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Case Study: PERT / CPM - Calculating Floats

Updated on November 20, 2011

NET WORK # 1

This is in continuation of my previous Case Study on CPM & PERT. Here I would describe ways and means to calculate Floats or Slacks. A little change has been made in Sketch # 3 in the previous article. Description has been reduced to one cell. Since there is not enough space for full description, identifying letters have been inserted in the respective Cells.

Two more Cells have been introduced for accommodating Free Float (FF) and Total Float (TF). All other figures are the same as shown in Net Work #1.

WHAT IS A FLOAT?

A float shows time available for delaying an activity without delaying Finish Date of the Project.

In other words, delay in some activity would not increase the project duration. Please note that Critical Activities cannot be delayed. However, Non-Critical Activities can start late or finished late within the given limitation. Other names for float are: slack, cushion, margin, excess time or flexibility.

For calculating floats, there are different Methods depending upon format of the Network used. There are two types of Net Works: Activity-On-Node (AON) and Activity-on-Arrow (AOA). Results are same in both cases.

Net Work # 2

TWO TYPES OF PRESENTATIONS

For better understanding, two versions of the same net work are given as per Network #1 and #2 and briefly described below:

AON ( see Net Work #1)

  • A new format used by project management softwares.

  • Better at showing different types of dependencies.

  • Easy to understand. Can be constructed through placing cards each with name of an activity. Good for group discussion.

AOA (see Net Work # 2)

  • Nodes or circles are the starting and ending points of activities.
  • Activities are represented by arrows showing relationships between activities.
  • Sometimes, dummy activities (dotted lines) are used for linking two activities.
  • Can only show finish-to-start dependencies.

THREE TYPES OF FLOATS

INDEPENDENT FLOAT (IF)

  • Shows the time available even if an activity has a Late Start and Early Finish.
  • It is most adverse type of float and often results in a negative figure.

FREE FLOAT (FF)

  • Also called Normal Float, it shows time for which an activity can be delayed without delaying the early start of successor activity/activities.

  • If there are more than one succeeding activities, minimum of the floats would be taken as free float.

  • FF will always be less than or equal to TF and never more.

  • In all critical activities, FF is always zero.

TOTAL FLOAT (TF)

  • It shows time for which an activity can be delayed from its ES without delay in project completion. (In FF, when one activity was delayed, the succeeding activity was started on time as per its ES and not delayed.)
  • As in FF, in case of more succeeding activities, minimum to be taken.
  • in TF, however, if one activity is delayed, the succeeding activity or activities would be affected or re-scheduled.
  • On Critical Activities, TF is always zero ( as well as FF)

SUB-SET OF AON

CALCULATIONS OF FLOATS UNDER AON

  1. INDEPENDENT FLOAT (IF) : EF – LS = 10 -4 =6
  2. FREE FLOAT (FF) : G(ES) –D(EF)= 10 – 4 =6
  3. TOTAL FLOAT (TF): D (LF) – D(EF)= 13 – 4 = 9

In case of free float, the formula is: Early Start of Successor Activities (G) minus Early Finish of Existing Activity (D). Naturally, if we can finish an activity early but the next will start sometimes later, we have a free float to delay our activity.

CALCULATION OF FLOAT UNDER AOA

  1. INDEPENDENT FLOAT (IF) : EF – LS = 10 -4 =6
  2. FREE FLOAT (FF) : G(ES) –D(EF)= 10 – 4 =6
  3. TOTAL FLOAT (TF): D (LF) – D(EF)= 13 – 4 = 9

formulae are:

  1. IF(i,j)=EF(j) -ES(i)-D(i,j)

  2. FF(i,j) = EF(j) - ES(i) - D(i,j), (If there are more than one activities, minimum thereof)
  3. TF(i,j) = LF(j) - ES(i) - D(i,j) (If there are more than one activities, minimum thereof)

DISPLAY OF CALCULATED FLOATS UNDER BOTH FORMATS

Network # 3 and Table #1 show calculated floats in their respective places. AON is verstile format and can accommodate all type of floats.  ( I have given only two types TF & FF but it can be expanded.) In case of AOA, the floats are to be shown separately which makes it rather inconvenient to follow.

NET WORK # 3

TABLE 1

TABLE #2

CONFLICTS IN CALCULATION & COMMON SENSE

Sometimes, floats given by formulae do not appeal to the common sense. It happens in both cases whether AON or AOA. The floats are, however, result of a natural flow and a visionary project manager would easily spot a flaw in calculation.

