# The Critical Path for the Adventurous Type

2 minute read    Updated:    Harwinder Singh

Critical Path Method (CPM) questions, specially those involving Network Diagrams, are among the trickiest questions on the PMP Exam. Fortunately, if you understand the concepts, the questions are not so difficult and offer a good scoring opportunity on the exam. But coming to the preparation, as with any other exam, we always aim a notch or two higher than what is required for the exam. As the saying goes, “Prepare for the worst, hope for the best” :)

Today I’m going to challenge you with a slightly unusual Network Diagram problem. Most PMP exam prep materials I have seen use Finish-to-Start relationships on the Network Diagram. In this article, you are going to see a Network Diagram with a Finish-to-Finish relationship. What? Yes, that’s right, Finish-to-Finish. So, bring your pen and paper and get ready to solve this problem.

Note: In all likelihood, this problem is beyond the scope of the PMP exam. But if you are an adventurous type, go ahead and take the plunge. We’ll have fun.

## Network Diagram with Finish-to-Finish Dependency

Refer to the Network Diagram below and answer the questions following it:

### Questions

1. Identify the Critical Path of the network.
2. What is the duration of the Critical Path?
3. Calculate the Early Start (ES), Early Finish (EF), Late Start (LS) and Late Finish (LF) for each activity on the Network Diagram.
4. Calculate the Total Float (TF) and Free Float (FF) for each activity on the Network Diagram.
5. If the duration of activity E is changed to 9 days, how will it impact the critical path?
6. 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?

### Solution

Please post your responses below and then tally them against the solution provided here:

Network Diagram with Finish-to-Finish Dependency

Image credit: Flickr / 1Happysnapper

1) Critical Path are BDOI and BEFHI
2) Duration of Critical Path=20
3) For Activity A ES=1, EF=4, LS=4,LF=7
For Activity B ES=1,EF=7,LS=1,LF=7
For Actity C ES=1, EF=5, LS=3,LF=7
For Activity D ES=8,EF=10,LS=8,LF=10
For Activity E LS=8,LF=12,ES=8,EF=12
For Activity F ES=9 EF=12,LS=9, LF=12
For Acitivy H ES=13,EF=15, LS=13, LF=15
For Activity I ES=16,EF=20, LS=16,LF=20

4) For Activity A TF=3,FF=3
For Activities B,D,O,I,E,H TF as well as FF=0
For Activity C TF=2,FF=2
For Activity F TF=0, FF=8

5) New critcal path=24

6) There will be no change in critical path

Hello Preetham,

That's a very good attempt.

My answers are slightly different from yours. I'll wait for a few more comments. Then we'll tally notes.

Thanks.

I used Preetham's format and simply changed the answers. This wasn't as simple as I initially thought but it was interesting.

Bob M

1) Critical Path is BEFHI
2) Duration of Critical Path=21 days
3) For Activity A ES=1, EF=4, LS=4,LF=7
For Activity B ES=1,EF=7,LS=1,LF=7
For Actity C ES=1, EF=5, LS=3,LF=7
For Activity D ES=8,EF=10,LS=8,LF=10
For Activity E LS=8,LF=12,ES=8,EF=12
For Activity F ES=9 EF=12,LS=9, LF=12
For Acitivy H ES=13,EF=15, LS=13, LF=15
For Activity I ES=16,EF=21, LS=16,LF=21

4) For Activity A TF=3,FF=3
For Activity C TF=2,FF=2
For Activity F TF=1, FF=0.
Everything else was 0,0.

5) New critcal path=25

6) Critical path would increase to 24 days.

1) Critical Path is BDGI
2) Duration of Critical Path=22
3) For Activity A ES=1, EF=4, LS=5, LF=8
For Activity B ES=1,EF=7,LS=1,LF=7
For Actity C ES=1, EF=5, LS=5,LF=9
For Activity D ES=8, EF=10, LS=8, LF=10
For Activity E LS=8, LF=12, ES=9, EF=13
For Activity F ES=9 EF=12,LS=10, LF=13
For Activity G ES=11,EF=16, LS=11, LF=16
For Activity H ES=13,EF=15, LS=14, LF=16
For Activity I ES=17,EF=22, LS=17,LF=27

4) For Activity A TF=4,FF=4
For Activity C TF=4,FF=3
For Activity F TF=1, FF=1
For Activity H TF=1, FF=2
For Activities B,D,G,I,E TF as well as FF=0

5) New critcal path=25d. Critical path is BEFHI

6) There will be no change in critical path

So far, Ramesh is the closest to the correct answer. I want to see couple more attempts before I post the solution.

So, keep it going guys.

