Since the late 1950s, a network-based approach to developing schedules has seen increasing use for all kinds of projects, including construction projects. Project activities are related to each other on a network, showing the order in which they are intended to be performed. The duration of each activity is estimated and calculations determine the timeframe within which each activity can be performed and the time at which the project can be completed. In addition, the calculations identify those activities that are most critical in establishing that completion time. Two methods have been used to develop project networks. One method uses arrows to represent the activities, with their endpoints depicting their relationships to other activities. The other method uses boxes or similar nodes to signify activities and arrows or lines to connect the nodes in the order in which the activities are planned to be carried out. Most project programmers currently use the latter activity-on-node method and we shall confine our discussion to this approach. In this section we describe the basics of activity-on-node scheduling and we then apply the method to the bridge construction project whose work breakdown structure is shown in Figure 5.7.
General concepts: a modest example
Consider a ‘project’ to construct a large footing that will support a bridge abutment or a piece of industrial machinery. Figure 5.8 shows the activities that might be required to carry out this project. The project begins with excavation, ordering and delivering reinforcing steel and setting up a pre-fabrication shop on the site. It proceeds through placement of forms, pre-fabrication of reinforcing steel, setting of steel in the forms, placement of concrete and removal of the pre- fabrication shop. After the concrete is placed and the shop is removed, an inspection takes place and the project is considered complete. (As usual, to stress the fundamentals, we have
oversimplified the real project, omitting such tasks as curing of the concrete, removal of forms and installing inserts into the concrete footing.) In drawing the network, we consider three questions for each activity:
1 What activity or activities, if any, must take place directly prior to this activity? 2 What activity or activities, if any, must take place directly following this
activity?
3 What activity or activities, if any, can take place concurrently with this activity? We observe several characteristics of an activity-on-node network in Figure 5.8. Each activity is represented by a node, a rectangle in this case. Arrows connect the nodes to show the order in which the work is to flow. Generally the sequencing is from left to right; in a complicated network, such sequencing might be violated, but the direction of the arrow always clarifies the work flow direction. Nodes with no arrows entering from the left represent activities that can start at the beginning of the project; they have no predecessors. In Figure 5.8, ‘excavate’, ‘order and deliver reinforcing steel’ and ‘set up pre-fabrication shop’ can begin as soon as the project begins. Likewise, nodes with no arrows leaving from the right depict the final activities in the project; they have no successors. In our example, the final activity is ‘inspection’. We also note that some work items can be done concurrently with others; for example, ‘remove pre-fabrication shop’ can be done while the ‘set steel’ and ‘place concrete’ activities are underway. Finally, we observe that Figure 5.8 makes no mention of the durations of the activities. At this stage, we are concerned only with the identity of the activities and their order. The position of a node in the diagram is not related to the time at which the activity takes place; the diagram is not drawn to any sort of time scale. While the planning function has many aspects, certainly one of the most important is this activity work flow definition. Much healthy discussion and debate should occur among members of the project team as they consider various alternative sequences and arrive at an agreement, albeit tentative and subject to modification, as to how the work flow will proceed. Once this diagram is complete, we proceed from this part of planning to the scheduling of the activities.
Figure 5.9 differs from Figure 5.8 in two respects. First, we have added an estimated activity duration to each node. In making these estimates, we will have to review the amount of work required by the activity, the anticipated crew size and productivity and equipment productivity. The cost estimate will be a helpful information source, as will records of actual time spent on similar tasks on previous projects.
The second addition in Figure 5.9 is the early start and early finish time for each activity. These times result from some basic calculations that will lead to an estimate of the overall project duration. An activity’s early start time is the earliest it can begin, based on the early completions of all preceding activities; its early finish time is its early start time plus its duration. For activities that can begin at the start of the project (those with no predecessors), we assign an early start time of 0. For all other activities, the early start time is the latest early finish time of its immediate predecessor activities. It is the latest early finish time because all predecessor activities must be completed before the activity under consideration can be started. Thus, for any activity,
ES = early start time = 0 for all ‘begin’ activities; otherwise = max (early finishes of all immediate predecessors);
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In Figure 5.9, the early start time for ‘excavate’ is 0, because it can begin at the beginning of the project. Its early finish time is 0 + 1 = 1. For ‘place forms’, the early start is 1, because it has only one predecessor, whose early finish is 1. For ‘pre-fabricate reinforcing steel’, the early start is ES = max (4, 2) = 4. Its early finish is 4 + 3 = 7. Note that Figure 5.9 shows all early starts and early finishes just above the nodes’ upper left and upper right hand corners, respectively. We proceed through the network from beginning to end, in a process sometimes called the forward pass, until we reach the end of the project. The result is an early finish time of 11 for ‘inspection’ and we conclude that the project can be completed in 11 working days if the indicated sequence is followed and the estimated activity durations are correct. If the network included more than one finish activity (that is, if another activity or activities could proceed concurrently with ‘inspection’), the project duration would be defined as the maximum of the early finishes for all finish activities.