For example, FF in case of activity 2-3 in AOA is different from the one shown under AON. The reason is that in AOA, dummies are used which distort the straight calculation.

Here we can resort to Gantt Chart to reconcile the difference as shown in Table #2.

Interference Float

Interference float is the difference between total float and independent float.

Supposing there is a conference of 5,000 participants in an Island. The conference would be for 5 days starting from 17th June and ending on 21st June. To transfer a large number of people, the flights to island would start from 1st June to 16th June and the return would be from 22nd June to 30th June. Suppose further that the Island has a lot of sight-seeing opportunities on the side.

Now if some big boss is interested only in conference, he or she can leave on 16th June and return by 22nd June. In this way, one day would still be available for shopping or sightseeing calculated as follows: (22 – 16 - 5). This one day is called Independent Float and is available in any case.

On other hand, total float (or total time for sightseeing) would be for 24 days when someone starts on 1st June and returns on 30th June.

So one cannot devote more than 24 days for sight-seeing while one has to spend one day because of flight schedule. It is evident that one can interfere or modify the schedule for sight-seeing for 23 days ( 24 -1).

WHY FLOAT IS IMPORTANT?

If every activity had a fixed start date and a fixed end date, it would be very difficult to complete the project in time.

Problems do occur such as shortage of funds or workers or machines. If there are floats, the manager can decide which activity to give priority and which one to re-schedule. In this way, it is possible not to let the project suffer because of shortages. Some activities can be slipped or splitted for a good cause.

In some other article, I would explain how these floats are used for a sound management.

A case study on floats is given at another hub Floats in a Network

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    • hafeezrm profile image
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      hafeezrm 3 years ago from Pakistan

      There is no such thing as "Dependent Float". If you mean "Independent Float", it is the most adverse float (sometime in negative). It is called Independent since it is available in any case. (Free Float is difference between Early Finish of current activity and Early Start of subsequent activity (if subsequent activities are more than one, minimum of all). Total Float is the difference between early finish and late finish of the same activity.)

      As against this, independent float is calculated ES of the next activity - late finish of the current activity. It could be negative

    • profile image

      Elizabeth 3 years ago

      I am an Engineering student at University, and I have a Project Management module. All the exam papers ask what the dependent float is. I have searched and searched, but I cant find anything on how to calculate dependent float. Can you be of any help?

    • profile image

      subramanian 3 years ago

      thank u....its very help full.

    • profile image

      Ishmael Ledimo 4 years ago

      I had no idea hw CPM worke until I read this case study, you made it look easy. It helped me a lot. Many many many thanks.

    • hafeezrm profile image
      Author

      hafeezrm 4 years ago from Pakistan

      Critical Activity cannot have a float. If an activity has a float, it is not Critical.

    • profile image

      RAHUL 4 years ago

      FLOAT FOR CRITICAL ACTIVITY IN PERT

    • profile image

      Fredrique' 5 years ago

      wonderful article ...thnks a lot

    • profile image

      delphine nyaboke 5 years ago

      the info is precise and that makes it awesome.

    • profile image

      MALIK MUGHERA AWAN 5 years ago

      a very informative and a very well define article of Floats.

    • hafeezrm profile image
      Author

      hafeezrm 5 years ago from Pakistan

      Thanks Mani for going through my article.

      End-float is not a term in project management but in engineering design. It is also known as 'Axial Float"

      http://www.diracdelta.co.uk/science/source/a/x/axi...

      There is no such thing as "Dependent Float". If you mean "Independent Float", it is the most adverse float (sometime in negative). It is called Independent since it is available in any case. (Free Float is only available if an activity is started early and ended early. Total Float depends upon early finish and late finish)

      As against this, independent float is calculated ES of the next activity - last finish of the current activity.

    • profile image

      mani 5 years ago

      sir what is the end float?

      what is the dependent float?

    • hafeezrm profile image
      Author

      hafeezrm 5 years ago from Pakistan

      Total float is the largest float. It can be zero or above but never below. In order to have a clear idea, please make a sketch and calculate float. You can never portray a situation where free or total floats are in negative. Study well and improve your knowledge on your own to have a life-long clear concept of float.

    • profile image

      ny 5 years ago

      maybe the total float can be in minus?

      (TotalFloat)ij = (LateFinish)j - (EarlyFinish)i - Tij

    • hafeezrm profile image
      Author

      hafeezrm 5 years ago from Pakistan

      Only independent float can be in minus. It is difference between early start and late finish. But it is not indicated in minus but zero.

