The most common type of network schedule in use today is the precedence diagram. Because of the popularity of prece-dence diagrams as opposed to arrow diagrams, this text is focused primarily on the use of precedence diagrams (arrow diagrams are discussed in Chapter 16). Also, most schedul-ing software in use today requires the user to input the infor-mation in the form of a precedence diagram. In precedence diagrams, activities are represented by nodes. The nodes are linked by lines that show the relationships that exist between the activities. The basic elements can be described as follows:
Nodes: These represent “Activities” and may be drawn in any desired shape. Often they are drawn as circles, boxes, or other common geometric shapes (see Figure 3.1). While the diagram presents only basic information about the construction of a pole barn, the logic should be apparent. The diagram is read from left to right, and the link lines show clear dependencies between the various activities.
Lines: Lines represent “Activity links,” which are used to represent the dependencies between activities. Links are interpreted from left to right to indicate the dependency relationship. There is one link in the network to denote each dependency between an activity and one of its immediately preceding activities (IPAs).
The precedence diagram consists of a series of nodes with lines (links) connecting them to illustrate the activities to be executed and the sequence in which they must be done.
The normal convention in the use of the precedence tech-nique is that an activity can be started after all links drawn to its left (starting) side have been “traversed.” This occurs when each of an activity’s predecessors has been completed.
After the activity is completed, all links leaving from its right-hand (finish) side can be traversed. Most of the discus-sion on the use of precedence diagrams will assume that all
C H A P T E R T H R E E
24 CHAPTER THREE
FIGURE 3.1 Precedence Diagram of a Simple Pole Barn.
Strip
FIGURE 3.3 A Finish-to-Start Relationship with a 28-Day Delay.
be hung. Similarly, footing excavation must be completed prior to placing concrete for the footing. For many activity relationships, this assumption is accurate or adequate. For manual computations on networks, this assumption is essentially necessary. While this finish-to-start relationship between activities is generally viable, these other types of relationships are also encountered. In various instances, the finish-to-start relationship is convenient for illustration purposes, but it may not be an accurate portrayal of the actual relationship that exists between two variables.
Examples of these other types of relationships will be described briefly.
A series of examples have been developed to show how different relationships might be encountered in a project schedule. The actual site conditions must be evaluated in virtually every instance to determine the appropriate relationship between any two activities. In some instances there will be more than one way to portray the activity rela-tionships. Consider the simple series of tasks that involve placing concrete in forms, curing the concrete, and stripping the forms, shown in Figure 3.2. These activities and their durations are shown with the traditional finish-to-start relationship.
At first glance, this sequence seems quite logical. The activity “Cure concrete” is typically one that does not entail the use of resources, other than time itself. With only time being consumed, the use of the activity “Cure concrete” is simply a means of putting a delay activity between placing the concrete and stripping the forms. These activities (placing concrete and stripping forms) might also be shown as being related by finish-to-start with a delay. Note that the start of stripping forms depends on the completion of the place-ment of the concrete followed by a designated delay. This is shown in Figure 3.3. Rather than creating the delay as a separate activity, it is made a component of the finish-to-start
relationship; namely, the concrete forms can be stripped 28 days after the concrete has been placed. The logic remains the same, but the presentation of the relationship is slightly modified.
While manual computations would be cumbersome with this type of delay, many scheduling software programs now have the capabilities of handling such situations with ease. Other types of relationships occasionally encoun-tered in construction may also be readily handled by such programs.
One type of relationship that might be encountered on occasion is the finish-to-finish relationship, in which two activities are related by the fact that they must both be com-pleted at the same time. Assume a simple task of setting a flagpole. The task will consist of digging a hole for the pole, setting the pole in the hole, positioning the pole in the hole, and backfilling the hole with the excavated materials. Note that the pole must be held in position until the backfilling is completed. Thus, the backfilling task and the positioning the pole task will be finished at the same time, as shown in Figure 3.4.
Consider a portion of a building construction project in which masonry work is performed on the exterior of the building. A few windows are also to be included in the
Strip
FIGURE 3.2 A Typical Sequence of Finish-to-Start Relationships.
FIGURE 3.4 Simple Task Showing the Finish-to-Finish Relationship.
Precedence Diagrams 25
Masonry work around
windows
Install windows
Install exterior
trim Construct
brick facade
FIGURE 3.5 Sequence of Finish-to-Start Relationship for Window Installation.
exterior walls of the building. When windows are installed in the masonry walls, additional masonry work must be performed around the window frames to complete the installation. In a conventional finish-to-start relationship, this would be depicted as shown in Figure 3.5. Essentially, the bricklaying activity is broken into two distinct activities in order to demonstrate the need to delay some bricklaying work until after the windows have been installed.
These activities may be reasonably close to describing the actual work sequence. The level of detail of the activity “Masonry work around windows” may not be consistent with the more general descriptions used for the other activities. While this may be suitable for most schedulers, consideration might be given to describing the activities as a finish-to-finish with a delay relationship.
This might be accomplished with the representation shown in Figure 3.6.