Note carefully that an activity’s early start and finish times are the earliest the activity can start and finish, based on prior activities. Not all activities must start and finish at those times in order to complete the project in 11 days. The next set of calculations determines the latest an activity can occur without overrunning the target project completion time. First, we must designate a finish time for the project. The usual practice is to set the project duration, as determined by the early start and finish calculations (11 in the case of our sample project), as the target. We shall adopt this practice for our sample, although we could have used some other target, such as a contractually obligated completion time.
We perform a set of backward pass calculations to determine a latest start and latest finish time for each activity, beginning at the end of the project. Figure 5.10 includes the results of these calculations, with late starts and late finishes shown under the lower left and right hand corners, respectively, of each node. An activity’s late finish time is the latest the activity must finish in order not to overrun the target completion time. It equals the target project completion time if it is a finish activity; otherwise, the late finish is the earliest of the late starts for all of the activity’s immediate successors. It is the earliest late start time because this activity must be completed prior to the start of all successor activities. The late start time is the late finish time minus the activity’s duration. Thus,
LF = late finish time = target completion time for all ‘finish’ activities; otherwise = min (late starts of all immediate successors);
LS = late start time = LF – duration.
In Figure 5.10, we have assigned 11 as the late finish for ‘inspection’. Its late start is thus 11 – 1 = 10. ‘Remove pre-fabrication shop’ has only one immediate successor, so its late finish is 10, the late start for ‘inspection’, and its late start is 10 – 1 = 9. Because ‘pre-fabricate reinforcing steel’ has two immediate successors, its late finish is determined as EF = min (7, 9) = 7 and its late start = LS = 7 – 3 = 4. The process continues backwards to the beginning until late times have been calculated for all activities.
We observe in Figure 5.10 that the early start and late start times for some activities are identical, whereas for others, the late start time is greater than the early start time. The difference between the late start and early start is a measure of the activity’s criticality or of how ‘tight’ is it, schedule wise. We call this difference the activity’s slack, or float. For any activity, a formal definition is SL = slack = LS – ES. It can also be calculated as SL = LF – EF or as SL = LF – ES – duration. In practical terms, slack is the amount of time an activity can slip beyond its early times without causing an extension of the total project duration.
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If an activity has slack equal to 0, it is said to be critical. Critical activities cannot be allowed to slip beyond their early times with causing an overrun of the project’s target completion time, because as their slacks equal 0, their late start and finish times are equal to their early start and finish times, respectively. In Figure 5.10, the critical activities have been identified; note that they form a continuous path from the beginning to the end of the project. This path formed by ‘order and deliver reinforcing steel’, ‘pre-fabricate reinforcing steel’, ‘set reinforcing steel’, ‘place concrete’ and ‘inspection’ is called the critical path. These are the activities whose time dimensions must be supervised most closely; any slippage along this path without a concomitant shortening of some other activity on the same path will cause a slippage of the total project duration. Furthermore, if it is desired to shorten the total project duration, one must focus on one or more of the critical activities; shortening only a non-critical activity, by working overtime, assigning more workers or otherwise improving its completion rate, will not result in any reduction in total project duration. In our example, we could save a day in the project duration by arranging to procure the reinforcing steel in three days instead of four, assuming no other changes were made.
Figure 5.10 provides a helpful visual picture of the results of our schedule analysis. Another way to present the results is in tabular form, as shown in Table 5.1. Here we list each activity, with its description, duration, early and late start and finish and slack. A final column indicates whether the activity is critical, based on the value of its slack.
Slack is defined for individual activities, but it is important to understand that slack is not additive along a path. In Figure 5.10 and Table 5.1, ‘excavate’ and ‘place forms’ each have 3 days of slack. We must not conclude that this short subpath has a total of 6 days of slack. Recall that slack is the amount an activity can slip beyond its early times without extending the total project duration. If ‘excavate’ slips by 3 days, ‘place forms’ will be forced to take place between its late start and finish times and any further slippage will cause the project to overrun its target completion time.
A bar chart provides another useful means of displaying the outcome of a network schedule analysis. Figure 5.11 shows the five critical activities in black and the four activities with positive values of slack in grey. The dashed lines extending to the right from the non-critical bars are an effective means of displaying each activity’s slack. The right-hand end of the dashed line is located at the activity’s late finish time and the difference between the late finish and early finish, shown by the dashed line, is the slack.
