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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