To use CPM, we develop a table or graph of the cost of a project as a function of the project's various possible completion dates. This can be obtained by either of two approaches.
The first approach is to start with the normal schedule for all project activities, and then to crash selected activities, one at a time, to decrease project duration at the minimum additional cost. This approach is illustrated in Figure 9-1. The normal schedule is shown in network 9-la. (Note the required dummy activity. We use the AOA representation to illustrate that this procedure can be used with PERT as well as with CPM.)
The critical path of network 9-1 is a-b-e. To reduce the total network duration, we must reduce the time required by one of the activities along this critical path. Inspecting Table 9-2 to see which critical activity can be reduced at the least cost, we find it is e, at a cost of $35 per day. If we crash e by one day, we have a seven-day project duration at a cost of $155, as shown in Figure 9-lb.
Crashing e by a day has created a second critical path, a-d-dummy. To reduce project duration further, we might cut one day off this new critical path in addition to another day from activity e. (Remember that the path a-b-e is also critical.) Activity d has the most favorable cost-per-day rate among the critical activities. This adds $30 to the $35 required to reduce e, for a total cost increment of $65. We will still have two critical paths. Another alternative, however, is to crash an activity common to both critical paths, activity a. Reducing a by one day at a cost of $40 is less expensive than crashing both e and d, so this is preferred (see Figure 9-lc). Because a cannot be further reduced, we now cut e and d to lower total project duration to five days, which raises the project cost to $260 (see Figure 9-ld).
Activity e has now been crashed to its maximum (as has a), so additional cuts will have to be made on b to reduce the a-b-e critical path. Cutting one day from b (which is expensive) and d results in the final network that now has a time of four days and a cost of $350, more than 200 percent of the cost for normal time. The project duration cannot be reduced further, since both critical paths have been crashed to their limits.
The second approach to CPM is to start with an all-crash schedule, compute its cost, and "relax" activities one at a time. Of course, the activities relaxed first should be those that do not extend the completion date of the project—that is, those not on the critical path. In our example, this is possible. The all-crash cost is $380, and the project duration is four days. Activity d, however, could be extended by one day at a cost saving of $30 without altering the project's completion date. This can be a. Normal Schedule 8 Days, $120
b. 7-Day Schedule, 5155
8 Days d. 5-Day Schedule, $260
Figure 9-1: A CPM example.
seen in Figure 9-le, where activity d is shown taking two days. Continuing in this manner would eventually result in the all-normal schedule of eight days and a cost of $120, as shown in Figure 9-la.
The time/cost relationships of crashing are shown in Figure 9-2. Starting at the right (all-normal), note that the curve of cost per unit of duration gets steeper an
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What you need to know about… Project Management Made Easy! Project management consists of more than just a large building project and can encompass small projects as well. No matter what the size of your project, you need to have some sort of project management. How you manage your project has everything to do with its outcome.