With the widespread use of microcomputers on construc-tion projects, it is reasonable to assume that most resource allocation on construction projects is done with the use of computers. An examination of the manual approach for resource allocation will give a clearer impression of how this is done. To demonstrate the manual solution, a simple network will be used. Although this will appear to be quite a manageable task, projects entailing many activities and many resources pose a considerable challenge in a manual solution.
The sample illustration uses a simple network with two different types of limited resources. The first step is to do a manual “forward pass” and then a “backward pass.” The primary purpose is to determine the late start dates for each activity. The network is still to be used in the solution, but most of the solution itself will be done on a tabular form.
On the tabular form, first list all of the activities, along with each activity’s required resources, duration, late start, and total float (early start may also be shown). Use a “status”
column to indicate which activities are eligible to be sched-uled and those that have been fully schedsched-uled. The resource
Resource Allocation and Resource Leveling 75
allocation can then begin. The solution will appear as a bar chart, with the resources being tallied at the bottom of the bar chart for each day.
After examining the network, indicate in the status col-umn which activity or activities can be started. This can be indicated by simply drawing a diagonal line in the status column next to each activity that can be scheduled. The next step is to actually schedule those activities. Naturally, any activity that does not utilize any of the limited resources will be scheduled as soon as it becomes eligible. The activities utilizing the limited resources will require further examina-tion, particularly if the available resources are exceeded when all eligible activities are scheduled simultaneously.
Obviously, not all activities can be scheduled if the available resources are exceeded. Thus, a rational and orderly approach must be used to determine which activities are to be scheduled. The decision for determining which activities are to be scheduled should be based on the rules or priorities given earlier.
With the parallel method, it is essential to review each activity that is eligible for each day in the project. With the series method, a similar approach is used, but once an activity is selected for scheduling, it must not be interrupted.
A sample network illustrating the series solution method is shown in Figure 6.2. Computations will show the steps to follow as the solution evolves.
The information needed to solve the series solutions is shown in Figure 6.2. The tabular information obtained from the forward and backward passes is shown in Figure 6.3.
Solve the schedule by the series method of resource allocation. The resource limits not to be exceeded are as follows: 5M (masons) 2H (helpers).
Resource limits are not to be exceeded under any circumstances.
In the first step, only Activity A is eligible for scheduling.
This is indicated by the slash placed next to Activity A in the eligibility column headed by a “/”. Activity A is then scheduled on Day 1 on the chart. Since Activity A requires two masons and one helper per day and since the duration is 1 day, the resources are applied to the first day. The status column in Figure 6.4 is shaded to indicate that Activity A has been scheduled.
At the completion of Activity A, Activities B and C are eli-gible for scheduling. Since the total number of available resources of five masons and two helpers is not exceeded, both activities are scheduled on Days 2 and 3 (see Figure 6.5). After Day 3, Activity C will be completed while Activity B still has 2 remaining days. The eligibility column of Activity C is shaded.
To schedule Days 4 and 5, Activity B has not been completed, so it will be scheduled as the highest priority.
When activity C was completed in the last step, Activities F, G, and H became eligible for scheduling. Of these, acti-vity G has the earliest late start, so it is considered first for
A
2M, 1H 1
B
2M, 1H 4
E
3M 4
J
2M, 2H 2
L
3M, 2H 2
K
2M, 1H 6
1
F
3M 3
G
1M, 2H 4
H
1M, 1H 2 C
2M, 1H 2
D
1M 1
M
2M, 1H
Duration Activity
Resources TF FF EF
ES LS
LF
FIGURE 6.2 Network Used in Series Solution Example.
76 CHAPTER SIX
FIGURE 6.3 Resource Allocation by the Series Method.
Act Resource Dur TF LS / 1 2 3 4 5 6 7 8 9 1
FIGURE 6.4 Allocation of Resources for Day 1.
