The graph below demonstrates something that every LEGO enthusiast quickly realizes: the more pieces in a set, the greater the number of different types of pieces. The same principle applies to projects: the more tasks needed to create the project product, the greater the variety of tasks. This is the first reason why projects can quickly become more complex as you add tasks.
The concept to understand this is quite easy. Imagine you have a LEGO set that has only five pieces. Let’s also imagine that each piece can connect to any other piece in any order. So, you take the first and connect another piece to it. Now, you have three possible pieces to attach to your joined pieces. You can represent it this way: 5 pieces to choose from X 4 pieces to choose from X 3 pieces to choose from X 2 pieces to choose from X the final piece left. If you keep choosing different pieces every time you build your five piece figure, you will end up with 120 different ways to build a figure.
Now, add a piece. The number of ways to build a six piece figure now shoots up to 720 different ways! I know some of you LEGO experts are disputing my exact numbers because not every piece can connect to another given piece but, you will admit that it only takes a few extra pieces to greatly increase the variety of things you can build. To see how this applies to projects, think of the network diagram tool.
In the example network diagram below, you see various tasks that are connected to each other in the order that they should be performed. Task A has to be completed before you start with Task B or Task C. Some tasks can be started at the same time with other tasks need the output from another task before it can start. The greater the number of tasks, the more paths you can create that links tasks together.
Thus, this is the first way that projects can quickly become more complex than what would appear from just looking at the number of tasks. A project with ten tasks is not only twice as complex as a five task project. The ten task project can be up to 30,000 times more complex in terms of the different paths that can be constructed (although it is more realistic to be around a 1,000 times more complex because of precedence relationships).
To add to this complexity are the constraints of scheduling, budget, and resources. Every project has a deadline and therefore you have a limited amount of time you can spend on a given task. You also have a budget that dictates how much money can be devoted to a task and to the resources that will perform the tasks. Even though it is common for a project to overrun the budget and take more time than scheduled, at some point you will run out of time, money, and/or resources. So, the triple constraints of time, money, and resources will limit the number of task paths you can create, there is the additional complexity of creating paths that optimize the use of time, money, and resources.
A third layer of complexity is the number one reason projects fail: communication. As a project manager, you will spend most of your time communicating with your project team and stakeholders. Your stakeholders and project team can also communicate with each other. For every person involved in your project, they have a channel to any other person involved in the project. In fact, knowing the number of people involved in your project tells you how many possible communication channels there are. Just multiply the number of people involved in the project times that same number minus one. Then divide that product by two. For example, if you have seven people involved in the project, there are 21 possible communication channels. Now, add another person. This adds an additional seven more communication channels.
Again, these are possible communication channels and you may have restrictions on who can talk to whom. Even so, as you continue add additional people, the number of communication channels can rapidly increase although not as quickly as when you additional tasks. Unlike tasks, the ever-increasing number of communication channels can quickly overwhelm you with information. It is like trying to monitor 21 radio stations and then seven more stations are added. Meanwhile, as you monitor the 28 stations, you are also trying to transmit to any number of the stations.
These are the three major ways a project can become complex: the number of tasks; the triple constraints of time, money, and resources; and the number of communication channels. Adding to the complexity is that each factor mixes with the other two factors to ramp up the complexity even more. That is why what seemed like a simple project can suddenly skid out of control when you add a few more people, a few more tasks, and your deadline/money/resources start to become scarce.
The source for the LEGO graph – Arbesman, S. (January 6, 2012). The Mathematics of Lego. Wired. http://www.wired.com/wiredscience/2012/01/the-mathematics-of-lego/