    • profile image

      ny 5 years ago

      which of the floats can be under zero? what does it mean? why the other's can't be under zero?

    • hafeezrm profile image
      Author

      hafeezrm 5 years ago from Pakistan

      Thanks Vijay.

    • profile image

      VIJAY 5 years ago

      VERY USEFUL

    • hafeezrm profile image
      Author

      hafeezrm 5 years ago from Pakistan

      Usually, a milestone is added. It is just a box saying start and two or three activities follow. Similarly, two activities may ending but not merging. In such case a milestone entitled END may be added and the preceding activities linked with it.

    • profile image

      muzammil 5 years ago

      sir,wat if there are more than one activities who don't have a predecessor,how do we represent that in an activity on node diagram

    • hafeezrm profile image
      Author

      hafeezrm 5 years ago from Pakistan

      Thank Cathy for your comments.

    • profile image

      cathy 5 years ago

      Thank you very much, now i know how i will tackle my assignment

    • hafeezrm profile image
      Author

      hafeezrm 5 years ago from Pakistan

      Thanks Zohaib Noor for your comments.

    • profile image

      zohaib noor 5 years ago

      Formal education will make you a living; self-education will make you a fortune. and for me you are very fortune .sir we love you may Allah gives you a very very long life ameen .

    • hafeezrm profile image
      Author

      hafeezrm 5 years ago from Pakistan

      Thanks Manjunath for your comments.

    • profile image

      Manjunath 5 years ago

      Dear Sir,

      Thanks for very clear presentation. Please keep up the good work.

      Manjunath, India.

    • hafeezrm profile image
      Author

      hafeezrm 5 years ago from Pakistan

      Thanks espengongo for your comments.

    • profile image

      espengongo 5 years ago

      Thank you Sir for your reply.

      The link about risk management is very usefull.

    • hafeezrm profile image
      Author

      hafeezrm 5 years ago from Pakistan

      PERT and CPM relate to time management. Estimated time for each activity is to be estimated through various techniques. Over the years, these techniques have become sold. So danger or risk is same as in opening a new shop or joining a new job and taking a new subject.

      PERT & CPM are not carried out in isolation but with Risk Management. This had been explained in another hub:

      http://hafeezrm.hubpages.com/hub/Project-Managemen...

    • espengongo profile image

      espengongo 5 years ago from Kinshasa, democratic republic of Congo

      Dear Sir,

      I just discover your hub and would like to thank you for your contribution on sharing your knowledge in project management.

      I went thru many readings about project Networks seeking for dangers and problems commonly faced by Project manger and the associated risks. Also i never understand in what circumstances these dangers or problem can be advantageous.

      For example, it is known that:

      - WBS is not easy to do

      - Duration estimates are most of the time subjective

      - near critical paths can become critical and affect project completion on time and schedule.

      Are these examples limitations of the project networks or really problems?

    • hafeezrm profile image
      Author

      hafeezrm 5 years ago from Pakistan

      Dear Sami,

      This example is not valid for floats. All floats are calculated taking estimates into consideration. But you have taken one estimate and one actual. In fact what you say, is relevant to time savings or delays.

    • profile image

      Sami 5 years ago

      I have a question.

      I know it is not possible for Float to be negative.

      For example,if a project expected to finish after 138 days. and it finished in 130. there will be differences in my project how can I avoid the negative float?

    • hafeezrm profile image
      Author

      hafeezrm 6 years ago from Pakistan

      Thanks Pirzada Sajad for your comments.

    • profile image

      Pirzada Sajad 6 years ago

      Thank you sir brilliant it helped me a lot. thanks a lot..

    • hafeezrm profile image
      Author

      hafeezrm 6 years ago from Pakistan

      Thanks Shaista for your comments.

    • profile image

      shaista tabassum 6 years ago

      very helpful article thnx a lot for such a good article .

    • conradofontanilla profile image

      conradofontanilla 6 years ago from Philippines

      I consider PERT/CPM a secret weapon of the allies in WWII because it enabled the building of a ship in 56 days instead of over 300 days before WWII.

    • hafeezrm profile image
      Author

      hafeezrm 6 years ago from Pakistan

      Thanks Maawra Salam for your comments.

    • profile image

      Maawra Salam 6 years ago

      Thank you Sir, article is informative.

    • hafeezrm profile image
      Author

      hafeezrm 6 years ago from Pakistan

      Thanks Vens for your comments.

