Since the project manager constructs the project schedule based on the activity duration estimates provided by the resource managers, the resulting schedule would be as shown. The expected duration of the project would be 15 periods.

If the project manager schedules to time (a resource schedule) rather than the completion of the prior activity, the actual expected duration of the project is 13.33 periods. In this case, the project manager receives praise for completing the project ahead of schedule and the activity managers receive praise for completing their respective activities ahead of schedule (although only 67 percent of the time). If the estimates of activity duration had not been increased and the project manager had planned to time, the actual expected duration of the project would have been 12.67 periods. Clearly, this is a better result than 13.33 periods in both duration and cost, but the project manager would be punished for failing to meet the scheduled completion date. Finally, if the estimates of activity duration had not been increased and the project manager had scheduled to completion of the prior activity, the actual expected duration of the project would have been 12 periods. Again, the ultimate causes of project delay are resource managers including local protection in activity times and the project management practice of scheduling activity start times based on the expected time estimates instead of scheduling activities to start based on the actual completion of the preceding activity when variability exists.

Cause: Murphy exists.

Cause: Resource managers are expected to finish activities when planned.

Cause: Resource managers do what they feel is necessary to ensure resource utilization and that the resources are available when promised.

These are addressed by Guidelines IV and X.

Problem 5: Early Consumption of Path Slack Figure 2-3 Problem 5 shows a simple PERT/CPM network. There are two paths in the network: A-C-E taking 28 periods and B-D-E taking 33 periods. The slack associated with the non-critical path is therefore 5 periods. Since activity E is critical (0 slack), all of the slack associated with the non-critical path can be "assigned" to activities A and C. Because a non-critical path has slack, a typical PERT/CPM project manager would assign a start date of 5 to activity A. The expected finish date for activity C would therefore be period 18. If one examines the portion of the critical path before activity E (namely B-D), it is obvious that the expected finish date for path B-D is also period 18. It should be clear from the example of variability and convergence points that if activity duration variability exists in this network, then activity E cannot be expected to start in period 18. Consequently, the actual expected duration of the project cannot be 33 periods, but rather it must be longer. Two problems exist in the practice of project management. First, all of the slack associated with the non-critical path was absorbed in the planning stage of the project. PERT/CPM treats path slack as if it is associated with a specific activity and provides little recognition that once consumed by early activities, it is not available for protection for later activity (it is called activity slack, not path slack). Second, the project is delayed because of scheduling activity start times based on the PERT/CPM-calculated late start date rather than scheduling activities to start based on the actual completion of the preceding activity when variability exists.

Cause: Murphy exists.

Cause: The projects is a major undertaking, which determines the success or profitability (goal) of the organization.

Cause: Project managers delay expenses by starting activities as late as possible.

These are addressed by Guidelines I, II, III, and IX.

Problem 6: Resource Contention Many researchers have recognized that the PERT/CPM assumption of infinite capacity does not accurately reflect the reality of finite capacity (e.g., Davis, 1966; 1973; Westney, 1991; Badiru, 1992; Davis et al., 1992; Dean, Denzler, and Watkins, 1992; Pittman, 1994; Zhan, 1994). When resource capacity is finite, the possibility exists that a single resource might be required to perform two or more activities simultaneously. Pittman defines resource contention as "the simultaneous demand for a common resource within a narrow time-span" (1994, 54).

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 that resource contention does not exist since the expected completion date of activity A1 is period 5 and the early start date of activity A2 is also period 5. The lower path C-A2 is the PERT/CPM critical path, taking 9 periods. However, if activity A1 takes 6 periods to complete (a 50 percent probability), then a resource contention problem occurs, causing activity A2 to start later than its early start date and thus extending the project duration. If all possible combinations of activity duration are enumerated, the actual overall project duration is 9.75 periods. Activity duration variability causes resource contention when activity A1 requires 6 periods and causes a convergence problem when activity A1 and activity B require the longer of their respective estimates of duration. The cause of project delay is the failure of PERT/CPM to recognize convergence points, and resource contention and limited resources when activity duration variability exists.

Cause: Network conventions require that all paths converge to one end node.

Cause: Projects consist of dependent sequential activities, parallel paths, and convergent points.

Cause: Murphy exists.

Cause: PERT/CPM does not protect against Murphy.

Cause: PERT/CPM does not recognize that some resources might be required for more than one activity.

Cause: PERT/CPM does not view activity slack strategically.

These are addressed by Guidelines III and VIII.

