Info

(aI BURST POINT

lb) sink

Figure 12-2. PERT sources (burst points) and sinks.

to proceed from one event or point in time to another. Figure 12-1 shows the standard nomenclature for PERT networks. The circles represent events, and arrows represent activities. The numbers in the circles signify the specific events or accomplishments. The number over the arrow specifies the time needed (hours, days, months), to go from event 6 to event 3. The events need not be numbered in any specific order. However, event 6 must take place before event 3 can be completed (or begin). In Figure 12-2a, event 26 must take place prior to events 7, 18, and 31. In Figure 12-2b, the opposite holds true, and events 7, 18, and 31 must take place prior to event 26. Figure 12-2b is similar to "and gates" used in logic diagrams.3

Elsewhere we have summarized the advantages and disadvantages of Gantt and milestone charts. These charts, however, can be used to develop the PERT network, as shown in Figure 12-3. The bar chart in Figure 12-3a can be converted to the milestone chart in Figure 12-3b. By then defining the relationship between the events on different bars in the milestone chart, we can construct the PERT chart in Figure 12-3c.

PERT is basically a management planning and control tool. It can be considered as a road map for a particular program or project in which all of the major elements (events) have been completely identified together with their corresponding interrelations.4 PERT charts are often constructed from back to front because, for many projects, the end date is fixed and the contractor has front-end flexibility.

3 PERT diagrams can, in fact, be considered as logic diagrams. Many of the symbols used in PERT have been adapted from logic flow nomenclature.

4 These events in the PERT charts should be broken down to at least the same reporting levels as defined in the work breakdown structure.

Figure 12-3. Conversion from bar chart to PERT chart.

One of the purposes of constructing the PERT chart is to determine how much time is needed to complete the project. PERT, therefore, uses time as a common denominator to analyze those elements that directly influence the success of the project, namely, time, cost, and performance. The construction of the network requires two inputs. First, a selection must be made as to whether the events represent the start or the completion of an activity. Event completions are generally preferred. The next step is to define the sequence of events, as shown in Table 12-1, which relates each event to its immediate predecessor. Large projects can easily be converted into PERT networks once the following questions are answered:

TABLE 12-1. SEQUENCE OF EVENTS

Immediate Activity

TABLE 12-1. SEQUENCE OF EVENTS

Immediate Activity

Activity

Title

Predecessors

Time, Weeks

1-2

A

1

2-3

B

A

5

2-4

C

A

2

3-5

D

B

2

3-7

E

B

2

4-5

F

C

2

4-8

G

C

3

5-6

H

D,F

2

6-7

I

H

3

7-8

J

E,I

3

8-9

K

G,J

2

• What job immediately precedes this job?

• What job immediately follows this job?

• What jobs can be run concurrently?

Figure 12-4 shows a typical PERT network. The bold line in Figure 12-4 represents the critical path, which is established by the longest time span through the total system of events. The critical path is composed of events 1-2-3-5-6-7-8-9. The critical path is vital for successful control of the project because it tells management two things:

• Because there is no slack time in any of the events on this path, any slippage will cause a corresponding slippage in the end date of the program unless this slippage can be recovered during any of the downstream events (on the critical path).

• Because the events on this path are the most critical for the success of the project, management must take a hard look at these events in order to improve the total program.

Using PERT we can now identify the earliest possible dates on which we can expect an event to occur, or an activity to start or end. There is nothing overly mysterious about this type of calculation, but without a network analysis the information might be hard to obtain.

PERT charts can be managed from either the events or the activities. For levels 1-3 of the WBS, the project manager's prime concerns are the milestones, and therefore, the events are of prime importance. For levels 4-6 of the WBS, the project manager's concerns are the activities.

The principles that we have discussed thus far apply not only to PERT, but to CPM as well. The nomenclature is the same for both, and both techniques are often referred to as arrow diagramming methods, or activity-on-arrow networks. The differences between PERT and CPM are as follows:

• PERT uses three time estimates (optimistic, most likely, and pessimistic as shown in Section 12.7). From these estimates, an expected time can be derived. CPM uses one time estimate that represents the normal time (i.e., better estimate accuracy with CPM).

• PERT is probabilistic in nature, based on a beta distribution for each activity time and a normal distribution for expected time duration (see Section 12.7). This allows us to calculate the "risk" in completing a project. CPM is based on a single time estimate and is deterministic in nature.

• Both PERT and CPM permit the use of dummy activities in order to develop the logic.

• PERT is used for R&D projects where the risks in calculating time durations have a high variability. CPM is used for construction projects that are resource dependent and based on accurate time estimates.

• PERT is used on those projects, such as R&D, where percent complete is almost impossible to determine except at completed milestones. CPM is used for those projects, such as construction, where percent complete can be determined with reasonable accuracy and customer billing can be accomplished based on percent complete.

Figure 12-4. Simplified PERT network.

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