    • profile image

      Vens 6 years ago

      VERY well written! Struggled with this quite a bit could not find a helpful approach - excellent!

    • profile image

      Muhammad Shoaib Ikram 6 years ago

      Good Morning Sir,

      I think, now i have understood, i have to carefully consider succeeding activity for both free float and total float. Sorry for disturbing you

    • profile image

      Muhammad Shoaib Ikram 6 years ago

      Without developing AON, how one can calculate total float in Gantt Chart

    • profile image

      SirLoin- Barbados 6 years ago

      Thank you very much. I had a problem with the independent float calculations and you cleared it up!

    • asadayub profile image

      asadayub 6 years ago

      The article is really very good. Floats are always very important in determining the Critical Time of the Project, because uncertainties are always there. A very comprehensive study is present in this hub. Thanks Sir.

    • profile image

      M BASHIR ALAM 6 years ago

      thanks for refering this article. this help me to clear my concepts about float.

    • profile image

      kamran 6 years ago

      thnx for providing such a detailed knowledge

    • Bilal Shahmeer profile image

      Bilal Shahmeer 6 years ago

      a very well define article of Floats

    • hafeezrm profile image
      Author

      hafeezrm 7 years ago from Pakistan

      Thanks Hardik for pointing out an obvious mistake. In fact, it is the absolute difference which is considered here. It does not matter whether you put EF at the start or at the end, we come up with a certain time lag between EF and LS or LS and EF. Deducting the duration, the independent slack would be found out.

      In free float, the slack is only valid if the activity is started immediately but in independent slack, no matter when you start (early or late), you will get the same slack.

      Sorry if I have confused you further. You can do it yourself since you are taking so much interest.

    • profile image

      Hardik 7 years ago

      Dear Sir,

      Thanks for the explanation.

      But independent float formula mentioned earlier is Late Start (LS) - Early Finish (EF) which gives answer as (13-3)-4=6

      But later in example you have mentioned formula for Independent float as Early Finish(=4) - Late Start(=10) - Duration(=3) gives answer as -9.

      So the answer is different.

      Kindly explain this.

    • profile image

      magdalene 7 years ago

      thanks brief and clear

    • profile image

      ojinuka valentine 7 years ago

      thanks a lot your material has been very helpful in my course of study.please keep it coming.

    • profile image

      Salem habib 7 years ago

      Hi, I came across this link following my query to explain Floats and i found much more than this..Thank you

      Salem,

      Montreal,Canada

    • profile image

      mfnforex 7 years ago

      Thank you

    • hafeezrm profile image
      Author

      hafeezrm 7 years ago from Pakistan

      Interference float is the difference between total float and independent float.

      Supposing there is a conference of 5,000 participants in an Island. The conference would be for 5 days starting from 17th June and ending on 21st June. To transfer a large number of people, the flights to island would start from 1st June to 16th June and the return would be from 22nd June to 30th June. Suppose further that the Island has a lot of sight-seeing opportunities on the side.

      Now if some big boss is interested only in conference, he or she can leave on 16th June and return by 22nd June. In this way, one day would still be available for shopping or sightseeing calculated as follows: (22 – 16 - 5). This one day is called Independent Float and is available in any case.

      On other hand, total float (or total time for sightseeing) would be for 24 days when someone starts on 1st June and returns on 30th June.

      So one cannot devote more than 24 days for sight-seeing while one has to spend one day because of flight schedule. It is evident that one can interfere or modify the schedule for sight-seeing for 23 days ( 24 -1).

      The formulas for calculating floats are:

      total float = latest end time - earliest start time – duration

      independent float = earliest end time - latest start time – duration

      interference float = total float - independent float

      This is the simple explanation. The matter gets complicated when many activities start or merge at one point. An engineer, Thomas W, has introduced another float called Safety Float in addition to the interference float. New concepts come up each day as R&D advances.

      Please do not hesitate to contact me if you need any further information.

    • profile image

      ram 7 years ago

      sir can you tell about the ineterference float

    • profile image

      jenna 7 years ago

      this article is presented in a simple but very informative way...thanks, it made me understand our lesson well.

    • profile image

      Shikha Mukherjee 8 years ago

      now its so easy to prepare for exams in barely 1 hr. thanks a tonne

    • profile image

      Vijay 8 years ago

      thanks.. very helpful

    • hafeezrm profile image
      Author

      hafeezrm 8 years ago from Pakistan

      Intially I misunderstood valued comments of Mark Russell. Now I see, he is pointing out a flaw under Free Float Formula of tradional network known as AOA (Activity On Arrow).