Case 1
-------
Path 1: A-D-G-I = 19
Path 2: B-D-G-I = 22
Path 3: B-E-F-H-I = 22
Path 4: C-E-F-H-I = 20

Critical Paths: Path 2 and Path 3
Activity: ES-EF-LS-LF-FF-TF
A: 01-04-04-07-03-03
B: 01-07-01-07-00-00
C: 01-05-03-07-02-02
D: 08-10-08-10-00-00
E: 08-12-08-12-00-00
F: 10-13-10-13-00-00
G: 11-16-11-16-00-00
H: 14-16-14-16-00-00
I: 17-22-17-22-00-00

Case 2
-------
Path 1: A-D-G-I = 19
Path 2: B-D-G-I = 22
Path 3: B-E-F-H-I = 26
Path 4: C-E-F-H-I = 24

Critical Path: Path 3
Activity: ES-EF-LS-LF-FF-TF
A: 01-04-08-11-03-07
B: 01-07-01-07-00-00
C: 01-05-03-07-02-02
D: 08-10-12-14-04-04
E: 08-16-08-16-00-00
F: 14-17-14-17-00-00
G: 11-16-15-20-04-04
H: 18-20-18-20-00-00
I: 21-26-21-26-00-00

Case 3
-------
Path 1: A-D-G-I = 19
Path 2: B-D-G-I = 22
Path 3: B-E-F-H-I = 22
Path 4: C-E-F-H-I = 20

Critical Paths: Path 2 and Path 3
Activity: ES-EF-LS-LF-FF-TF
A: 01-04-04-07-03-03
B: 01-07-01-07-00-00
C: 01-05-03-07-02-02
D: 08-10-08-10-00-00
E: 08-12-08-12-00-00
F: 06-13-06-13-00-00
G: 11-16-11-16-00-00
H: 14-16-14-16-00-00
I: 17-22-17-22-00-00

Hi Harwinder,

Can you pls let us know the correct answer and the reasoning behind it?

Cheers,
Chandru

Hello Chandru,

I'll post the detailed response within next 2-3 days. Just caught up with work these days.

Thanks.

My Lesson learnt

Hello All,

I passed PMP Exam on Jan 9 2010. I would like to share my experience

I started serious study in Mid November. I went through the following books

2. PMP Exam Prep - Rita Mulcahy
3. PM Exam how to pass it with your First Try
4. PMP exam prepartion - Kim Heldman
last but not the least PMBOK guide

If you are a beginer and find PMBOK is too tough to understand then you can start with Head First PMP as I found it very simple and easy to Grasp.

Rita Mulchay book is good however you need patience to read it completely so my suggestion is use it for Reference especially for problems and also This book covers Procurement managemnt in detail. This chapter you can read from here.

Kim Heldman book is different. All the books available in the market follows the structure of PMBOK, however KIm Heldman has done great job. She has orgnized the chapters in the order of the processes and not in terms of knowledge areas, you can get good understanding of how knowledge areas fit into each other. Also the practice tests available in this book and CD are exceptionally good.

Andy Crowe book is so so. It does not cover mant important topics like Team building (Forming .. storming..) Also does not explain the use of EEF and OPA in detail. However there is one advantage. This book gives 1 week free subscription to Andy Crowe`s velociteach website, here you will have CBT , pratcice exams and also if you are looking for 35 contact hours you can get them here.

Then Read PMBOK atlest once. after reading the above books PMBOK makes lot of sense.

I caution people against buying the PM Prepcast and also Numerous online CBTs, I found PM Prepcast by Mr.Fischner is ok, but not very good. His covergae on Risk managment, EVM is good, however in some places he becomes news reader as he just goes on talking as if he is reading PMBOK for you and critcizes PMBOK as dry.. forgetting the fact that his session is becoming too dry and boring. If you are a book hater and good listener then you can try your luck here. Some CBTs like Rita`s are too costly and your orgnization may not sponser so much money.

It is good idea to practice the numerous practice exam available for free. I did alomost a dozen exams.

Develop a habit to read Mr. Harwinder`s blog. He has done great job. He can think of bringing out a prep book by himself.

I gave the exam in japan, so i did not face problem in getting the booking for the exam date. Also if you stay in tokyo-yokohama area you will have exam center close to you.However it is a good idea that you visit the exam center if possible so that on the exam day you need not roam around searching for the adress. The exam center in Yokohama was on 9th floor calm and quiet.

I wish all the aspirants all the best.

Sujeeth

Hello Sujeeth,

Congratulations !! I'm so glad to hear this news. Thanks for your strong recommendation and sharing your extremely useful lessons learned.

May I request you to re-post your lessons learned on the http://www.deepfriedbrainproject.com/2009/03/pmp-certification-exam-lessons-learned.html page? It would give better visibility to the information. After you post them there, I'll delete them from this page.