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INTRODUCTION
PERT is an acronym for "Programme Evaluation and Review Technique". This was created as a means to plan and accelerate the development of the Polaris Ballistic Missile. In USA the defence department developed a nuclear missile to be launched from beneath the ocean's surface by a mobile submarine, which would be an effective deterrent against aggression by an enemy. This paved way to plan how to design, develop and plan the different stages in the production of a missile and how quickly this task could be completed. A planning and scheduling technique named PERT gave the answer to these questions.
In any new venture, uncertainties are bound to creep in. PERT incorporated these uncertainties into a model, which provides a reasonable answer to these uncertainties. There are certain statistical aspects scheduling large projects consisting of numerous activities whose completion times are uncertain and are independent of one another. PERT is an event-oriented technique. By 'event' we mean reaching a certain stage of completion of the project.
Another technique, Critical Path Method, abbreviated as CPM, has emerged simultaneously. It is also a network technique but it is concerned with obtaining the trade-off, between cost and completion date for large projects. In any project consisting of several activities each activity can be completed in a normal duration with normal cost. If we employ more persons or skilled people or given overtime to the workers, the activity could be completed in a reduced duration known as crash duration. But this involves an increased cost in the form of additional resources. With CPM the amount needed to complete the various activities is assumed to be known with certainty. So, the direct costs for the activities increase and hence the cost of the project also increases. By reducing the activity duration of some or all possible completed ahead of the schedule. This will naturally reduce the overhead cost for the entire project. On one hand the direct expenses increase, if we shorten the activity duration, but, the indirect expenses for the project are reduced. We have to strike a balance or an optimum time schedule, or a least cost schedule is to be obtained. This is the purpose of the Critical Path Method. Thus CPM is not concerned with uncertain job times as in PERT. PERT is useful in research and developmental projects, whereas CPM is mostly used in construction projects, or in situations already handled, so that the details like the normal completion time, crash duration and cost of crashing are already known.
The following are the suggested applications when PERT or CPM is found useful.
The construction of a building or of a highway. Planning and launching a new product. Scheduling maintenance for a project. The manufacture and assembly of a large machine tool. To conduct a music or drama festival. Preparation of budget for a company.
CONCEPT OF NETWORK
The first step in the application of CPM / PERT is to develop a network representation of the project plan.
A 'network' is defined as a graphic representation with a flow of some type in its branches. It represents nodes and branches. Below in table 1, we represent different systems satisfying the definition of network in the physical world.
The project of budgeting can be displayed in a network or project graph by an arrow diagram. Jobs are shown as arrows leading from one node to the other as in Figure 2.
E
B
A D
C
Fig. 2
From the arrow diagram 2, we infer that activity A is the first job. Jobs B and C start only after A is over. A is called the predecessor of B and C and B and C the successors of A.
RULES FOR CONSTRUCTION OF NETWORK
(a) Each activity is represented by one and only one arrow. This means that no single activity can be represented twice in a network.
(b) No two activities can be identified by the same end events. This means that there should not be loops in the network.
(c) Time follows from left to right. All the arrows point in one direction. Arrows pointing in opposite direction must be avoided.
(d) Arrows should not cross each other.
(e) Every node must have at least one activity preceding it and at least one activity following it, except for the nodes at the very beginning and at the very end of the network.
DUMMY ACTIVITIES
There is a need for dummy activities when the project contains groups of two or more jobs which have common predecessors. The time taken for the dummy activities is zero.
Suppose we have the following project of jobs with their immediate predecessors.
Jobs Immediate
predecessors A - B - C - D A, B E B, C
Activity B is the common immediate predecessor of both D and E. A is the immediate predecessor of D alone and C is the predecessor of E. Let B lead into two dummy jobs D 1 and D 2 and let D 1 be an immediate predecessor of D and D 2 of E as shown in Figure 3.
A D
D 1
B
D 2 E
C
Fig. 3
Dummy arrow represents an activity with zero time duration. It is represented by a dotted line and is introduced in a network to clarify activity pattern under the following situations.
(i) It is created to make activities with common starting and finishing events distinguishable.
(ii) To identify and maintain the proper precedence relationship between activities those are not connected by events.
Consider an example where A and B are parallel (concurrent activities). C is dependent on A and D is dependent on both A and B. Such a situation can be represented easily by use of dummy activity as shown in Figure
C 2 4 A
D 1 1 B D 5 3
Fig. 4
Activity A B C D E F G H I J K Immediate Predecessor - A - B,C C G,H D B F G E,I,J
Solution:
B 4 H F A 8 1 2 D 2 9 D 6 G D 3 I 5 J K C D 1 7 10 11 3
E
Fig. 7 Example A project has the following activities. The relationships among the activities are given below. Construct the network.
A is the first operation. B and C can be performed parallel and are immediate successors to A. D,E and F follow B. G follows E. H follows D, but it cannot start till E is complete. I and J succeed G. F and J precede K. H and I precede L. M succeeds L and K. The last operation N succeeds M and C.
Solution:
D 5 H
3 E 7 B 4 I L 1 2 6 J M N F 8 9 10 11 K
Fig. 8
Example
Activity A B C D E F G H I J K L Predecessor - - A A B B C,D E C,D G,H F J,K
C
D
A 3 I
G
7 J L
B
E H 8
K
F
Fig. 9
Example Draw network from the following list of activities.
Job Name
Immediate predecessor
Job Name
Immediate predecessor a - l k b a m k c b n k d c o d e b p o f e q b g e r n h c s l, m i c, f t s j g, h, i u p, q k j v u
C G
D(14) E
E(10) F
F(7) H
F I
F L
F I
G(21) L
H(7) J(15)
I(12) J
K(30) L(15)
- Draw network diagram for the following activities whose predecessors are given in the table below.
Job A B C D E F G H I J K Immediate Predecessors - A B C B E D,F E H G,I J
TO FIND THE CRITICAL PATH
After listing all the activities with their precedence relationship we project these activities in a project graph represented by arrows or Activity On Node diagram (AON). Now we have to find the minimum time required for completion of the entire project. For this we must find the longest path with the sequence of connected activities through the network. This is called the critical path of the network and its length determines the time for completion of the project. The activities in the critical path are so critical that, if they are delayed, the project completion date cannot be met and the project finish time will have to be extended. We shall now see how to identify the critical path, the critical activities and the duration of the project. The meaning of path and length of a path should first be made clear. Let us take following example.
