Case Study: Using CPM or PERT in time planning & control

For over three decades, I worked for a development bank. My main job was to evaluate proposals for setting up of industrial projects initially as an Officer and later as Head of the Division. I have many interesting stories to share in project planning and implementation. One such story is the success of Pakistan Mineral Water Corporation (PMWC) in water-bottling. The company no more exists. It has since been swallowed up by multinational brands of bottled-water like AVA, Aquafina & Culligan.

In early 1986, three companies, including PMWC, applied for water- bottling plants. The market justified only one. I called sponsors of the companies and told them that I would recommend the case of one which could demonstrate its ability to go into production before October 1987. “What is that for!!!” all spoke at the same time. “Well, as a bottlers you should know upcoming Cricket Cup at Karachi” I told them and added, “Anyone who catches the event would have an instant success.” Only one, J. Rashid of PMWC, turned up with a rudimentary sketch of CPM which convinced me of his ability to beat the deadline.


Simply put, CPM stands for Critical Path Method used in planning and controlling time. It helps estimate time for project completion, pin-points activities critical for achieving the target. Above all, it gives a graphic view of the activities of a project which is easy to understand in one go.



As per information provided by J. Rashid, the project required basic facilities like land, building and machinery which have been shown in Table #1 along with estimated time. As would be observed that after acquiring land, the company can go for three activities: (i) placing order for machinery, (ii) construction of building, (iii) placing order for plastic bottles for water filling.

When buildings are complete, machines can installed and the same time, racks can be erected for storing plastic bottles. Thus the company can go for trials runs as necessary pre-requisites are in order.

Format of a network or CPM varies. Basic structure is given in the text books or Software (MS Project 2007) which can be suitably modified. Personally, I like a detailed format for presentation.

Here each box or node has nine cells as shown in its legend. ES means Early Start while EF mean Early Finish.

In sketch # 1, some information has already been inserted about a particular activity such as ID, Description & Duration. The activities are also placed keeping their relationships in view.

Sketch # 1


Let us start with ES & EF. This is simple except where we confront a Merge Event. We would insert Zero ( or expected date ) in the first cell of activity #1. Since duration for this activity is 1 month, the EF would be 0 + 1 = 1. Same would be carried for activities #2, #3 & #4 and EF worked out accordingly.

The ES of activity #5 would be 9, same as EF of its predecessor #3. It is natural; you cannot start erecting racks (#5) unless buildings (#3) are complete.

When you go next to activity #6, you would see two activities (#2 & #3) are merging. Obviously, you cannot start installation of machines (#6) unless the machinery has arrived as per order (#2) and buildings (#3) are complete. Here we would take maximum of EF of the both as both must be complete before #6 can be started. In the same way, we can complete rest of the diagram. We find that the project would take 19 months to be completed as shown in Sketch # 2 below:

Sketch #2


As the name implies, we move backward to the origin. In this example, the project completion time is 19 months. So its Early Finish (EF) or Late Finish (LF) must be the same. In other words, call it early or late, it must be finished by 19th month.

We start from last activity #8 and insert 19 in its LF cell. This activity has duration of 4 monthss. Calculating backward, we find that its LS should be 15th months (19 - 4 =15 ). In other, if #8 was started as late as on 15th months and it takes 4 months, it could still meet the deadline of 19 months.

We go back further and trace tails of any arrows touching #8. We find two, one linking with #7 (Store Raw Materials) and other with #6 (install machinery). We would put 15 in the LF Cells of #6 & #7. We can now calculate their LS by deducting from 15 their respective durations. For example, the LS of #6 should now be 9 (15-6=9).

We can continue likewise till we hit a "Burst Event" like #3 & #1. For explanation, #1 would be better as three activities are leading back to this activity. (There are three tails touching #1.) In such a situation, we shall take minimum of the LS of the three which is one month and it would be LF of #1. Why? The longest activity after #1 is #3. In order to enable #3 to start on time, it is essential that the preceding activity is completed well in time.

The complete working is shown in Sketch # 3 below:

Sketch # 3


PERT stands for “Project Evaluation and Review Technique”. It is almost the same as CPM except for the following differences:

  • CPM is for repeated projects while PERT is for first-timers.
  • CPM is used both for time and cost whereas in PERT only time is taken care of.
  • Because CPM is for repeated projects, there is a track-record or database of previous projects. It enables the manager to be realistic in their estimates. For PERT, being for first time projects, one has to ask the knowledgeable persons to give time-estimates for each activity as to (i)Minimum time as in most favorable conditions, (ii) Maximum time as in most unfavorable conditions and (iii) Normal time. Thereafter a weighted average is calculated as shown in Sketch #4.


Sketch #4


Once time has been estimated, the rest is the same as in CPM.

