constant. Without altering the project time, resource level-ing is an effective means of smoothlevel-ing the utilization of resources. In other words, resource leveling is an effective means of reducing the number of resources required on
“spike” days, and it also fills in resources on low resource utilization days. In addition, the day-to-day fluctuation of resource needs will be reduced. The method of resource leveling that will be described uses a minimum-moment algorithm.1Essentially the resource requirements on a pro-ject are smoothed or leveled by making use of the available free float. The activities are first arranged by an early start schedule. With resource leveling, one can systematically evaluate the impact of using any float associated with each activity.
The minimum-moment algorithm that will be used for the resource leveling assumes that once an activity has been started, it cannot be interrupted. Another assumption is that resource consumption is constant over the duration of an activity. The network logic is not questioned when resource leveling is done; however, this should be done if the final solution is not considered acceptable. This method will not alter the critical activities but will focus on the merits of shifting any noncritical activities by reducing their float. In the final solution, resource buildups should be minimized.
A number of different approaches can be used for resource leveling. If the project duration is held constant, the different methods will have the same objective: to use up available float if smoothing of resources will occur.
THE MANUAL SOLUTION FOR RESOURCE LEVELING
As with the manual solution for resource allocation, the manual solution for resource leveling is typically limited to simple networks. Although computers can solve these problems much more readily, the objective of this exercise is simply to present the basic principles of resource leveling calculations.
It is assumed that activities cannot be interrupted; once an activity has started, it must be completed. Note also that only one resource is leveled at a time. It is assumed by leveling one resource that other resources will similarly be leveled to some extent. It would also be very difficult to address the resource leveling process manually on a project for which several different resources were to be leveled simultaneously.
Since the duration of the project is fixed, the critical activi-ties are not manipulated, meaning only the start times of activities with positive free float can be adjusted.
The sample begins with a bar chart showing all activities of the network in their early start positions. The resource being leveled is tallied on one line (iteration zero). This will show the extent of the resource utilization and whether there is an unacceptable buildup of resource needs during the pro-ject. If an identical number of resources were required each day, no leveling would be required. This is generally not the case. The smoothing of most resources occurs by using the minimum-moment approach. This smoothing effect will be visible with each iteration as the resources will be tallied each time an activity start date is altered.
After the early-start bar chart is developed and the resources have been tallied, the resource leveling process begins. With the minimum-moment algorithm procedure, the process begins at the end of the project duration and works systematically in a “backward” fashion to the begin-ning of the project. For each day in the bar chart, all the activities that could be scheduled to occur on the day in question are considered. For each activity that is considered, the optimal number of float days to be utilized is established.
This is done by calculating an improvement factor for each potential change in the start date. For example, if an activity has 3 days of free float, an improvement factor is determined when the start date uses up 1 day of free float, when 2 days of free float are used, and when all the float days are used.
Carpenters
Project duration
FIGURE 6.25 Distribution of Carpenter Utilization After Leveling.
1A detailed discussion of the minimum-moment algorithm is presented in Robert B. Harris, Precedence and Arrow Networking Techniques for Construction (New York: John Wiley & Sons, Inc., 1978), 277.
88 CHAPTER SIX
FIGURE 6.26 Sample Network to Demonstrate Resource Leveling.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
FIGURE 6.27 Summary of Resource Utilization with No Resource Leveling.
The calculation of the improvement factor forms the basis of the leveling decisions. The general equation for deter-mining the improvement factor (IF) can be stated as follows:
where
A = activity designation
N = number of free float days consumed
R = the number of resources used by the activity per day
Rv= number of resource days currently assigned to those days that will be vacated when the activity start date is changed
Ro= number of resource days currently assigned on those days that will be occupied when the activity start date is changed
Nr= the smaller value of the number of days of free float consumed and the duration of the activity The improvement factor must be 0 or some positive value in order for a benefit to be derived by reassigning the start date of an activity. The largest improvement factor determines the number of free float days to use. If improvement factors are calculated for several activities, the governing value is the activity with the largest improvement. If two activities are tied with the same improvement factor, priority reassigning of the start date is given to the activity with the most resources per day. If a tie still exists, the activity that will use up the largest number of free float days is selected. If still tied, the activity
IF (A, N) = R * (Rv - Ro - R * (Nr))
with the latest start date is selected. If a tie still exists, priority is given to the activities on the basis of input order.
