Theory of Constraints Handbook - James Cox Iii [31]
Figure 2-3 Problem 6 shows a simple PERT/CPM project with eight activities and two paths. In this example, variability of activity duration is ignored and only the expected activity duration estimate is used. The letter on the node designates the use of resources. There are only seven resources used to complete the eight activities. Resource D is used twice—once on node D1 and again on node D2. Typical PERT/CPM planning concludes that the lower path A-C-D2-F-G is the critical path, taking 30 periods, and the upper path A-B-D1-E-G is non-critical with 1 period of slack.
By examining the network, one can clearly see that resource D is required by activity D1 and activity D2 in period 8. Since resource D can only be used on one activity at a time, the activities must compete for the use of a limited resource. Either activity D1 uses resource D or activity D2 uses resource D, but both cannot use resource D simultaneously. By scheduling D1 and then D2 on resource D or vice versa, the duration of the project will be extended beyond 30 periods. The ultimate cause of project delay is the failure of PERT/CPM to recognize resource contention when resources are scarce.
Cause: PERT/CPM does not recognize that some resources might be required for more than one activity.
Cause: Resource utilizations are performance measures important to the organization’s success.
These are addressed by Guidelines III and VIII.
Problem 7: Resource Contention and Priority Planning It should now be clear that the PERT/CPM assumption of infinite capacity extends project duration when resource contention and limited resources exist. Figure 2-3 Problem 7 demonstrates the effect on project duration of priority planning to overcome resource contention. The network shown has five activities and four resources. Once again, activity duration variability is ignored, and only the expected activity duration estimates are used. Typical PERT/CPM planning concludes that the lower path B-C2 is the critical path, taking 26 periods to complete, and the upper path A-C1-D is the non-critical path with 3 periods of associated slack.
If all activities are started on the early start date, the problem of resource contention occurs in period 15. If activity C2 is scheduled to use resource C first, then activity C1 must wait for the completion of activity C2 in period 26 before C1 can begin. In this case, the upper path and thus the project will not be completed until period 39. Conversely, if activity C1 is scheduled to use resource C first, then activity C2 must wait for the completion of activity C1 in period 15. In this case, the lower path and thus the project will not be completed until period 35. In either case, the duration of the project is greatly extended, but the difference between the two scheduling choices is not insignificant. The ultimate cause of project delay is the failure of PERT/CPM to provide a heuristic to prioritize resource use among activities when resource contention and limited resources exist.
Cause: Priority of resource use may affect on-time project completion.
Cause: PERT/CPM does not recognize that some resources might be required for more than one activity.
Cause: PERT/CPM does not provide priority rules to support project completion.
These are addressed by Guidelines VI and VIII.
Problem 8: Variability, Convergence, and Resource Contention Activity duration variability can compound the problem of resource contention. In Fig. 2-3 Problem 8, a simple PERT/CPM four activity, two-path project network is shown. There are only three resources required. If a uniform distribution of activity duration estimates is assumed, then the expected duration of each activity is as follows: E(A1) = 5, E(B) = 3, E(C) = 5, and E(A2) = 4. Typical PERT/CPM calculations conclude