return
Customer
Return
Customer's
Customer
Internal or External
Manufacturing
system
performance
Total Productive
Maintenance
Marketing
Effectiveness
Supply chain
performance evaluation
Figure 6: Different application scenarios of P Cube
Conclusion
Monitoring of business processes, at both macro-level and micro-level, is very important for managing and
improving all aspects of a business. Several researchers have come up with different approaches for effective
monitoring of processes. But DEA approach, based on which TCS’ tool “P Cube” has been developed, has been found to
be the most effective approach, and is used by many organizations, both in the manufacturing and service sector. The
tool not only takes into account all the critical inputs and outputs, it also has the advantage of dynamically adjusting
the weights of the inputs and outputs. This provides level playing ground to all the peer units, ensuring wider
acceptability within an organization.
11
P Cube - A Data Envelopment Analysis Based Solution for Business Process Intelligence
Acknowledgements
1.
Sanjeet Singh, Assistant Professor in the Operations Management Department at Indian Institute of
Management Calcutta, for introducing the concept of Data Envelopment Analysis (DEA).
2.
M N Pal, Professor in the Operations Management Department at Indian Institute of Management Calcutta, for
exploring the use of Data Envelopment Analysis in Total Productive Maintenance (TPM).
3.
Anurag Dubey, Head, Business Intelligence & Performance Management (BIPM) Service, TCS Manufacturing
Industry Solutions Unit, for his continuous support in building the P Cube Solution.
4.
Anand Nanda, team member of Business Intelligence & Performance Management (BIPM) Service, TCS
Manufacturing Industry Solutions Unit, for his dedicated effort in the development of the P Cube solution.
12
About BIPM Service of Tata Consultancy
Services
Business Intelligence and Performance Management (BIPM)
service is the integration of three practices BI, EAI, and KM into
one BIPM Service. The service has been providing consulting
services to several Fortune 500 companies and there was an
increasing need to integrate these three practices to address
enterprise’s problems in holistic manner. BIPM service has a
consultant base of more than 9000 associates, rendering services
to over 300 clients globally.
About Tata Consultancy Services (TCS)
Tata Consultancy Services is an IT services, business solutions and
outsourcing organization that delivers real results to global
businesses, ensuring a level of certainty no other firm can match.
TCS offers a consulting-led, integrated portfolio of IT and ITenabled services delivered through its unique Global Network
Delivery ModelTM , recognized as the benchmark of excellence in
software development.
A part of the Tata Group, India's largest industrial conglomerate,
TCS has over 143,000 of the world's best trained IT consultants in
42 countries. The company generated consolidated revenues of
US $6 billion for fiscal year ended 31 March 2009 and is listed on
the National Stock Exchange and Bombay Stock Exchange in
India.
For more information on P Cube, please contact us at
manufacturing.solutions@tcs.com
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