Table 5.1 Activity table for footing construction project
Description Duration (days) Early start Early finish Late start Late finish Slack Critical? Excavate 1 0 1 3 4 3
Order and deliver reinforcing steel 4 0 4 0 4 0 ✓
Set up pre-fabrication shop 2 0 2 2 4 2
Place forms 3 1 4 4 7 3
Pre-fabricate reinforcing steel 3 4 7 4 7 0 ✓
Set reinforcing steel 2 7 9 7 9 0 ✓
Place concrete 1 9 10 9 10 0 ✓
Remove pre-fabrication shop 1 7 8 9 10 2
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144 The Management of Construction
Sometimes there is confusion surrounding the numbering system used to determine start and finish times; the bar chart may be a helpful means of clarifying the numbers. When we say the project begins at ‘time 0’, we mean the beginning of Day 1. On an early start–early finish basis, ‘set up pre-fabrication shop’, for example, begins at ‘time 0’, lasts 2 days and ends at ‘time 2’. We could also say that it begins at the beginning of Day 1 and ends at the end of Day 2, which coincides with the beginning of Day 3. The calculated start and finish times shown in Figure 5.10 and Table 5.1 are the ends of the indicated days. ‘Inspection’ must start at the end of Day 10 (which is the beginning of Day 11) and must finish at the end of Day 11.
Computer applications: a larger example
In Figure 5.7, we showed a work breakdown structure for a hypothetical bridge construction project. Although this WBS lacks all of the details that would normally be included in such a structure for a project of this magnitude, it is sufficiently detailed to apply the principles outlined above to the development of its schedule. Figure 5.7 shows 45 elements at the lowest levels of their respective branches; these elements form the basis of our schedule network. First, we assemble an activity-on-node network, as shown in Figure 5.12. The process of assembling this plan involves as many members of the project team as possible; the result is an excellent communication tool for explaining the intended sequence of activities. There is considerable value in such an exercise, even if it is not followed by the numerical scheduling analysis we discuss below.
Figure 5.12 deserves several observations. First, this plan is only one of several orders in which the 45 activities could be carried out. It represents the best efforts of the project team, based on the information available at the time it is developed. The plan shows, for example, that the foundation work will proceed from the north abutment to the south abutment and then to the pier. It is subject to modification as the planning process and the execution of the plan proceed. Second, the plan assumes that nine activities can begin concurrently at the beginning of the project. The drafter of the diagram has taken some liberties in placing some of these nodes (‘painting subcontract’, for example) toward the right of the diagram rather than at its extreme left, but the principle that a node without a predecessor node is a ‘begin’ node still applies. Third, in a few cases, we have violated the ‘left-to-right’ flow of work, in the interest of a reasonably compact diagram. Finally, the project will be complete when two activities, ‘move- out’ and ‘producer statement’, have been completed.
The next step is to assign durations to each activity and perform basic scheduling calculations. We show the results of these calculations in several ways, in output from Microsoft Project 2000®. First, Figure 5.13 shows a bar chart containing our 45 activities. Each activity is shown at its earliest times, beginning at its early start time and ending at its early finish time. Critical activities are shown in black (shown in red in Microsoft Project) and arrows show the various precedence relationships. We have assumed that the project will begin on 29 March 2004 and that work will be accomplished 5 days per week. Based on the estimated activity durations and the sequencing in Figure 5.12, the project will be completed on 26 November 2004.
Microsoft Project 2000® allows the assignment of lag times to the connectors between activities. A lag time is a non-work duration that must occur between activities. In our project, the curing of concrete must take place after it is placed and before the structure is loaded. Although not shown on the bar charts and network diagrams, we have assigned lag times after several concrete placement activities. In particular, after the ‘pier structure’ is completed, there is a 20-working day (= 28 calendar-day) lag before the ‘north girders’ can be placed. Figure 5.13
shows this 4-week gap in the schedule clearly and indicates that no work will be occurring on the project while the pier concrete cures. Perhaps some revision of the programme could lead to a more efficient sequencing of activities during this time period!
One interesting feature of our analysis software is the capability to include all elements of the work breakdown structure, in a hierarchical fashion as shown in Figure 5.14. In fact, Figure 5.13 is a subset of the activities in Figure 5.14. The 45 lowest level elements that are the work packages or activities in our network are shown in regular text and their bars on the chart are black or shaded depending on whether they are critical (shown in colour in Microsoft Project), identical to those in Figure 5.13. All other elements are summaries, exactly as depicted in our WBS; they appear in bold text and as hatched/bars on the chart. In total, there are 62 elements, not including the one element at the top that represents the total project, of which 17 are summary elements. Other
features of Figure 5.14 are the addition of an identification (ID) number and duration for each activity and the exclusion of connecting arrows from this version of the chart.
The duration of a summary activity may be confusing. This software considers a summary activity’s duration to be the total length of time between the start of the first activity in that summary’s branch and the completion of the last activity in the branch, even though there may be gaps when no work is taking place. An example is the summary for ‘pier’, which shows a 90-day duration. ‘Pier piling’ is scheduled to begin on 3 May 2004 and ‘pier structure’ is scheduled to be completed on 3 September 2004, 90 working days later. Note that the total