Multiple Project Gedankens

Problem 1: Resource Contention across Projects Many researchers have recognized that the PERT/CPM assumption of infinite capacity does not accurately reflect the reality of finite capacity (e.g., Davis, 1966, 1973; Westney, 1991; Davis et al., 1992; Dean et al., 1992; Dumond, 1992; Badiru, 1993; Kerzner, 1994; Pittman, 1994; Zhan, 1994). When resource capacity is finite, the possibility exists that a single resource might be required to perform two or more activities simultaneously. Recall Pittman defines resource contention as "the simultaneous demand for a common resource within a narrow time-span" (1994, 54).

Figure 2-4 Problem 1 shows two independent projects diagramed as a single "mega-project." This method has been suggested by numerous researchers (Lee et al., 1978; Kurtulus and Davis, 1982; Kurtulus, 1985; Kurtulus and Narula, 1985; Mohanty and Siddiq, 1989; Bock and Patterson, 1990; Tsubakitani and Deckro, 1990; Deckro et al., 1991; Kim and Leachman, 1993; Lawrence and Morton, 1993; Yang and Sum, 1993; Vercellis, 1994), although there has been considerable debate over how to schedule resources.

The activity duration for each of the six activities in Fig. 2-3 Problem 1 is deterministic (i.e., there is no variability). Activities B1 and B2 require the use of the same resource. Since there is only one of each type of resource and both activity B1 and activity B2 require the use of resource 2 in periods 7 through 15, a resource contention problem exists across the two projects. If resource contention is ignored as in typical PERT/CPM planning, project 1 has a planned completion date of period 17; project 2 has a planned completion date of period 18. There are two possible orderings of the use of resource 2-B1 then B2 and B2 then B1. If the project manager runs B2 then B1, project 2 would have the same completion date as typical PERT/CPM planning would estimate, but the completion date of project 1 would be delayed while activity B1 waits for activity B2 to finish using resource 2. If the project manager runs B1 then B2, activity B2 must wait for activity B1 to finish using resource 2, thus extending the completion of project 2. PERT/CPM does not provide mechanisms for determining how to optimally sequence activities on common resources across projects to provide realistic project completion times.

Cause: PERT/CPM does not recognize that some resources might be required for more than one activity across projects.

This is addressed by Guidelines VIII and XII.

Problem 2: Priority of Resource Use across Projects Figure 2-4 Problem 2 shows two simple projects diagramed as a single mega-project. Resource 3 is used by activities C1, C2, and C3. Typical PERT/CPM planning calculates the critical path for project 1 to be 23 periods and the critical path for project 2 to be 35 periods. There are three possible orderings for the use of resource 3 by the three activities: C2-C1-C3 (solution 1 designated S1); C1-C3-C2 (solution 2 designated S2); and, C1-C2-C3 (solution 3 designated S3). Any of the three possible solutions-S1, S2, or S3-will delay the completion of the critical path of at least one of the two projects. In fact, solution 3 (C1-C2-C3) will delay the completion of both projects. Additionally, one can imagine the effects of multitasking or job splitting. Although PERT/CPM assumes that an activity, once started, cannot be stopped and restarted, it is common in practice for resource managers to do just that in order to appease various project managers. PERT/CPM does not provide guidelines on when and how to multitask, a common practice in industry.

FIGURE 2-4 Seven problems with PERT/CPM management of single projects identified by Walker (1998).

Cause: Priority of resource use across projects may affect on-time project completion.

Cause: PERT/CPM does not provide priority rules to support project completion.

These are addressed by Guidelines VI, VIII, and XII.

Problem 3: Resource Contention across Projects Caused by Variability of Other Resources Figure 2-4 Problem 3 shows two simple projects diagramed as a single mega-project. Each project has only two activities. Only one activity (activity N in project 2) has any associated variability. Resource 1 is used by activity L1 in project 1 and by activity L2 in project 2 in immediate succession. Typical PERT/CPM calculations estimate the completion date of project 1 to be period 8, and the completion date of project 2 to be period 8. The dashed arrow in Fig. 2-4 Problem 3 shows the order of use of resource 1 as activity L1 then activity L2.

If all possible combinations of activity duration are enumerated, the completion date of project 1 is unaffected by the activity duration variability. However, when activity duration variability results in shorter than expected duration of activity N, a resource contention problem between activity L1 and activity L2 causes the delay of the completion date of project 2. Resource 1 is still in use by activity L1 when activity N is completed in period 2 (its optimistic estimate). As activity L2 cannot begin until activity L1 is completed, project 2 is unable to take advantage of an optimistic completion. A resource contention problem does not exist when activity N is completed in its pessimistic estimate. Therefore, only the late (pessimistic) duration time is added to the enumerated total, and the completion date of project 2 is later than planned. PERT/CPM does not recognize the impact of statistical fluctuation and dependent events on project completion. It should provide guidelines on buffering resources and paths against statistical fluctuations.

