- Dr. Martin Lockstrom

Measuring Complexity in a Simple Way

INSIGHTS

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).

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 iBusiness

Size yi

Size Partition at Size Partition at Establishment Level Structure Complexity

pik

Complexity Metric KI = yinik=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 ConclusionMost 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.