Floats in a Network

This is in continuation of a hub: Case Study: PERT/CPM – calculating floats. Some terms used in the said hub would be repeated for a complete understanding of the concepts and techniques.

A float is a slack or cushion or flexibility or margin for delay. It shows time available for delaying an activity without delaying the Project. It would not result in either increase in duration or cost of the project.

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.

In this hub, only network based on AON would be used.

Node means box or bud or bulge or knob. In network, such a node is represented by a square normally divided into 9 sectors. These can be increased or decreased as per convenience or requirements. It is not necessary to fill in all the cells or compartment but some can be left empty for any future reference. Each node contains information like Project Description, Project ID, its duration, early start and finish, late start and finish and floats like free float & Total Float. This is shown in the side sheet.

To calculate float, an example of Desert Hospital is being given. It has thirteen activities which are shown along their duration in weeks and precedence.

NET WORK DIAGRAM (AoN)

A project network is a graph showing the sequence in which project activities would be completed. It is event-oriented technique not just showing start and finish but the way, the activities are linked together and the manner in which these are to be carried out. It is applied to large-scale, one-time, complex, non-routine projects.

The network technique was first developed by Frederick Taylor and later refined by Henry Ford . DuPont Corporation's CPM was developed at the same time.

From the data given in the question, the following network is drawn. Necessary steps have been discussed in the earlier hub on Float.

Floats or slacks are only available in non-critical activities shown linked by blue lines.

To start with two types of floats would be calculated: (i) Free Float (FF) and (ii) Total Float (TF).

FREE FLOAT (FF)

The FF indicates maximum delay from early start of an activity without delaying the earliest start of any of its immediate successor activities. The formula is: FF = ES of immediate succeeding Node (or activity) minus ES start of existing Node minus its duration. It can be shortened to ES of immediate succeeding Node minus EF of the exiting Node. If there are more than one succeeding Nodes, minimum would be the Free Float of the existing Node.

In the side sheet, F has only one succeeding Node, H. Hence ES of H, 7 minus EF of F would be equal to Zero.

E is succeeded by two Nodes i.e. J & K. Therefore, FF would be minimum of the two as shown below:

FF for Node E:

• ES of J – EF of E = 10 – 7 = 3 or
• ES of K – EF of E = 10 – 7 = 3,
• Therefore, FF for E = 3

Likewise FF for Node H would be:

• ES of J – EF of H = 10 – 10 = 0 or
• ES of K – EF of H = 10 – 10 = 0,
• Therefore, FF for H = 0

TOTAL FLOAT (TF)

TF refers to maxim flexibility or margin available for delaying an activity. Here an activity can be started as early as possible and finished as late as possible. Therefore it would provide more flexibility.

Its calculation is easy. For a Node touched by only one tail, it would be difference between EF and LF of the same Node.

TF for E:

• LF of E– EF of E = 12 – 7 = 5

TF for H:

• LF of H – EF of H = 12 – 10 = 2 or

Three more floats would be discussed now:

1. Independent Float
2. Interference Float
3. Safety Float

INDEPENDENT FLOAT

• Shows the time available even if an activity has a Late Start and Early Finish.
• the delay possible for an activity if all preceding activities start as late as possible whilst all subsequent activities start at their earliest time
• It is most adverse type of float and often results in a negative figure.

In case of Node F, its EF = 7, while its LS=5 and duration is 4. So Independent Float would be 7 - 5 -4 = -2 or Zero which is higher. In other words, if this float is in negative, it is to be shown as zero float or no float.

INTERFERENCE FLOAT

There are two versions of Interference Float.

In the first version, it is like manipulation and it is calculated as Interference Float = TF – Independent Float. While Independent Float is available in all cases, Total Float is available only if an activity is started at its earliest and finished at the latest time. The difference between the two shows the extent to which one can avail margin or flexibility.

Second version is the reduction, total float can bring in the next succeeding activities and is represented by TF – FF.

As per first version, the Inference Float for activities 'F' would be TF - Ind. Float or 2-0 =0. In the second version, it would remain 2 (TF - FF or 2 - 0 = 2) as incidentally both Free Float and Independent Float are zero.

SAFETY FLOAT (SF)

The SF of an activity is the leeway for scheduling, all its predecessors without affecting its self. It is calculated as:TF + Int F = FF + SF. One can find out SF, when all other relevant floats are available. (This float is not so popular. It was introduced by Thomas W in his article "Four Floats Measures for critical Path Scheduling."