Cause: Murphy exists.

Cause: PERT/CPM does not protect against Murphy.

Cause: PERT/CPM does not recognize that multiple projects are interrelated due to the shared use of common resources.

These are addressed by Guidelines VI, VIII, and XII.

Problem 4: Resource Contention across Projects Caused by Variability of Common or Other Resources In Fig. 2-4 Problem 4, two simple projects are diagrammed as a single mega-project. The activity durations in project 1 are variable, while the activity durations in project 2 are deterministic. Resource X is used by activity X1 in project 1 and by activity X2 in project 2 in immediate succession. Typical PERT/CPM calculations estimate the completion date of project 1 to be period 8, and the completion date of project 2 to be period 12. The dashed arrow in Fig. 2-4 Problem 4 shows the order of use of resource 1 as activity X1 then activity X2.

If all possible combinations of activity durations for the two projects are enumerated, the completion of project 1 is unaffected by the activity duration variability of activities W and X1. However, when activity duration variability results in longer than expected duration of project 1, a resource contention problem between activity X1 and activity X2 causes the completion date of project 2 to be later than planned. PERT/CPM does not recognize the existence of these three core drivers and does not provide a mechanism to reduce their collective impact on project completion.

Cause: Murphy exists.

Cause: PERT/CPM does not protect against Murphy.

Cause: PERT/CPM does not recognize that multiple projects are interrelated due to the shared use of common resources.

These are addressed by Guidelines VI, VIII, and XII.

Problem 5: Early Consumption of Project Slack Figure 2-4 Problem 5 shows two simple projects diagramed as a single mega-project. The critical paths of each project are as follows: project 1 A-B-C = 16; project 2 E-D2 = 15. The non-critical path of project 1 (A-D1-C) has two periods of associated slack. Typical PERT/CPM management would delay starting activity D1 in project 1 by the amount of slack available. If activity D1 is started on its late start date, activity D2 in project 2 and thus the completion of project 2 will be delayed by one period. PERT/CPM does not look at the impact of contention across projects on project lateness.

Cause: PERT/CPM does not view activity slack strategically.

Cause: The project is a major undertaking that determines the success or profitability (goal) of the organization.

Cause: Project managers delay expenses by starting activities as late as possible.

These are addressed by Guidelines I, II, III, IX, and XII.

Problem 6: Planning to Time Rather Than Activity Completion Figure 2-4 Problem 6 shows two simple projects diagrammed as a single mega-project. Each of the two projects has only two activities, and each activity has some associated activity duration variability. The expected duration of each activity is as follows: E(A) = 4, E(B1) = 2, E(B2) = 5, and E(D) = 5. Typical PERT/CPM planning would yield the following estimates of the date of project completion: project 1 complete in period 9, and project 2 complete in period 7.

The typical PERT/CPM manager would try to plan to start each activity based on the estimated time of completion of the preceding activity. Since E(A) = 4 and E(B1) = 2, the manager would plan to start activities B2 and D in periods 4 and 2, respectively. If all possible activity durations are enumerated and activities B2 and D are started based on the expected time of completion of A and B1, respectively, the expected completion dates of project 1 and project 2 exceed their PERT/CPM-planned completion dates. The expected completion date of project 1 is 9.5 periods versus 9; the expected completion date of project 2 is 7.625 periods versus 7. PERT/CPM does not look at the impact of scheduling to time instead of completion of proceeding activity across projects on project completion.

Cause: PERT/CPM does not recognize that some resources might be required for more than one activity.

Cause: PERT/CPM provides resource schedules based only on technological relationships and time estimates.

These are addressed by Guidelines XI and XII.

Problem 7: Increasing Planned Activity Duration Estimates In this case (Fig. 2-4 Problem 7), the activity duration estimates have been increased by one period to reflect that managers may recognize that activity duration variability exists (see Fig. 2-3). The revised estimates of activity duration are as follows: E(A) = 5, E(B2) = 3, E(B1) = 6, and E(D) = 6. If the reader examines Fig. 2-3 Problem 4, he will find that increasing activity duration estimates leads to PERT/CPM-planned projects being late; increasing planned activity times in the multiple project environment also causes projects to be late.

