ACTIVITY ARROWS
In network diagramming, the symbol for an activity is an arrow. The arrow represents linear timeline movement from left to right, start to finish. The production continuity is the arrow moving from a preceding activity to a succeeding activity. Arrows in a velocity network diagram represent the activity itself, not the direction of movement. Neither the angle of slope nor the arrow’s length is a factor in the scheduling, simply the designer’s choice. Each arrow in the velocity network diagram represents either an independent activity or an interdependent activity. Its respective activity numbers iden- tifies each arrow.
In the example diagram in Fig. 5.1, the activity arrow designated (3–7) is ‘‘Install caissons.’’ The according tasks that will fulfill that activity, in their order of precedence, are as follows:
1. Accept winning bid and award contract. 2. Schedule municipal inspection.
3. Order and deliver reinforcing steel cages. 4. Lay out the exact location of the hole. 5. Excavate caisson.
6. Install rebar cages.
7. Connect cages to foundation continuous rebar. 8. Place concrete.
9. Strip forms. 10. Clean up site.
In Fig. 5.1 we see the sequential path that represents the job logic of the production. Although the activity (3–7)‘‘Install caissons’’ is in actuality the task of pouring concrete into the predrilled holes over the preinstalled rebar, the task is dependent on activities 1 through 7 having been completed before the concrete truck shows up on the job site. If any of those activities are incomplete or delayed, there will be a direct effect on activity 8. Thus we have established the critical path for this part of the network schedule.
DUMMY ARROWS
Dashed-line arrows in CPM diagramming are the symbols for dummy arrows, which are diagramming symbolism showing the constraint depen- dency between activities. Any dummy activity acting as a constraint is shown as a dashed line with zero elapsed time. The direction of the arrow shows the production order of activities, and a dummy arrow shows what activities constrain the start of another activity or activities.
FIGURE5.1 Job logic.
In Fig. 5.2, the dashed arrow (7–8) is a dummy arrow showing the constraint of (8–12), starting until both (6–7) and (6–8) have finished. There is no similar constraint upon activity (7–12), so it can start when (6–7) finishes. It is not dependent (constrained) on the completion of (6–8). It also shows that the CPM job logic must move forward from this activity. If two or more activities begin to run simultaneously, the computer reads only the same i–j number of both activities. So the project scheduler gives each activity its own i–j number for the computer to use as a relative cell address for that specific data, showing it on the network diagram as a dummy arrow.
In Fig. 5.3, five activities in this network diagram can start and finish at the same time and be completed in timelines parallel to one another. However, the computer reads only the same i–j number of (21–28) for all five activities, thereby making it impossible to separate the activities in the computer program. To overcome this lack of separation and control, the project scheduler uses dummy arrows to assign i–j numbers to each activity, thereby giving each activity its own computer cell address. The project scheduler who assigns different i–j numbers to any activities that are running in parallel also uses dummy arrows.
Fig. 5.3 shows how these five parallel activities can be run simulta- neously and can be further utilized in time management as parallel activities
FIGURE5.3 Parallel activities.
adding to total float. By the use of distinct i–j numbers assigned to each of the five activities, dummy arrows are used as shown in Fig. 5.4 to show the interdependent relationships. Now the five parallel activities shown in Fig. 5.3 retain the interdependency relationship of each activity to the other and are further identified by distinct i–j numbers. The computer program now identities them as activities (21–24), (21–22), (21–23), and (21–25), as seen in Fig. 5.4.
I –J NUMBERS
In CPM, events are the exact day an activity starts or finishes. They are also dates of milestone completions. Events are assigned identification numbers for computer processing. The starting event number is the i number, and the completion event is the j number. The i–j number is used as a relative cell address for recording the activity’s data. If CPM diagrams were to be prepared using random activity numbering, all activity numbers in the entire network would have to be renumbered to allow any new or changed activity to fit in a sequence with the other activities.
Therefore, it is a basic CPM requirement that, when event numbers are assigned, the finishing event number at the head of the arrow must be greater that the starting event number at the tail of the arrow, and the j-value of each activity must be greater than its i-value. A typical CPM network can involve hundreds of separate activities that must remain flexible in scheduling, so the experienced project scheduler assigns the activities i–j numbers only after the entire network has been completed and is ready for its first cooking or trial- run computation.
Using the vertical and horizontal axes of graph coordinates, i–j events can be displayed in either plane. The vertical numbering method is more widely used, which numbers all events in a vertical column in sequence from top to bottom that equates to a parallel timeline those groups of activities then moving from left to right. There is no significance to the event numbers themselves except as means of identifying activities, so if the CPM format of keeping the j-value of each activity greater than its i-value is used, blank cells can be left in the numbering system so that spare numbers are available for changes or additional work that may come up. Sequential i–j numbering pro- vides this flexibility in scheduling, while also providing the computer with program logic data for events and activities locations on the network diagram.