Act Resource Dur TF LS / 1 2 3 4 5 6 7 8 9 1
FIGURE 6.5 Allocation of Resources for Days 2 and 3.
scheduling on Day 4. Examination of the resources needed to complete Activity G are such that the number of helpers required along with Activity B would be three, more than the two that are available. Thus, Activity G cannot be scheduled. The next priority is then Activity F, which can be scheduled without exceeding the five masons and two helpers (see Figure 6.6). Activity H cannot be scheduled because of the resource limits.
At the end of Day 5, Activity B will be completed. The eligible activities now also include Activities D and E. On Day 6, the first activity scheduled is Activity F (previously started). Activity E has the earliest late start, but this would exceed the resources available. Activity D is then considered and found to be eligible for scheduling. This
is followed by Activity G, which is also scheduled for Day 6 (see Figure 6.7).
The same procedure is followed for each day until all activities have been scheduled. The completed schedule is shown in Figure 6.8. The project duration is now 20 days, 4 days longer than if the resource limits had been ignored.
Figure 6.9 shows the network used to apply resource limits with the series solution. This same network will now be used to show how the parallel solution is derived.
Solve the schedule by the parallel method of resource allocation (see Figure 6.10). The resource limits are as follows: 5M (masons) 2H (helpers).
Resource limits are not to be exceeded under any circumstances.
Resource Allocation and Resource Leveling 77
Act Resource Dur TF LS / 1 2 3 4 5 6 7 8 9 10
A 2M 1H 1 0 1 2/1
B 2M 1H 4 0 2 2/1 2/1 2/1 2/1
C 2M 1H 2 6 8 2/1 2/1
D 1M 0H 1 1 7
E 3M 0H 4 0 6
F 3M 0H 3 7 11 3/0 3/0
G 1M 2H 4 6 10
H 1M 1H 2 8 12
J 2M 2H 2 1 8
K 2M 1H 6 0 10
L 3M 2H 2 6 14
M 2M 1H 1 0 16
FIGURE 6.6 Allocation of Resources for Days 4 and 5.
Act Resource Dur TF LS / 1 2 3 4 5 6 7 8 9 10
A 2M 1H 1 0 1 2/1
B 2M 1H 4 0 2 2/1 2/1 2/1 2/1
C 2M 1H 2 6 8 2/1 2/1
D 1M 0H 1 1 7 1/0
E 3M 0H 4 0 6
F 3M 0H 3 7 11 3/0 3/0 3/0
G 1M 2H 4 6 10 1/2
H 1M 1H 2 8 12
J 2M 2H 2 1 8
K 2M 1H 6 0 10
L 3M 2H 2 6 14
M 2M 1H 1 0 16
FIGURE 6.7 Allocation of Resources for Day 6.
In the first step, only Activity A is eligible for scheduling.
As with the series method, this is indicated by the slash placed next to Activity A. Activity A is then scheduled on Day 1 on the chart (Figure 6.11).
At the completion of Activity A, Activities B and C are eligible for scheduling. Since the total number of resources
of five masons and two helpers is not exceeded, both activi-ties are scheduled on Days 2 and 3. After Day 3, Activity C will be completed while Activity B still has 2 remaining days (Figure 6.12).
To schedule Days 4 and 5, Activity B has not been completed and Activities F, G, and H are also eligible for
Act Resource Dur TF LS / 1 2 3 4 5 6 7 8 9 1 0
1 1
1 2 3
1 1 4
1 5
1 6
1 7
1 8
1 9
2 0
2 1
2 2 A 2M 1H 1 0 1
B 2M 1H 4 0 2 C 2M 1H 2 6 8 D 1M 0H 1 1 7 E 3M 0H 4 0 6 F 3M 0H 3 7 11 G 1M 2H 4 6 10 H 1M 1H 2 8 12 J 2M 2H 2 1 8 K 2M 1H 6 0 10 L 3M 2H 2 6 14 M 2M 1H 1 0
2 4 4 5 5 5 4 4 4 5 2 3 3 2 2 2 2 3 3 2 1
Masons Scheduled
Helpers Scheduled 2 2 1 1 2 2 2 2 2 2 2 2 1 1 1 1 2 2 1 16
FIGURE 6.8 Schedule of Activities for the Project.
