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.

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.

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.

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.

• 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.)
• 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)

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.

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),

3. TF(i,j) = LF(j) - ES(i) - D(i,j)

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.

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.

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.