      But I still do not get why he has used MIN (ESD j1, j2... - EFDi) for calculating free float of an individual activity.

      'Maximum' and 'Minimum' apply for calculation of Forward & Backward Pass that is what the text books say.

      But at the same time, Mark Russell has exhibited a deep knowledge and I wish he had given a simple example to stregthen his views.

    • profile image

      Mark Russell  8 years ago

      Your suggested formula for calculating free float for an activity on arrow network (The original Du Pont CPM algorithm) I - J is incorrect and cannot be applied in all scenarios. For example when you have two or more preceeding activities converging into the same finish event, which becomes the start event of a succeeding actvity, the ESD of that succeeding activity is governed by the maximum EFD value of one of the preceeding activities as a result of the forward pass calculation. Only this value will be recorded as the ESD event of the succeeding activity. Therefore the formula for calculation of free float for an activity I to J is flawed. Instead Free float calculations need to be undertaken for each individual link to the non critical I activity i.e. j1, j2 etc. Then the smallest of of the individual free float values will become a free float of activity I, i.e. MIN (ESD j1, j2... - EFDi).

      ESD being the Earliest Start Date / EFD being the Earliest Finish Date of an activity i to j.

    • profile image

      syed Asif Hussain 8 years ago

      Dear Mr. Hafeez,

      Thank you very much, your way of explanation makes one to understand with ease.

    • profile image

      SUFYAN MAJEED 8 years ago

      A.A

      THANKS FOR ADDING UP IN OUR KNOWLEDGE, AND ALWAYS BE EAGER TO RECEIVE SUCH VALUABLE INFORMATION.

    • profile image

      RAJA ISRAR 8 years ago

      ASLAM-O-ALAIKUM

      THIS ARTICLE IS REALLY IMPORTANT TO READ, BECAUSE IT ENHANCE OUR KNOWLEDGE IN THE FIELD OF PROJECT MANAGEMENT.

      REGARDS

    • SAAD RAIS profile image

      SAAD RAIS 8 years ago

      ASSALAM O ALAIKUM

      you done a great job but these tables are little complex to understand...but they will help me in many cases

      thanks

      regards

      SAAD RAIS

    • profile image

      asad sheraz 8 years ago

      this article is very informative i learn many thing through by this aricle

    • hafeezrm profile image
      Author

      hafeezrm 8 years ago from Pakistan

      Dear Usman, I have given my comments to Adeel. I think your question was about the same. If not, write to me specifically.

    • Fahad_Khan profile image

      Fahad_Khan 8 years ago from Karachi

      This case study helped me a lot, the graphical representation was very useful.

      Regards,

      M. Fahad Khan

    • profile image

      MUHAMMAD DANIAL 8 years ago

      ASSALAM U ALAKUM

      VERY INFORMATIVE. CLEARING MY CONCEPTS MUCH MORE.

      THANK YOU

    • profile image

      KIRAN MEHTAB 8 years ago

      very much informative article :)

    • profile image

      Husna Fatima 8 years ago

      Thanks you are providing such a great information about flot it is really informative

      thanks a lot

    • hafeezrm profile image
      Author

      hafeezrm 8 years ago from Pakistan

      Dear Adeel Aleem,

      IF=(f-e-c) is a formula. It can be expanded to read:

      Independent Float(IF) = Early Finish (EF) - Late Start (LS) -Duration. In the table you are referring to all columns have been given sub-headings starting from A to G for ease of recognition. Hope this makes clear.

    • mubin_ashraf profile image

      mubin_ashraf 8 years ago

      Thats really informativeI think that these pictorial views give me more understanding to have in your articles.

      Regards,

      Mubin Ashraf.

    • profile image

      Adeel Aleem 8 years ago

      IF (f-e-c), FF(f-d-c) , TF(g-d-c) is this given or we can identify ourselves the subtraction of activities??? if it is given so uptill now it is clear to me and if we have to identify ourselves so how we can identify the subtraction of activities among each other??

    • profile image

      Adeel Aleem 8 years ago

      i can't understand the table 1, the IF(f-e-c), FF(f-d-c), TF(g-d-c).. how these activities are subtracting with each other for a float???

    • profile image

      Numan Nazir 8 years ago

      The importance of Floats is obvious from the article.......

      Thank you v. much..

    • profile image

      sanam khan 8 years ago

      good article, very informative.

    • profile image

      Kashan Pirzada 8 years ago

      Good Article

      Thanks!