Extensions to PERT/CPM for Scheduling Project

There have been several extensions to both network and chart forms of project schedul­ing. At times these extensions are quite sophisticated; for example, the application of fuzzy set theory to aid in estimating activity durations in cases where activity durations are difficult to estimate because project activities cannot be well defined (McMahon, 1993). In this section we briefly discuss one significant extension of traditional scheduling methods, precedence diagramming. (Elihu Goldratt’s Critical Chain (1997) is also a sig­nificant addition to traditional scheduling methods. It uses networks that combine pro­ject scheduling with resource allocation. It is discussed in Chapter 6 on resource allocation.)

1. Precedence Diagramming

One shortcoming of the PERT/CPM network method is that it does not allow for leads and lags between two activities without greatly increasing the number of subactivities to account for this. That is, our regular network methods described earlier assume that an activity can start as soon as its predecessor activities are completed. Sometimes, however, the restrictions are more complex—for example, when a follow-on activity cannot begin until a certain amount of time after (or even before) its predecessor is completed (or sometimes started). For instance, a successor may have to wait for paint to dry or cement to harden. In this case, we might add a fictitious activity after painting or pouring the cement that takes the required time (but no resources) and then let the follow-on begin. For a leading activity, we might break the predecessor activity into two activities a fol­lowed by b and let the follow-on start after a is completed and operate in parallel with b, the remainder of the predecessor activity. In construction projects, in particular, it is quite common for the following restrictions to occur. (Node designations are shown in the Predecessors column in Figure 5-21.)

• Finish to Start Activity 2 must not start before Activity 1 has been completed. This is the typical arrangement of an activity and its predecessor. Other finish-start arrangements are also possible. If the predecessor information had been written “1 FS + 2 day,” Activity 2 would be scheduled to start at least 2 days after the com­pletion of Activity 1, as shown in Figure 5-21. For instance, if Activity 1 was the pouring of a concrete sidewalk, Activity 2 might be any activity that used the sidewalk.
• Start toStart Activity 5 cannot begin until Activity 4 has been underway for at least 2 days. Setting electrical wires in place cannot begin until 2 days after framing has begun.
• Finish to Finish Activity 7 must be complete at least 1 day before Activity 8 is completed. If Activity 7 is priming the walls of a house, Activity 8 might be the activities involved in selecting, purchasing, and finally delivering the wallpaper. It is important not to hang the paper until the wall primer has dried for 24 hours.

• Start to Finish Activity 11 cannot be completed before 7 days after the start of Activity 10. If Activities 10 and 11 are the two major cruising activities in a pre­paid weeklong ocean cruise, the total time cannot be less than the promised week. The S-F relationship is rare because there are usually simpler ways to map the required relationship.

Precedence diagramming is an AON network method that easily allows for these leads and lags within the network. MSP handles leads and lags without problems. Network node times are calculated in a manner similar to PERT/CPM times. Because of the lead and lag restrictions, it is often helpful to lay out a Gantt chart to see what is actually happening. Most current project management software will allow leads, lags, delays, and other constraints in the context of their standard AON network and Gantt chart programs.

2. Final Thoughts on the Use of These Tools

Three decades ago it was common to hear, “No one uses PERT or CPM.” It was not true. One decade ago we heard, “No one uses that probability stuff.” It was not true. We even heard, “No one uses_____ computer package,” which was also untrue. These statements were not true a decade ago—and they are even less true (if that is semantically possible) today. Current software makes it easy to use networks and Gantt charts. Current software handles three-time estimates of duration and can do all the calculations almost instantly. Current software makes simulation a straightforward procedure.

Excel® and other popular spreadsheets can calculate variances and find expected times. MSP can do some of these calculations, but not others. MSP does not find the standard deviation or variance of three-time duration estimates and cannot find the probability of completing a task or the entire project within a given time limit. Probability calculations are, however, easily handled by simulation. The analyst, of course, must examine the paths, and select those for further analysis. The software can do the arithmetic, but the analyst must enter the appropriate numbers and ask for the appropriate calculations for each path to be analyzed, and then find the probabilities. With large networks, this will probably be a massive and tedious task. On the other hand, it is almost never required to enumerate and evaluate all paths in a simulation—even if simulation could do so rapidly.

As we have noted several times, the same arguments and methods are appropriate for managing uncertainty in resource usage and preparing project budgets. The calculations and simulations are the same as those used with task and project duration.

When struggling with risk analysis and management, it is well to remember why the PM must engage the struggle. The PM is responsible for keeping the project within its budget and on time. This chapter is devoted to developing the information the PM requires to meet these responsibilities. The PM does not manage the project as a totality; rather he or she manages the specific tasks and subtasks that make up the project. The methods introduced above are intended to help the PM understand precisely where man­agement effort is needed.

As we noted briefly above, it is relevant to point out that identifying one or more paths as critical might actually be detrimental to project performance—if the PM is not managing the project team as well as the project. If the PM is not alert to the possibility, activity slack may lead to neglect of noncritical activities. As Parkinson teaches us, work tends to fill the time allowed, and activities lose their slacks. For example, noncritical paths may slip far enough behind schedule that they become critical—simply because the project team perceives them to be of low priority. At the same time, the apparently critical path may finish ahead of schedule because of the extra management attention it receives.

Goldratt (1997, Ch.13) refers to other causes of project delay resulting from “human nature.” There is, for instance, the “student syndrome.” Given the deadline for a home­work assignment, students often plead for more time. Given more time, many simply postpone starting the assignment. Goldratt also reminds us that if a task is finished early, its successor tasks are still started when they were originally scheduled. The result is that delays resulting from tasks finishing late are not offset by the potential gains from those that finish early. There is also the fact that “five plus five equals thirteen.” If one team member estimates that one task will require 5 days and a second team member estimates that a successor task will require 5 days, the boss then estimates that the pair will require 13 days—just to be safe. The work, of course, will expand to require at least 13 days.

If the PM becomes entranced with the technology of the project and fails to man­age the project team, the team itself can become confused and frustrated as the reality of the project unfolds. Today’s path-slack disappears and a new critical path is born— only to change tomorrow when some other path becomes critical. In such cases, and they are common in reality, it is not easy to remind oneself that recognizing and analyz­ing uncertainty does not cause uncertainty—nor does it cause uncertainty to disappear. The PM’s job includes teaching project team members enough about risk that they can understand its nature and, thereby, cooperate in developing ways to deal with it.

At this point, it is helpful to remember that there are problems for which risk analy­sis, by whatever method, is probably not required. Routine maintenance and routine construction projects are among such cases—unless the projects are quite large or have not been performed recently. In most such projects the routine character of the work means that the variances of task durations are quite small and the cost of carrying out a careful risk analysis is rarely justified.

In the next chapter, we turn our attention to resource allocation and the problems of controlling the use and flow of resources. We also deal with the issue of integrating schedule and budget by examining the nature of time-resource trade-offs.

Source: Meredith Jack R., Mantel Jr. Samuel J., Shafer Scott M., Sutton Margaret M. (2017), Project Management in Practice, John Wiley & Sons, Inc. 3th Edition.