Complexity is all around us. In our daily lives, we see complexity in the flow of traffic, changes in the weather, population changes, organizational behaviors, shifts in public opinion, stock markets, urban development and epidemics. Like all these systems in our lives, businesses are also complex systems, often created by the joining of several other complex systems.

The traditional approach to analyzing complex systems is called "reductionism," which simply means large systems are broken into their constituent elements, and each element is studied independently. This approach is regularly used when businesses try to find efficiencies in their internal processes, but is often ineffective for a number of reasons.

The size of complex systems is usually prohibitive for purposes of analysis. While identification of each component in a system may be straightforward, understanding the detailed intricacies and interactions between components proves to be very difficult. A reductionist approach usually requires many assumptions and approximations to be made. These approximate "models" of the system must be tweaked to accurately reflect the real world. The models then become ineffective for decision making when any of the assumptions prove to be wrong.

Complex systems are characterized by their non-additive nature. In the business world, it is obvious that "The whole is greater than the sum of the parts." Consequently, even if it were possible to understand the individual components of a complex system in all their detail, an understanding of the system as a whole would not be a simple "addition" of these individual understandings. A more scientific way to express this non-additive nature is to say that complex systems are highly non-linear.

Non-linear systems do not react as might be expected during growth. This phenomenon has been seen many times when businesses try to expand. Overall productivity is not a simple function of the number of people or available resources. If a company is producing 10,000 units a day with 100 employees, they can’t necessarily double production with 200 employees. Production will often respond in a non-linear fashion, either by being much more or less than expected. Strong and profitable companies often suffer from this effect when they try to grow too quickly.

So, if reductionism is an ineffective method for analyzing complex systems, what methods are effective?

Over the last few decades, a new science has emerged to better understand how complex systems function. Complexity Science is the study of systems made up of many complicated components that interact in non-linear ways. Complexity science has taught us that the dynamics of all complex systems, whether they be biological or man-made, are very similar. This has given rise to a new set of methodologies and tools for analyzing these systems.

Since complex systems behave in non-linear ways, it becomes necessary to detect when and how changes will occur. Borrowing from the earlier example, if productivity is not directly correlated with the number of employees and resources, then how can we know what resources are necessary to meet a given level of production? These necessary levels or "jumps" in resources are called phase transitions, and Complexity Science has given us ways to identify when and where or where they will occur. Once we find the phase transitions we then "know" what changes must be made to produce a desired effect.

One of the truly remarkable findings in Complexity Science is "emergence" or the phenomenon in which global behaviors spring from a few simple rules. In a business system, these rules may be: "fill trucks completely before sending them out", "one box should contain 25 pieces", or "shifts last for exactly eight hours." The resulting behavior may be that packages always tend to arrive to late.

The classic example of emergence comes from examining the way birds flock. Flocking appears to be a game of "follow the leader" where each bird falls in according to rank. In reality, each bird is simply following a few basic rules. Rules like: "avoid hitting other birds", "Fly in the same general direction as the rest of the birds", and "fly with birds of your own species." From these rules, we get the emergent behavior of flocking.

Agent-Based Modeling is a technique derived from Complexity Science that enables us find emergent behaviors in complex systems. Software "agents" replicate their real world counterparts by following a few simple rules. These agents are then run in a simulation environment where emergent behaviors are actually "generated." An Agent-Based Model can then be used to determine which rules should be changed in order to produce a new emergent behavior.

For a simple example of how an Agent-Based Model may be used to solve a business problem, imagine a company that always tends to be late with deliveries. A simple model could be built to replicate the real world system. In this example, the trucks, factories, warehouses and assembly lines might be modeled as independent software agents, each with their own set of simple rules. The agents would then be allowed to run freely in a simulation environment. The simulation should quickly replicate the late shipments that are occurring in the real world.

The model would then be allowed to make changes to its set of rules. For example, trucks may be allowed to leave the factory when they are only half full, or employees may be allowed to work less, or asked to work more. The simulation then evaluates the new performance against the objective of no late deliveries. The model can quickly find the set of rule changes that maximizes the desired objective.

Similarly, the Agent-Based Model can be used to identify the phase transitions, or high-leverage points where a minimum amount of resources and labor will generate the highest returns. Identifying these points is key to making the best business decisions.

Over the next decade, lessons from Complexity Science promise to generate some of the most astounding improvements in business, government and military operations. Early adopters have already achieved significant results. New products can rapidly penetrate consumer markets by understanding how marketing messages travel through social networks. Both automobile and pedestrian traffic have been analyzed so that freeways aren’t as likely to back up and amusement parks can have smoother flows when rides are down. Battle scenarios can be simulated to find which strategies are most effective for a given enemy, and drug traffic can be reduced by determining which parts of the network are most critical. It will be exciting to see what remarkable results are around the corner.