MILESTONES
Milestones are benchmarks of long-term and short-term progress events that require some reasonable progress in activities or tasks toward a desirable
outcome. Milestones are specific, time-limited objectives that, in combina- tion, are sufficient to achieve those progress goals. Milestones are placed in the schedule to produce
Motivation for project team and contractors Utilization of competitive advantages
Repair schedule of competitive disadvantages
Acceptable progress to the owner and project team if those milestones are met on time and within budget
Measurement of actual progress versus scheduled progress
At this stage of the process in installing milestones, the scheduler should be thinking in broad terms. As one studies particular areas of the schedule, one develops progress objectives that can be related as milestones. Milestones should reflect both strategic planning as well as current period objectives. They should also represent success, not the absence of failure or the reme- diation of existing problems. This is an important concept for the professional project scheduler to grasp and use in developing the schedule. Unscrewing a problem isn’t progress if the problem should not have happened, so mile- stones should mark progress only. Positive benchmarking is important; milestones should be specific and measurable objectives. They should also appear as projections of progress evaluations at the end of each construction phase. Interim milestones should measure phases of progress that are critical to meeting long-term project timing. They should ‘‘back down’’ from the specified completion date to the present in sequential order.
Once you have identified milestone phase areas, schedule dates for those events and the completion objectives that go with them. If you are scheduling with a group, such as the project team, it is important to agree upon the goals and objectives of each phase, leading to the establishment of milestones as benchmarks to evaluate the progress toward those goals and objectives. It is necessary to agree upon milestones prior to establishing phases, because milestones should lead the completion of each phase.
To reach CPM milestone events on time, it is necessary to back down to the present. If you are to reach the critical completion date, where must the project be in one month? In two months? Next quarter? To actually achieve your CPM milestones, it will be necessary to periodically re-evaluate start and finish events and use float to close gaps in timing. In planning the schedule, don’t spend unreasonable amounts of time on making‘‘perfect phases,’’ but instead create obtainable and realistic milestones by which you can measure the project’s progress.
The best planning process is to estimate durations based on what you know and on your company’s historical data. Include in the schedule periodic sorts, or summary reports, that will test the milestones objectives for the
coming quarter. This tactic will improve future milestone projections. Remember that the purpose of planning is to reduce risk. The best schedule plan is one that allows you to test your estimates before they cost lots of money. This is always your client’s perspective and should be yours as well. We schedulers do this by running‘‘what-if?’’ scenarios with varying activity early and late starts, and varying the activity early and late finishes. A test of the schedule’s quality is the extent to which completion events are balanced against float. Every project schedule needs to be built upon these basic criteria: 1. Each macroactivity step, defined into phases. This should be detailed enough to be measurable and give guidance to those who are responsible for managing that area of work.
2. The person responsible for seeing that the activity is completed. This is usually the prime contractor, the site supervisor, a project team member, or an activity subcontractor.
3. Activity cost in relationship to total budget. This should include time estimates and indirect, and direct costs. In the budget sort, a calculation needs to appear with this data to build a cost-tracking analysis.
4. Project phases deadlines. These should include the actual time available by the subcontractor responsible for the activity, including its assigned early and late start and finish events.
All four steps should be closely monitored up to and including project closeout. In larger and more sophisticated projects, this basic outline of plan elements will be more complex but will still follow these basics in a larger configuration. Time and cost estimates are made in greater detail for each activity.‘‘Event dependencies’’ are established, which must be accomplished before others can be begun. Resources that must be devoted to each are listed, then broken out from the total budget. Resources are then allocated with priority weighing, to ensure critical path activities are resource-covered first. Progress-checking milestones and specific sorts are built in to the procedure to ensure project schedule compliance.
JOB LOGIC
The logical sequence of the project’s construction activities, factored by local practical limitations, is referred to as job logic. The activities chosen may represent relatively large segments of the project or may be limited to only small steps. To use a previous example, a concrete slab may be a single activity on a small job, but on a larger job it will be broken into the separate steps necessary to construct it, such as excavation, sub-ex preparation, erection of forms, placing of steel, placing of concrete, finishing, curing, and stripping of
forms. As the separate activities are identified and defined, the sequence relationships between them must be determined (See Fig. 5.5). These relation- ships are referred to as job logic and consist of the necessary time durations and sequential order of typical local construction operations that are unique to your geographic area.
It is a basic fundamental in CPM that each activity must have a de- termined starting event, which may be either its own start or the finish of the preceding activity. Activity durations cannot overlap their finish events. Therefore, job logic is established to provide operations sequences within practical constraints. Established job logic is then used to build program logic within the computerized CPM program. By determining the job logic, activities can have their interdependencies critically examined during all phases of the schedule, before errors occur costing delays and money.
LOGIC LOOPS
The logic loop is a paradox in network planning. It indicates that a critical activity must be followed by another critical activity that has already been completed. Even as I read that last sentence I realize it doesn’t make any sense, but bear with me and I’ll try to explain. The term‘‘logic loop’’ is really an oxymoron, since a logic loop is anything but logical. Logic loops should be called illogic loops, but again, we professionals like to keep our industry jargon as confusing as possible. If, in our network schedule, one arrow was inadvertently connected to the wrong node, its path might well be shown to the computer to run backward. Although this seems obvious in a simple, single-path CPM schedule, if we multiplied the paths by hundreds of activities such as in large commercial or industrial network diagrams, logic loops can be easily overlooked in the planning stage.
