What is my scheduling objective? Minimizing the project lead time

Figure 1 displays a project network with 11 activities and finish-start precedence relations between them. Each number above the node denotes the estimated duration of the activity while the number below the node is used to refer to the resource demand. It is assumed that the availability of the resource is restricted to six units for all periods of the project. The right part of the picture displays an earliest start schedule  respecting the precedence relations of the project. Each activity is represented by a rectangle with the horizontal length the activity duration and the vertical height the renewable resource requirement/demand. The earliest start schedule shows a resource conflict between period 8 and 13 since the total use of the renewable resource by activities 3, 4, 5, 6 and 7 exceeds its limited availability of 6. In order to solve this resource conflict, activities need to be shifted further in time to time periods where resources are still available (see “Linking resources to activities: Resource availability and resource demand”).

 

Solving resource conflicts results in activity shifts in time in order to schedule them at periods where resources are still available. Activities 3 and 6 cause a resource conflict in figure 1, and must therefore be shifted such that the over-allocations disappear. A simple shift of these activities results in a resource-feasible project schedule as shown in figure 2 with a total project duration of 26. 

 

 

However, this schedule has been constructed without any scheduling objective to optimize, and hence, the shifts of activities 3 and 6 are rather random choices. In figure 3, activities 5 and 6 have been delayed, resulting in a different resource-feasible schedule. In this schedule, time is indeed optimized, resulting in a resource-feasible project schedule with the lowest possible project duration. 

 

 

Note that the critical path in figure 1 is equal to the activity sequence 1 - 2 - 3 - 6 - 9 - 11 while the critical chain of figure 3 is equal to activity sequence 1 - 2 - 4 - 6 - 9 - 11 (see “The critical path or the critical chain? The difference caused by resources”).