Note that the “Install windows” activity is now associ-ated with the finish of the “Construct brick facade” activity.
The exterior trim work cannot begin until both of these activities are completed, but there is an added stipulation that the window installation must be completed a certain amount of time before the brickwork is completed. It is during this delay period that the necessary masonry work around the windows would take place.
In Figure 3.7, the network shows where a series of activities have finish-to-finish with a delay relationships. The removal of the old paint must be completed 1 day prior to the completion of the activity involving sanding and prep-ping the wood. In addition, the wood sanding and prepprep-ping must be completed 2 days prior to the completion of the painting activity.
The start-to-start relationship is another type of activity relationship that is encountered during construction opera-tions. Let’s consider the task of putting in a new tile floor in the foyer of a commercial building. Some of the activities to accomplish this are shown in Figure 3.8. In this example, one key activity is to spread grout on the floor to receive the tiles, and the other activity of interest is to set the floor tiles.
Because of the short set time of the grout, there is essentially no delay between applying the grout and setting the tiles;
that is, tiles must be set in the fresh grout. While the tile-setting task must wait a few moments for the grout to be initially applied, for all practical purposes, they must begin at the same time.
Another relationship that occurs in construction is the start-to-start with a delay. First, consider the construction of a simple stud wall that will receive insulation and dry-wall (for simplicity, it is assumed there is no plumbing or electrical wiring in the walls). Suppose several rooms are
Install windows
Install exterior
trim Construct
brick facade
FF with delay
FIGURE 3.6 Sequence of Finish-to-Finish with a Delay Relationship.
Sand and prep
wood
Paint wood Erect
Move in
FF/1 FF/2
Remove old paint
Inspect work
Disassemble scaffolding
Move out
FIGURE 3.7 Activities with Finish-to-Finish with a Delay Relationships.
26 CHAPTER THREE
Set tile flooring
Clean up floor area Clear
debris from floor surface Remove
old floor covering
SS
Spread grout
FIGURE 3.8 Activities with a Start-to-Start Relationship.
Install drywall Begin wall
insulation Construct
stud wall
Complete wall insulation
FIGURE 3.9 Sequence of Finish-to-Start Relationship for Wall Construction.
being constructed for an office building. The conventional finish-to-start relationship might show the activities as in Figure 3.9.
These activities show that the insulation must be started before the drywall installation can begin. However, once the insulation work has begun, the drywall installa-tion can also begin. Note that it is assumed that the insulation installation requires considerably less time than the drywall installation. That is, once the insulation work begins, it is assumed that this work will easily outpace or stay ahead of the drywall installation. The above logic might also be presented as a start-to-start with a delay as depicted in Figure 3.10.
With this depiction, it can be seen that the drywall installation can begin a stipulated amount of time after the wall insulation has begun. Since several offices are being constructed, it is assumed that after the insulation is installed in the walls of one office the drywall can be installed. The specifics of the particular offices involved are not shown in the schedule, as this might be regarded as needless detail.
Figure 3.11 shows the activities of a simple painting project of erecting scaffolding, removing old paint, prepar-ing wood for repaintprepar-ing, paintprepar-ing wood, inspectprepar-ing the work, and disassembling the scaffolding. The three activities of primary interest are removing the old paint, preparing
the wood for repainting, and painting the wood. There is a start-to-start relationship with a 1-day delay between removing the old paint and preparing the wood for repaint-ing. There is also a start-to-start relationship with a 2-day delay between preparing the wood for repainting and paint-ing the wood.
The information in Figure 3.11 might be shown in yet another manner. Figure 3.12 shows these same activities, but with their relationships shown as combinations of both start-to-start (SS) and finish-to-finish (FF) relationships, perhaps the most realistic portrayal of the actual relation-ships between these activities. While quite realistic, this is not a very common way of actually presenting these activity relationships. Activities that have SS and FF relationships must be carefully paced in order that all criteria can be satis-fied. Some computer software programs can recognize all of these relationships, although showing a combination of SS relationships and FF relationships for the same two activities is not as common in the available software. In this example, the start-to-start relationship might be preferred if the three activities in question have progressively longer activity dura-tions. On the other hand, the finish-to-finish relationship might be preferred if the successive activities normally have shorter durations.
Another type of relationship that might exist is the start-to-finish sequence. At first, this type of relationship might appear to be illogical or even irrational. However, there are numerous situations for which the start-to-finish (typically with a delay) relationship is appropriate to illustrate
Install drywall Install
wall insulation
SS with delay Construct
stud wall
FIGURE 3.10 Sequence of Start-to-Start with a Delay Relationship.
Precedence Diagrams 27
the relationships between different activities. In reality, this is actually a fairly common relationship that exists between many activities. A few of these types of relationships will be shown to demonstrate how common they really are. Con-sider the traditional finish-to-start relationships depicted in Figure 3.13. From this information, it is evident that the concrete forms are set prior to tying the reinforcing steel and that the concrete is placed after the rebar has been tied and the concrete has been ordered from the supplier. This information may appear to be logical, but it is not entirely accurate. For example, the ordering of the concrete is not dependent on setting the concrete forms.
