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Program management tools make a few assumptions, and use only a few technical terms.
PERT and CPM assume that all activities have distinct beginning and ending points. In the earlier example of constructing an addition to a house, the landscaping activity might not need to be a distinct activity-as time is available, workers could push the fill back around the foundation, police the site, and grade the soil. But PERT could not readily take those random opportunities into account.
PERT and CPM also assume that the estimates of the time needed can be well-defined mathematically. It takes a fair bit of experience to accurately gauge the time a task will take. Barring such experience, time estimates will be highly variable and the quantitative measures of "normal" time and the probability estimates of completion time will be highly unreliable.
Third, resources must be able to be shifted from one activity to another. In the housing addition example, a carpenter's slack time cannot be shifted to an electrician's job or vice versa (the Trades and the Building Inspector would not approve). On the other hand, the dollars spent for hiring labor can be shifted from carpenters to electricians fairly easily. It depends on whether you are scheduling your work crews or hiring workers whether or not (in this example) you can shift resources.
Fourth, quantitative analysis in PERT and CPM assume that cost is a direct function of time and that those costs are evenly spread over the time (i.e., there is no "lumpiness" of activities). For example, the cost of sheetrocking is mostly in the early stages of screwing the sheetrock to the studs and the original taping. The subsequent sanding and additional layers of mud take a relatively short time, but require at least a day for drying between each application of mud. There is no cost to this drying time, but it cannot be shortened. In cases like these, fractional increases or decreases in time may not make sense.
Finally, PERT and CPM assume that the time value of money is not an issue. In other words, there is no need to consider discounting of future costs (or benefits), nor are there indirect monetary benefits to time (other than those incorporated in the costs to "crash" the time). For most projects, these assumptions are acceptable. For really large-scale projects (like the Polaris submarine project, or even the construction of, say, a civic center), the model can be adjusted to include discounting or (for example) the time-value of money as reflected in the construction-mortgage rate.
There are also a few technical terms used in PERT and CPM:
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