When an activity start date is changed to a later date, the free float available to that activity is reduced. However, the activity still has flexibility in that the start date could now be earlier. This is known as back float. Suppose an activity has 5 days of free float, and through the leveling process its start date is delayed 3 days. This activity will now have 2 days of free float and 3 days of back float.
When resource leveling calculations are made, an accounting should be kept of the number of days of back float for each activity. Just as calculations were made to deter-mine if the free float of activities should be consumed, similar calculations must be made to determine if the back float of activities should be used. Note that when a “backward pass” is made, an activity start date is reassigned if the improvement factor is zero. A value of zero means that no smoothing is generated by reassigning the start date. Since this is not detri-mental to resource utilization results, the reassignment is made to “make room” for other activities. That is, by shifting the start dates, free float is given to other activities that might otherwise not have free float. When the entire project has been evaluated with the forward pass that considered the back float, the resource leveling process is completed.
A simple network will demonstrate the process of performing a manual resource leveling solution. The network is shown in Figure 6.26 along with a table that shows the resource (R) utilization per day along the duration of the project (Figure 6.27). Note that resources are needed for each day, but the total number of resources required each
Resource Allocation and Resource Leveling 89
day varies considerably. The activities in Figure 6.27 are shown in their early start positions, and the free float of the activities is shown as dashed lines. The extent that the resources will be successfully leveled will depend on the net-work logic and the resources required of the individual activities.
The following process is by no means the only way that the procedure can be followed. Variations of the process might be justified, but circumstances will not always favor one method over another. The process of leveling begins with a backward pass where the project is evaluated 1 day at a time. The purpose of this backward pass is to evaluate the merits of utilizing some of the free float to create a more effi-cient resource utilization. In conducting this backward pass, first consideration is given to Day 17. Since there is no activ-ity that has any free float on that day, there is no opportunactiv-ity to make any changes in resource utilization. On Day 16, there is a free float day associated with Activity H, so we will now consider moving Activity H to determine if the resources can be leveled. When we examine Activity H, it is obvious that it actually has several days of free float. We will consider assigning Activity H to each of the days of free float to find the optimal allocation. The ideal location will be determined from the improvement factor. The improvement factor is determined for moving activity H 1 day, 2 days, 3 days, and so on. Improvement factors will be determined for seven possible positions (7 days of free float) to which Activ-ity H could be assigned. The improvement factors are shown as follows:
From the improvement factors, it is clear that the uti-lization of any of the free float will improve the resource utilization of Activity H. The maximum improvement is
IF (H,7) = 3 * (20 - 8 - 3 * (2)) = 18
realized when 3 days of free float are used. The movement of Activity H and the status of resource use are shown in Figure 6.28.
After Activity H has been moved, the backward pass can continue. The next day to consider is Day 15. Free float does occur on this day, but this belongs to Activity H, which has already been moved to its ideal location. The backward pass continues to Day 14, on which Activity F has free float. As no other activities have free float on Day 14 (Activity H was moved in Cycle 1), improvement factors will be computed for each possible location of Activity F.
There is a clear advantage in moving Activity F to utilize its free float. In this cycle (Cycle 2), the improve-ment is the same whether we move Activity F 5 or 6 days.
When ties occur, the normal procedure is to move the maximum number of days, primarily to allow additional space for other activities. Although no other activities could benefit from this move of 5 versus 6 days, to be consistent we will move the maximum of 6 days. The summary of the resource use after Cycle 2 is shown in Figure 6.29.