In the upcoming articles, I would cover probabilities of project completion in different situations, relationship amongst activities, slacks and resource management.

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Comments 42 comments

asifkamran 7 years ago

nice case

hafeezrm profile image

hafeezrm 7 years ago from Pakistan Author

For Mr. Shahnawaz Sheikh.

In CPM & PERT, there is a small difference in working and that too only in the initial stage. While for PERT, we use a weighted average of minimum, maximum and most likely, in CPM we are already given a completion time and so there is no need to compute. In PERT, we use the formula: (minimum x 1)+(maximum x 1)+( most likely x 4). The total would be divided by 6 since weights are six (1+1+4) to arrive at Time Estimate.

Hope this clarifies you query?

khalid akhter 7 years ago

Its a realy very nice xplanation of PERT n CPM..i learned a lot for this practical xample as i have already learn these 2 mthod in ICMA ...but u desribed it very well ..nice case stdy

hafeezrm profile image

hafeezrm 7 years ago from Pakistan Author

For Shahnawaz Otho. Please read my comments, third from the top. It further explains the nature of sketch #3.

Malik Tahir 7 years ago

Thank You very much for sharing such a knowledgeable case.

I will ask you for help later on.........

Uptil now, each and every aspects of case, are clear.

linjingjing profile image

linjingjing 7 years ago

Good article


Numan Nazir 7 years ago

Thank you v. much.....

Am I rite if i interpret sketch # 3 as:

If the company starts late....It is Intalling racks, machinery and packing orders at the same time. Must start pacing orders by the 11th month and must finish it by the end of the 13th month....Must start install Machinery in Month 9.....and the company is instaaling machinery and packing orders in month # 11....

mubin_ashraf profile image

mubin_ashraf 7 years ago

That's really informative

I think that these pictorial views give me more understanding to have in your articles.


Mubin Ashraf.

Asif Kamran 7 years ago

thank yo so much for sharing your articale

Fahad_Khan profile image

Fahad_Khan 7 years ago from Karachi

I've saved this case study for future reference. Thanks a lot to Mr. Hafeez Ur Rehman for this excellent work.Regards,Muhammad Fahad Khan.

sufyan majeed 7 years ago

very informative article

osama 7 years ago

why the most likely to happen take the weight 4

hafeezrm profile image

hafeezrm 7 years ago from Pakistan Author

It is a normal condition others ( minimum or maximum, optimistic or pessimistic, most favourable or un-favourable) have less chances. Considering law of probability normal condition is likely to occur many times in a given scenario and therefore given the weight of 4. By normal condition mean usual condition. If there are power outage for 4 hours a day, it is said to be normal or most likely. If condition improve for an extended period of time to no-power outages, it would become normal.

osama 7 years ago

thanks for your care ,but iam asking why specialy 4 not 3 or 5 (i need an explanation from the point of statistical view)

hafeezrm profile image

hafeezrm 7 years ago from Pakistan Author

PERT Formula for Variance is developed after long deliberations by the statisticians. They have given a weight of four to most-likely event. (Certainly, this weightage is not mine).

hafeezrm profile image

hafeezrm 7 years ago from Pakistan Author

CPM is used for repeated projects. It is based on track record or database already with us. But when we want to venture into some projects which we have never handled before, we are bound to use PERT where we ask knowledgeable persons to give us optimistic, pressimistic and normal time estimates. By taking their weighted average, we can have an idea about expected duration.

tanu 7 years ago

really this text helped me a lot

and cleared my doubts..

thanks .

Abu Bakar 6 years ago

A very good lecture well explained Thank You

Bilal Shahmeer profile image

Bilal Shahmeer 5 years ago

very informative case study sir it would really help us in our course. Thank you for shearing this with us.

kamran 5 years ago

very informative article.

Sajid Iqbal profile image

Sajid Iqbal 5 years ago

I have studied it deeply and come to know the soul of the article. thanks

asadayub profile image

asadayub 5 years ago

Respected Sir, the article is really very good. Although, you had taught this article to us in the Class, but its really very interesting to read the material of which you had a little knowledge. This enhances your Knowledge more and more. Thanks a lot for such nice Hubs.

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Rikbea 5 years ago

Dear Readers,

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anurag singh 5 years ago

very helpful case study,thanks for sharing with us.

hafeezrm profile image

hafeezrm 5 years ago from Pakistan Author

Thanks Anurag Singh for your comments.

shaista tabassum 5 years ago

gud article

hafeezrm profile image

hafeezrm 5 years ago from Pakistan Author

Thanks for going through my article.

honey 4 years ago

very informative sir

hafeezrm profile image

hafeezrm 4 years ago from Pakistan Author

Thanks Honey for your comments.

