# Network Diagram with Finish-to-finish Dependency

Most Critical Path problems that PMP aspirants encounter involve Finish-to-start (FS) logical relationship. Last month I challenged you with a slightly unusual Critical Path Method problem, involving Finish-to-finish dependency. Even though (in my personal opinion), such problems are beyond the scope of PMP exam, they are still quite fun to work with. Four gallant project managers attempted to solve the problem. Though their solutions were not 100% correct, they came pretty close to solving it. It was quite a laborious activity and I really appreciate the effort and time they put into it. I know that you all are pretty eager to know the solution. So, let’s dive in.

## Finish-to-finish Dependency

Before I give the solution, let’s understand the key to solving such problems. We begin with the definition of Finish-to-finish (FF) relationship in a Network Diagram in Critical Path Method, according to the PMBOK^{®} Guide, 5th Edition:

Finish-to-finish (FF): A logical relationship in which a successor activity cannot finish until a predecessor activity has finished.

In simple terms, two activities can run concurrently, but one cannot finish before the other finishes. Example? The PMBOK^{®} Guide gives a good example too. Writing a document (predecessor) is required to finish before editing the document (successor) can finish.

I came across another good example (I think it was on Tap University site) of Finish-to-finish relationship. The example is of baking a cake. We all know that in order to bake a cake, the oven needs to be heated first. While the oven is getting heated, you can prepare the batter. When the oven is heated to the desired temperature, you put the batter in the oven and bake the cake.

The first activity (predecessor) here is heating the oven, and the second activity (successor) is baking the cake including preparation of the batter. Both the activities can be performed concurrently, but the predecessor must finish before the successor finishes. Of course, there is a delay (the baking time) between the two activities. This delay is known as ‘Lag’.

Usually, in Finish-to-finish relationship, there is a lag between the two activities. In our example, we didn’t use any lag between activity E and activity F to keep things simple. Activity F (successor) can run concurrent to activity E (predecessor), and can finish as soon as activity E finishes. This is the *key* to solving this problem. Compare this to a Finish-to-start relationship, where the predecessor activity must finish before the successor can even start.

#### Solution

- Identify the Critical Path of the network.

Answer: The Critical Path is Start-B-D-G-I-End. Refer to the following network diagram for complete soluton (downloadable PDF file hosted on PM Hangout): - What is the duration of the Critical Path?

Answer: 22 days - Calculate the Early Start (ES), Early Finish (EF), Late Start (LS) and Late Finish (LF) for each activity on the Network Diagram.

Answer: Refer to the network diagram. - Calculate the Total Float (TF) and Free Float (FF) for each activity on the Network Diagram.

Answer: Refer to the network diagram. If you want to learn how to calculate TF and FF, refer to Total Float vs. Free Float in CPM. - If the duration of activity E is changed to 9 days, how will it impact the critical path?

Answer: The Critical Path will change to Start-B-E-F-H-I-End. The Critical Path duration will be 25 days (originally 21 days). - If the duration of activity F is changed to 8 days (with activity E's duration kept at the original value), how will it impact the critical path?

Answer: There will be no change to the Critical Path. Activity F can start earlier and still finish on the same date. Therefore, Critical Path will remain the same.

I hope you enjoyed this challenge. Look forward to more such fun posts in future. Questions, comments, suggestions?

Image credit: Flickr / Craigemorsels

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