A more realistic portrayal of the information would be created if the start-to-finish relationship with a delay was
used, as shown in Figure 3.14. It is assumed that the local crete supplier has stipulated that orders for ready-mix con-crete should be made at least 5 days prior to the day the concrete is to be delivered. That is, the concrete placement will start 5 days after the concrete has been ordered. Between the ordering of the concrete and the concrete placement activities is a finish-to-start with a delay. It should be apparent that the concrete order should be placed prior to the concrete place-ment, but one might be tempted to order the concrete after the rebar has been tied. Note that this might delay the actual concrete placement due to the 5-day lag between ordering the concrete and having the concrete delivered.
Of the different types of relationships, perhaps the least used in the past was the start-to-finish relationship.
Sand and prep
wood
Paint wood Erect
scaffolding Move in
SS/1
SS/2 Remove
old paint
Inspect work
Disassemble scaffolding
Move out
FIGURE 3.11 Activities with Start-to-Start with a Delay Relationships.
Sand and prep wood
Paint wood Remove
old paint
Inspect work
Disassemble scaffolding
Move Erect out
1
1
2
2 Move
in
FIGURE 3.12 Activities with Start-to-Start and Finish-to-Finish Relationships.
Tie rebar
Order concrete from supplier
Place concrete
in forms Set
concrete forms
FIGURE 3.13 Sequence of Finish-to-Start Relationship for Concrete Placement.
Tie rebar
Order concrete from supplier
Place concrete
in forms
SF/ 5 Set
concrete forms
FIGURE 3.14 Sequence of Start-to-Finish with a Delay Relationship for Concrete Placement.
28 CHAPTER THREE
Consider the start-to-finish relationships shown in Figure 3.15.
These SF relationships are shown with delays, but similar examples could just as well exist without delays. For exam-ple, the purchase of materials that require no lead time would be typical SF relationships without delays. Training could be shown as an SF relationship without a delay, but this would give the training personnel no flexibility in sched-uling the training session.
By examining the examples in Figure 3.15, it should be apparent that a distinct difference exists in the start-to-finish relationships than in the other types of relationships.
One apparent difference is that the activity that must be finished first is generally not associated with any other activity in the network; that is, the essence of the relation-ship is that the activity is linked specifically to one activity.
In Figure 3.15 (a), the example shows that setting the pre-fabricated trusses can start after the trusses have been ordered 45 days earlier. This lag will ensure that the truss manufacturer has the necessary time to fabricate the trusses, assuming that 45 days is the stipulated lead time. In Figure 3.15 (b), concrete rebar is inspected, but only after the inspection has been requested 3 days earlier. In this case,
inspectors are not on-site every day, and they will conduct an inspection only when they are given 3 days’ advance notice. Naturally, the request for the inspection is not directly linked to any other activity, so the start-to-finish relationship is appropriate. This figure also shows that the concrete placement can start 7 days after the concrete deliv-ery has been requested. It is common for concrete deliveries to be scheduled in advance. In this instance, a 7-day advance notice of the delivery is required. It should be understand-able why the placing of the order for the concrete is not directly linked to the satisfactory inspection but rather to the placement of the concrete. Figure 3.15 (c) shows that scaffold erection can begin 10 days after the necessary scaf-fold erection training has been completed. In this instance, the 10 days may not be a necessary requirement, but this might allow the company sufficient time to schedule the training with its own personnel.
There may be numerous activities on a single project that involve the purchase of materials. If they are included in a precedence diagram, they might be best presented in the form of a start-to-finish with a delay. Figure 3.16 demon-strates how several different start-to-finish relationships
Set prefabricated
trusses
Place order for trusses
Install roof deck
SF/(–45)
(a) Start-to-finish with delay relationship for long lead-time purchases Complete
stud wall construction
(b) Start-to-finish relationship for requested inspections and for specific delivery times Inspect rebar
and forms
Call for a form inspection
Place order for concrete
Place concrete
SF/(–3) SF/(–7)
Tie rebar and set concrete
forms
(c) Start-to-finish relationship involving training Erect scaffolding
Conduct scaffolding
training
Lay masonry
wall
SF/(–10) Place
concrete slab
FIGURE 3.15 Examples Demonstrating the Use of Start-to-Finish with a Delay Relationships.
Precedence Diagrams 29
FIGURE 3.16 Sequence of Start-to-Finish with a Delay Relationship for Vault Work.
might be encountered in a single network. Note that, before the layout work will be done in the vault, a training session will be held on confined space entry work. Prior to the deliv-ery and installation of the equipment, the equipment must be ordered, possibly with a long lead time. Finally, before the vault area is inspected, the inspection must be scheduled, typically with a few days’ advance notice.
The finish-to-start with a delay, finish-to-finish with a delay, start-to-start with a delay, and start-to-finish with a delay are commonplace in computer programs. While no manual approaches will be presented for computing infor-mation for such relationships, popular computer programs have little difficulty performing this task.