ASMA NAZ 4 years ago


hafeezrm profile image

hafeezrm 4 years ago from Pakistan Author

Thanks Asma Naz for your comments.



this case study is very informative and it helped me to understand all that points which i did nt get in class so thank you very much in order to share this case study.

hafeezrm profile image

hafeezrm 4 years ago from Pakistan Author

Thanks Zohaib for your comments.

Asif ali 4 years ago

Any body help me below mention question.

Identify the projects in which an organization can use PERT. Explain with examples.

hafeezrm profile image

hafeezrm 4 years ago from Pakistan Author

PERT is used when undertaking a new project which is first of its kind for any sponsor. Generally, all R&D projects fall into this category. In fact, PERT is useful in uncertain conditions. Atkins Hotel at Islamabad, Pakistan is an example.

Muhammad Adil khan 4 years ago


Its a realy very nice explanation of PERT and CPM.And also very informative case study.I thanks a lot For sharing your knowledge.

hafeezrm profile image

hafeezrm 4 years ago from Pakistan Author

Thanks Muhammad Adil Khan for your comments.

zohaib noor 4 years ago


excellent work i read your hub pages regularly .

anaz 4 years ago

Thank you sir for your demonstration . How the lag and lead affect the critical path.

hafeezrm profile image

hafeezrm 4 years ago from Pakistan Author

In critical path, there is neither lead nor lag rather it is bumper to bumper boxes and that is way it is called critical.

mmm 3 years ago

giev me solution

Shale Oil Company’s Aston, Ohio, manufacturing complex comprises several operating units. These units process the crude oil that is pumped through and transform it into a multitude of hydrocarbon products. The units run 24 hours a day, 7 days a week, and must be shut down for maintenance on a predetermined schedule. One such unit is Distillation Unit No. 5, or DU5. Studies have shown that DU5 can operate only 3 years without major equipment breakdowns, and excessive loss of efficiency. Therefore, DU5 is shut down every 3 years for cleaning, inspection, and repairs.

DU5 is the only distillation unit for crude oil in the Aston complex, and its shutdown severely affects all other operating units. Some of the production can be compensated for by Shale refineries in other locations, but the rest must be processed and stored before the shutdown. Without proper planning, a nationwide shortage of Shale gasoline could occur. The time of DU5’s shutdown is critical, and the length of time the unit is down must be kept to a minimum to limit production loss. Shale uses PERT as a planning and controlling tool to minimize shutdown time.

The first phase of a shutdown is to open and clean the equipment. Inspectors can then enter the unit and examine the damage. Once damages are determined, the needed repairs can be carried out. Repair times can vary considerably, depending on what damage the inspection reveals. Based on previous inspection records, some repair work is known ahead of time. Thorough cleaning of the equipment is also known to improve the unit’s operating efficiency. The table below lists the many maintenance activities and their estimated completion times.


1. Determine the expected shutdown time and the probability that the shutdown can be completed 1 week earlier.

2. What are the probabilities that Shale finishes the maintenance project 1, 2, 3, 4, 5, or 6 days earlier?

3. Shale Oil is considering increasing the budget to shorten the shutdown. How do you suggest the company proceed?

mmm 3 years ago

this tabal

Preventive Maintenance of DU5

Activities Time Estimates (in Days)

Optimistic Most Likely Pessimistic

1-2 Circulate wash water throughout unit 1 2 2.5

2-3 Install blinds 1.5 2 2.5

3-4 Open and clean vessels and columns 2 3 4

3-5 Open and clean heat exchangers; remove tube bundles 1 2 3

3-6 Open and clean furnaces 1 2 4

3-7 Open and clean mechanical equipment 2 2.5 3

3-8 Inspect instrumentation 2 4 5

4-9 Inspect vessels and columns 1 2 3

5-10 Inspect heat-exchanger shells 1 1.5 2

5-11 Inspect tube bundles 1 1.5 2

6-12 Inspect furnaces 2 2.5 3

6-17 Retube furnaces 15 20 30

7-13 Inspect mechanical equipment 1 1.5 2

7-18 Install new pump mechanical seals 3 5 8

8-19 Repair instrumentation 3 8 15

9-14 Repair vessels and columns 14 21 28

10-16 Repair heat-exchanger shells 1 5 10

11-15 Repair tube bundles; retube 2 5 10

12-17 Repair furnaces 5 10 20

13-18 Repair mechanical equipment 10 15 25

14-20 Test and close vessels and columns 4 5 8

15-16 Install tube bundles into heat-exchanger shells 1 2 3

16-20 Test and close heat exchangers 1 2 2.5

17-20 Test and close furnaces 1 2 3

18-20 Test and close mechanical equipment 1 2 3

19-20 Test instrumentation 2 4 6

20-21 Pull blinds 1.5 2 2.5

21-22 Purge all equipment with steam 1 3 5

22-23 Start up unit 3 5 10

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