A
2M, 1H 1
B
2M, 1H 4
E
3M 4
J
2M, 2H 2
L
3M, 2H 2
K
2M, 1H 6
1
F
3M 3
G
1M, 2H 4
H
1M, 1H 2 C
2M, 1H 2
D
1M 1
M
2M, 1H
Duration Activity
Resources TF FF EF
ES LS
LF
FIGURE 6.9 Parallel Solution Example.
78 CHAPTER SIX
Act Resource Dur TF LS / 1 2 3 4 5 6 7 8 9 1
FIGURE 6.10 Resource Allocation by the Parallel Method.
Act Resource Dur TF LS / 1 2 3 4 5 6 7 8 9 1
FIGURE 6.11 Allocation of Resources for Day 1.
Act Resource Dur TF LS / 1 2 3 4 5 6 7 8 9 1
FIGURE 6.12 Allocation of Resources for Days 2 and 3.
scheduling. Of these, Activity B has the earliest late start, so it is considered first for scheduling on Day 4. Activity G is considered for scheduling, but this cannot be done as the resources needed to complete Activity G are such that the number of helpers (three) required along with Activity B would exceed the two that are available. Thus, Activity G cannot be scheduled. The next priority is then Activity F, which can be scheduled without exceeding the five masons and two helpers (see Figure 6.13). Because of resource limi-tations, Activity H cannot be scheduled at this time.
At the end of Day 5, Activity B will be completed. The eligible activities now also include Activities D and E. On Day 6 of the eligible activities (D, E, F, G, and H), the first activity scheduled is Activity E (earliest late start). Activity D is then considered eligible for scheduling and is scheduled to
start on Day 6. This is followed by Activity G, which is also scheduled for Day 6 (see Figure 6.14). Note that Activity F has a lower priority owing to its late start date, and it cannot be scheduled at this stage without exceeding the resource limits. Thus, Activity F will be discontinued after Day 5.
The same procedure is followed until all activities have been scheduled. The completed schedule is shown in Figure 6.15. Because of the criteria that permit an activity to be interrupted, note how Activities F and G are now scheduled differently than they were with the series method. Such interruptions of lower-priority activities often result in reduced project durations. Note that the series solution of the same network also resulted in a pro-ject duration of 20 days, but that different activities were scheduled on certain days.
Resource Allocation and Resource Leveling 79
Act Resource Dur TF LS / 1 2 3 4 5 6 7 8 9 10
A 2M 1H 1 0 1 2/1
B 2M 1H 4 0 2 2/1 2/1 2/1 2/1
C 2M 1H 2 6 8 2/1 2/1
D 1M 0H 1 1 7
E 3M 0H 4 0 6
F 3M 0H 3 7 11 3/0 3/0
G 1M 2H 4 6 10
H 1M 1H 2 8 12
J 2M 2H 2 1 8
K 2M 1H 6 0 10
L 3M 2H 2 6 14
M 2M 1H 1 0 16
FIGURE 6.13 Allocation of Resources for Days 4 and 5.
Act Resource Dur TF LS / 1 2 3 4 5 6 7 8 9 10
A 2M 1H 1 0 1 2/1
B 2M 1H 4 0 2 2/1 2/1 2/1 2/1
C 2M 1H 2 6 8 2/1 2/1
D 1M 0H 1 1 7 1/0
E 3M 0H 4 0 6 3/0
F 3M 0H 3 7 11 3/0 3/0
G 1M 2H 4 6 10 1/2
H 1M 1H 2 8 12
J 2M 2H 2 1 8
K 2M 1H 6 0 10
L 3M 2H 2 6 14
M 2M 1H 1 0 16
FIGURE 6.14 Allocation of Resources for Day 6.
80 CHAPTER SIX
Act Resource Dur TF LS / 1 2 3 4 5 6 7 8 9 1
FIGURE 6.15 Schedule of Activities for the Project.