The backward pass continues. Free float days are noted on many days (Days 13, 12, 11, etc.), but many of these rep-resent free float of Activities H and F, and in some cases it is really the back float of Activities H and F. It is only when the backward pass gets to Day 7 that the free float of Activities C and D is encountered. Activities C and D cannot be sched-uled to occur later than Day 7 (during the back float days created by moving Activities F and H) because they must be finished before Activity G is started. Since both these activi-ties have free float on Day 7, improvement factors will be calculated for each. Note that Activity C has 4 days of free
IF (F,6) = 4 * (9 - 3 - 4 * (1)) = 8 P
FIGURE 6.28 Summary of Resource Utilization After Cycle 1.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
FIGURE 6.29 Summary of Resource Utilization After Cycle 2.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
FIGURE 6.30 Summary of Resource Utilization After Cycle 3.
float and Activity D has 5 days. Their improvement factors are determined as follows:
From the improvement factors, it is evident that the greatest improvement occurs when Activity C is moved for-ward 4 days (when ties occur, always move the greatest num-ber of days). At the end of Cycle 3, the resource utilization is as shown in Figure 6.30.
As we are about to continue the backward pass, it should be apparent that Day 7 should still be considered. Activity D does have free float, so it should be considered next. Note that Activity D could have been moved in Cycle 3 but did not have an improvement factor as large as Activity C.
IF (D,5) = 3 * (13 - 3 - 3 * (1)) = 21
The improvement factors for moving Activity D are now recomputed:
Activity D should be moved 3 days. Note how the improvement factors for Activity D have changed after first moving Activity C. The procedure is followed as before to yield a summary of resource utilization, as shown in Figure 6.31.
The essence of the solution is now as shown in Figure 6.31. Remember that when activities use up free float, back float is created. The back float may become free float for some preceding activities. In the process of performing the computations, whenever there was a positive improvement factor or a tie in the improvement factor for different posi-tions, the activities were always moved the maximum amount of time. This was done to create free float for other activities so as to increase the flexibility of scheduling. The activities must now be examined to determine if any activi-ties should be moved to use up some of the back float. This is done by starting on Day 1 and conducting a forward pass. As
IF (D,5) = 3 * (9 - 7 - 3 * (1)) = -3
Resource Allocation and Resource Leveling 91
FIGURE 6.31 Summary of Resource Utilization After Cycle 4.
back float is encountered, improvement factors are com-puted. In this process, Day 2 is noted to contain back float for Activities C and D. Therefore, improvement factors are computed for both activities as follows:
All improvement factors are negative except one. The improvement factor of Activity D is zero when it is moved back 1 day. Note that this means that there is no improve-ment, but it does schedule the activity earlier so as to give greater flexibility to the overall network. The summary of resource use is shown in Figure 6.32.
As the forward pass continues, improvement factors are computed for Activities F and H.
IF (H,1) = 3 * (4 - 5 - 3 * (1)) = -12
From the improvement factors, it is determined that activity F can be moved back 1 day. The final results are shown in Figure 6.33. Note how the use of resources per day has been significantly leveled between Cycles 0 and 6.
This is purely a mechanical solution and does not take into account unique project characteristics. Thus, this is the manual solution, but further study of the network and the consideration of changes in scheduling logic should be explored.
A final comment seems warranted on this method of resource leveling: This approach will generally give an acceptable solution in that the “spikes” and “dips” in resource needs will be smoothed. However, the solution may not be an optimal one. It must be recognized that the solu-tion is developed in an iterative fashion. This means that the approach simply evaluates the impact of considering the merits of reassigning the start dates of those activities under
IF (F,6) = 4 * (7 - 5 - 4 * (1)) = -8
FIGURE 6.32 Summary of Resource Utilization After Cycle 5.
92 CHAPTER SIX
FIGURE 6.33 Summary of Resource Utilization After Cycle 6.
consideration. The overall impact of a decision is not con-sidered. Although the decision may not be optimal, it will generally be sufficiently close to being optimal as to not war-rant further concern.