Critical Path Method Language

The critical path method has its own language. It can be understood only when the significance and meaning of the terms used in the language are properly known and understood.

Operations (Activities)

Any project that is undertaken involves several activities (Operations). The project can be stated to have been completed, when all the activities are completed. Activities on the node (node is a system in which activities shown by circles) system are shown by a circle. Different operations are numbered and written inside the circle, as shown in the following figure.

The time required for the completion of an operation is written on the left hand top corner of the circle. The above mentioned figure is read as ‘Operation number 5’ and has its schedule time of 4 days.

Pre-operation

When there are two operations, of which unless one is completed, another cannot be started, the one which needs to be completed first is known as a pre-operation. For example, viz. 1) Construction of the foundation, and 2) Construction of building cannot be undertaken unless the building foundation is completed. In this case, the building foundation can be stated to be the pre-operation (PER-OPR) which can be written on the left side as shown in the figure given below :

The arrow shows the relation between these two operations.

Post Operation (PER-OPR)

The operation which follows the pre-operation is known as post operation (PER-OPR). Sometimes, an operation has more than one pre-operation. For example, suppose a workshop has to be constructed. The construction of the roof can be started only when the super-structure and steel fabrication work is completed.

In this example, Roofing is the post operation (PER-OPR) of the pre-operation (Pre-opr) viz. ‘Steel fabrication’ and ‘super structure’.

Concurrent Operation

Sometimes there are certain operations which can be started separately, at the same time. For example, the operations of steel fabrication and construction of the super structure can be taken up as concurrent operations. Thus, they do not have any pre-operation. These operations are known as concurrent operation.

Earliest Finish (TE)

The earliest possible time for completing any operation can be shown in a rectangle. It should be written at the top right corner and outside the operation circle.

In the above figure, the operation number 1) can be completed within 5 days and does not have any ‘PRE-OPR’. Hence, ‘earliest-finish’ is 5 days. Operation number two requires 10 days time, and its ‘PRE-OPR’ takes 5 days. Thus, the ‘Earliest Finish’ of this operation is 5 + 10 = 15 days. Thus, operation No. 2 can be completed with 15 days after work is started.

When an operation has more than one ‘PRE-OPR’, the earliest finish time is the largest earliest finish of ‘PRE-OPR’ + Schedule Time for the operation under consideration.

The operation can be presented in the following figure.

In the above figure, the earliest finish time for the operations ‘x’ and ‘y’ is 5 and 10 days respectively. They do not have PRE-OPR (their earliest finish time = schedule time).

The earliest finish for z  = largest earliest finish of PRE-OPRS + Schedule time for Operation ‘z’.

                                            =  10 + 15  = 25 days.

Therefore, 10 days is the largest earliest finish for the operations ‘x’ and ‘y’.

Latest Finish Time (TL)

It is the time by which the operation must be completed, so that the schedule date for completing the project is not delayed.

For the last operation :

Latest finish = Earliest finish

For the operations :

Latest finish = Latest finish of the post operation – Time required for post operation

If an operation has more than one post operation, the smallest among them is taken first and it is written in a triangle below the operation circle.

The operation time for D is 10 days and its earliest finish is 40 days, while its latest finish time is 45 days.

Critical Path

A path among the network, in which the ‘Earliest Finish’ and the ‘Latest Finish’ are equal, is known as the ‘Critical Path’. It is represented by a double or a thick arrow line, to distinguish it clearly from other path.

Slack

Slack is a difference between the latest finish time (T_L) and the earliest finish time (T_E). In the event of ‘D’, slack is (45 - 40).

Earliest Start : It is the shortest possible time by which a certain job can be completed.

Earliest time = Earliest finish time – operation time.

Latest Start : It is the latest possible time by which the job can be started.

Therefore, Latest Start = Latest finish time – Operation Time

Positive Slack : If  T_L – T_E is positive, it represents a situation where the program is moving fast possibly because extra resources are available in materials, men and machines.

Negative Slack : If  T_L – T_E  is negative, it represents that the program is lagging behind the schedule.

Zero Slack : If T_L – T_E  is zero, it represents an ideal situation, which falls on the ‘Critical Path’.