Few businesses know how to measure complexity and, worse still, manage it. This white paper presents a clear and concise solution that can be easily implemented in any performance measurement system. It provides an accurate understanding of how companies can manage complexity on a continuous basis, as well as operate more efficiently without being prematurely hit by the law of diminishing returns.

1. - Dr. Martin Lockstrom
Measuring Complexity in a Simple Way
INSIGHTS

2. According to the old adage, you cannot
manage what you cannot measure. This is
no less true when it comes to complexity
management. In our experience, very few
companies have a stringent definition and
KPIs for complexity that can be applied
throughout the organization; without
that coherence, it is impossible to make
comparisons across companies and
business units.
The simplest way to measure complexity
is to simply“count the number of things”
in a given area of study. However, such
a simple approach wouldn’t actually
measure complexity in a true sense, but
rather, merely the size or magnitude
of those things. Hence, we have to
complicate things a bit by also looking at
how the items that drive complexity are
interrelated and distributed. For instance,
if we measure organizational complexity
through the number of staff per business
unit, it is clear that a company which has 5
business units with exactly 100 employees
in each is simpler than a company with
5 business units where the headcount in
each business unit is 20, 150, 100, 80, and
66, respectively.
In order to deal with this challenge, we can
utilize a similar but slightly different variant
of entropy from statistical mechanics.
Here, entropy can be defined as“the
amount of information needed to specify
the exact state of a system”. In a business
context, this implies that the more complex
the organization, the more information
required to describe it, and hence, the
harder it is to manage. At some point, the
limitations of human cognitive capabilities
become a bottleneck to effective
management.
One way of measuring complexity can
be by using Shannon’s entropy [14],
which measures the minimum amount
of information needed to complete a set
without any losses and can be calculated
as H(X)=∑n
k = 1
-pk
log pk
with pk
log pk
≡ 0
when pk
= 0.1
p denotes the fraction or share
of an entity out of a total.
Let’s consider the following illustrative
case: For a business with a simple structure
(only one establishment, i.e. n = 1), its
entropy equals 0 (H(X) = 0). For a given
number n of establishments within a
business, the most complex structure
would be for a uniformly distributed
business with (1/n, 1/n, …, 1/n) since
the number of entities vis-à-vis the size
of each piece of information is in this
way maximized. Its entropy would be
maximized with H(X) = log n. If a complex
1
The concept is borrowed from the science of information theory, and is a measure of the uncertainty associated with a random variable X having n possible values
x1, x2, ..., xn using a distance between two probability distributions. It is defined as the expected value of the logarithm of the inverse probabilities: H(X)=E⌊logP-1
(X=x)⌋= H(X)=∑n
k = 1
-pk
log pk
with pk
log pk
. We have 0 ≤ H(X) ≤ log n with H(X) = 0 when X takes only one value with a probability of 1 (P(X = xi) = 1) and H(X) = log
n when all n possible values of X follow a uniform distribution (P(X = xi) = 1/n).

3. business contains many establishments
but one represents a very large proportion
of its size, the entropy would be very low
since the uncertainty is highly reduced
once we know the information related to
the main piece of the business.
Consider five companies A-E, each with
500 employees. Company A has one BU
Table 1. Example of business complexity2
Business i
Business
Size yi
Size Partition at Size Partition at Establishment Level Structure
Complexity
pik
Complexity
Metric
KI
= yi
nik=1 k=2 k=3 k=4 k=5
A 500 1.000 0.000 0
B 500 0.500 0.500 0.301 151
C 500 0.900 0.025 0.025 0.025 0.025 0.201 101
D 500 0.500 0.125 0.125 0.125 0.125 0.602 301
E 500 0.200 0.200 0.200 0.200 0.200 0.699 349
with 100% of its employees; company B
has two BUs with a 50/50 distribution of its
employees, and so forth.
Here are some observations: Business
A has only one establishment so its
complexity factor and its complexity metric
are 0. Business B has two establishments
equally divided. Its complexity factor is
ηi = log 2. Businesses C, D and E have five
establishments. However, C is heavily
concentrated on one establishment so its
complexity factor is highly reduced, while
E is uniformly distributed among its five
establishments so ηi = log 5.
2
Source: Godbout, S., Youn, S., ” Measuring the Complexity and Importance of Businesses in Order to Better Manage our Data Collection Efforts”,

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Author Profile
Dr. Martin Lockstrom
Principal Consultant, Building Tomorrow’s
Enterprise, Infosys Labs
Martin is a specialist in Supply Chain and
Operations Strategy, Outsourcing/Offshoring
and International Management. During a
six-year stint in China, he established the
research and education activities at the SCM,
Sustainability and Automotive academic centers
at China Europe International Business School,
Shanghai.
He established the first endowed chair
for Purchasing and SCM in China at Tongji
University, Shanghai, and was also responsible
for setting up Supply Chain Management
Institute China, an international network of SCM
research and education hubs.
Martin co-founded Procuris Solutions, an IT
company specializing in SCM-related solutions,
offering consulting services to companies like
Accenture, Ariba, BMW, Clariant, Dell, Dow,
Ernst & Young and Intel, among others.
He has a Ph.D. in Supply Chain Management
from European Business School, Germany, a
bachelor’s and master’s degree in Industrial
Engineering and Management, from Chalmers
University of Technology, Sweden. He speaks
Swedish, English, German and Chinese, has
published over 50 articles and papers and
presented at more than 60 conferences.
Summary and Conclusion
Most companies have a clear definition
and understanding of the concept
of complexity, but few know how
to measure and manage it. In this
article, we have proposed a clear and
concise solution, which can be easily
implemented in any performance
measurement system. By continuously
managing complexity, companies
will be able to not only operate more
efficiently, but also grow without
being prematurely hit by the law of
diminishing returns from excessive
overhead costs.