In the vertical method of notating event nodes, which is more widely used, numbers of all events are in a vertical column in sequence from top to bottom, which equates to a parallel timeline. Because of the vertical config-
uration, activity job logic can have logic loops in those vertical groups of activities without the scheduler realizing that they are there, the error then moving from left to right on the timeline with the activity group.
I advise you to study the network diagram carefully at the beginning of the development of the schedule to confirm the job logic of the structure and to search carefully for logic loops. The best method to safeguard against them is to use sequential i–j numbering. The computer sort printout cannot indicate any clues to the presence of logic loops under the use of a random i–j numbering system, so random numbering guarantees a greater likelihood of error by allowing logical loops to remain undiscovered. Accordingly, to make ultimate use of computer program logic—the database—which in this case is the i–j numbers, we must number the activities sequentially.
PROGRAM LOGIC
Program logic can best be described as the way the computer puts together the time sequence for the activities involved in the project. The program logic for the sequence of operations in our example of Fig. 5.5, would be based on the following job logic:
This is the type of data strategy that the project scheduler decides initially, and then the project team approves in the planning stage. For the purposes of CPM, job logic requires that each of the activities in the network a definite event to mark its starting point, and another to mark its completion point. This event may be either the start of the project or the completion of preceding activities.
It is a basic tenet of CPM that the finish of one critical activity cannot overlap the start of a succeeding critical activity. When this happens, the work
Activity Sequence Symbol I–J #
Accept winning bid and award contract 1 BC 1
Schedule municipal inspection 2 MI 2
Order and deliver reinforcing steel cages 2 OD 3
Layout the exact location of the hole 2 LC 4
Excavate caisson 3 EC 5
Install rebar cages 4 IR 6
Connect cages to foundation rebar 4 CR 7
Place concrete 5 PC 8
Strip forms 6 SF 9
must be further subdivided into more detail. It is a fundamental rule of CPM that a critical activity cannot start until all those critical activities preceding it have been completed.
LOGIC-BASED SCHEDULING
Now we’ll take all of the previous elements and combine them into an example that will illustrate logic-based scheduling. Examine the basic layout of a small commercial project’s logic-based schedule, as shown in Fig. 5.6. Because all phases have similar traits but different activities, we will examine only one phase of the schedule. The foundation’s phase activities, in their job logic, include all subactivities up to and including installing the building’s founda- tion (see Figure for numbers 11–22).
11. Demolish existing structure 12. Remove existing parking lot 13. Survey and set engineering stations
14. Lay out footings, caissons, building envelope 15. Dig footings 16. Drill caissons 17. Install utilities 18. Form work 19. Set rebar 20. Install cages 23. Pour concrete 22. Strip forms
The foundation phase begins as soon as the site development phase finishes with the demolition activity, which can be done as the last part of the site development or the first part of the foundation clearing, thereby having
free float that the scheduler can use to either constrain or accelerate the activity event. The phase begins with demolition of the existing building and removal of the old parking lot. These events run in series because the same subcontractor can do them simultaneously. Activities (17) and (14) can run in parallel, as layout can be done right behind the surveyors. Activities (15) and (18) run in parallel, because the same subcontractor can do them at the same time. However, activities (14) through (21) are in series because each requires the completion of the preceding activity.
Each activity has subtasks within it that require sequential completion. Subtasks within (19) Set rebar, for example, include order and fabrication of the specified reinforcement steel, delivery, and placement of that steel. (20) Install cages would also have a final subtask of pre-pour rebar placement inspection by the municipal inspector before (21) Pour concrete could be done (usually the next day). Each activity’s duration is given in events and time- scaled in working days.
The noncritical path for the foundation phase lies through activities 13, 17, 18, and 19. The critical path lies through activities 10–16, 20, 21, and 22. To decrease total phase duration in our network scheduling, we seek ways to shorten the critical path activities’ durations. If we could shorten the path through the Footings activity by more than seven days, the critical path would shift to the Form work path. If we could shorten the path through the Form work by 3 days, we would have two critical paths of (15) Footings and (18) Form work running in parallel duration of 10 days.
In network scheduling, when activities are combined in a network in which one activity shares a dependency on a processor activity with another activity, a parallel arrow is introduced into the network, as illustrated in Fig. 5.6, to show the interdependency relationship, as in the case of activities (17– 19) and (19–24) to the critical path activities (13–21) and (21–24). A dummy arrow along either path, or subpaths, would indicate a constraint on that ac- tivity by a predecessor on that path. A dummy arrow representing a constraint differs from an activity arrow in that it does not represent time, only activity event dependency. All other arrows represent both time and dependency.
To illustrate the timescale difference between paths 1, 2, and 3, activity