If all possible combinations of activity duration are enumerated and activities B2 and D are started based on the (revised) expected time of completion of A and B1, respectively, the expected completion date of project 1 is equal to its planned completion date given the revised estimates of activity duration. The expected completion date of project 2 is less than its planned completion date given the revised estimates of activity duration. The probability of on-time project completion is 100 percent for project 1 but only 50 percent for project 2. The augmenting (or "fudging") of activity duration estimates has bettered the probability of on-time completion of project 1 (over Fig. 2-3 Problem 6) and has not worsened the probability of on-time completion of project 2.

However, augmenting the activity duration estimates has caused the planned completion date of each project to be later than would be the case without increasing activity duration estimates. Both of the individual project completions have been extended for minimal or no gain in probability of on-time completion.

In this case, the project manager receives praise for completing the projects ahead of schedule and the activity managers receive praise for completing their respective activities ahead of schedule (though only 67 percent of the time). If the estimates of activity duration had not been increased and the project manager had planned to time (as in Fig. 2-4 Problem 6), the expected completion date of project 1 would have been 9.5 periods and the expected completion date of project 2 would have been 7.625 periods. Clearly, this is a better result than 10 periods and 8 periods (projects 1 and 2, respectively) both in time and in cost, but the project manager would be punished for failing to meet the planned completion date. Additionally, had the activity duration estimates not been increased and the activities had been planned to completion, the expected completion dates of projects 1 and 2 would have been the same as their respective planned completion dates. PERT/CPM does not discuss the impact of overestimating activity times across projects on project completion.

Cause: Murphy exists.

Cause: Resource managers are expected to finish activities when planned.

Cause: Resource managers do what they feel is necessary to ensure resource utilization and that the resources are available when promised.

These are addressed by Guidelines IV, X, and XII.

The Use of PERT/CPM Critical Paths in the Single Project Environment

In conducting research on project management using simulation as compared to using project management in practice, some differences are noted. In most simulation models, the succeeding activity is linked to the completion of the proceeding activity (scheduling by activity completion). For example, if activity A was scheduled to finish at time 10 but finished early at time 7, then activity B started at time 7 instead of waiting until the scheduled start time of 10. This seems to be the common practice in conducting research on project management.

In practice, however, with the growing use of project management software (Krakow, 1985; Lowery and Stover, 2001), the convention is to schedule by time (scheduling by time). Each resource is given a project schedule indicating when the resource is to start a given activity and how long it is to last. Where software is not used, either convention applies. Seldom, however, can a resource immediately reschedule what it is doing to start an activity early unless given warning.

The point here is that research does not simulate reality in its simplest form. In practice, where projects are large, several functions are involved, and project management software is used, projects seldom benefit from optimistic (early) completions. This means that the project is assured of being late unless extraordinary actions are taken to keep the project on schedule. If activities are only completed in their mean and pessimistic times, then activity times and project times are consistently understated. The project will always be late.1 Cause: Theory does not support practice.

This is addressed by Guideline XI.

The Use of PERT/CPM Critical Paths in the Multiple Project Environment

Two approaches are recommended in the research-the use of single project critical path and the use of a mega-project network connecting all projects to plan and controlling all projects simultaneously. Little research has been conducted to determine which of these is the better approach. Given the errors in logic of simulating projects as described previously, any research comparing these approaches needs to be reconsidered. Clearly, if resource contention exists across projects, then this must be reconciled to determine appropriate critical paths for each project and clearly, if one or a few resources are heavily loaded in most projects, then a mega-project approach is desired to ensure effective use of the constraining resource across projects.

In practice, 90 percent of projects occur in a multi-project environment and little research has been conducted in this environment. In practice, few organizations use the project networks to control projects and little research has been conducted on how to control across multiple projects. After the original project plans are established, few bother with constantly updating the plans and rescheduling in the computer. Given all of the causes of failures of projects, one can see why a manager may not go to the trouble to constantly update every delay on every activity in a network.

Cause: No well-defined method of planning and controlling projects in a multi-project environment exists.

This is addressed by Guideline XII.

Summary of the Micro Issues

That which is of the most importance here is not that researchers have not recognized that PERT/CPM is limited by its assumptions, but rather that the effects of these assumptions have been both underestimated and unstated. Many researchers have indeed recognized these assumptions, but there has been no systematic effort to eliminate the effects. By examining the gedankens, the reader will recognize that if the practitioner is forced to commit even one of the errors identified previously, then the project is probably going to be late. Additionally, the magnitude of the system effect (late, over budget, or under completed projects) is increased with each problem and each occurrence of each problem.