The critical path method (CPM) tool is a network diagram technique for analyzing, plan- ning, and scheduling projects. It provides a means of representing project activities as nodes (see Figure 6.3) or arrows, determining which of them are “critical” in their impact on project completion time, and scheduling them in order to meet a target date at a minimum cost.7
Originally developed for use in large, complex, and cross-functional projects, the CPM tool is now employed in smaller projects as well. Having a CPM schedule helps the project manager to see the total completion time, understand the sequencing of activ- ities, ensure that resources are available when needed, monitor those that are critical, and measure progress.
THE CRITICAL PATH METHOD DIAGRAM 155
a
d b
e f c
g h
Activity Description Duration
(days) Immediate
Predecessor Project Kick‐ off
Get materials for a
Get materials for b Manufacture a Manufacture b Customize a
Release Assemble a & b
b,c b,c
d,f a
a
e
g
0 10
20 30 20 40 20 0 a
b
c d e f g h
Start Finish
Figure 6.3: Example Critical Path Method Diagram
Constructing a CPM Diagram
Constructing a CPM diagram is an exercise in patience and discipline that involves pro- ceeding through several major steps. In it, as with all schedule development tools, a crucial step is to determine the level of detail and to identify activities. Although this step usually belongs to the scope planning process, we include it here because it helps explain the tool development in an integrated way.
The process of building a CPM schedule is destined to produce a better product if quality information about scope, responsibilities, resources, and the overall schedule management system is available.
Project scope provides schedulers with the knowledge of the project activities that need to be scheduled. Clear definition of responsibilities—who does what in the project—points to who has the best information about the individual activities and should therefore schedule them. To develop realistic schedules, these “owners” of the activities also need to know which resources are available and when. Finally, the schedule management system will direct schedulers in developing and using the CPM.
Determine the Level of Detail and Identify Activities
How can large or small individual activities influence the number of activities in the CPM?
A rule at one company may help clarify this point. Large-fab construction projects run at around 2,000 activities, lasting from two to four weeks. This helps everyone realize what level of detail is acceptable and what is unacceptable. The goal for scheduling is to account for the complexity and size of the project in a way that gives the team
enough information—not too little and not too much—to direct the daily work, identify interfaces between workgroups, and monitor progress at an effective level (see “Why a Team Approach to CPM Development?”).
When the level of detail is set, you are ready to perform the following activities:
1. Brainstorm and identify activities that are necessary to complete in order to finish the project. This can be done by means of the WBS, perhaps the most systematic and integrated way of activity identification (see the Work Breakdown Structure section in Chapter 5).
2. Refocus the attention on the established level of detail. If the number of activities is lower than the intended number, continue breaking down larger activities. If the number of activities is over the target number, combine related activities to reach the desired detail.
Why a Team Approach to CPM Development?
Using a project team to build a CPM diagram is perhaps the most effective way of doing it. Here is why:
■ Team members are usually the best source of knowledge about their piece of the schedule.
■ Each team member can see where and why he or she is critical to the suc- cess of the project.
■ The team can find creative ways to best sequence and shorten the duration of activities and the total project.
■ As a unit, the team can focus its energy and mind on mission-critical activities.
■ Involvement of team members enhances commitment and a sense of ownership of the project.
Sequence Activities
Sequencing is about identifying dependencies between activities by determining an activity’s immediate prerequisite activities, calledpredecessors. A portion of the depen- dencies will be arranged in pure “technological order.” These are termedhardorlogi- caldependencies, meaning that the technology of work mandates such sequence. An example is that one must write the code before testing it; the other way around is not possible. Disregarding hard dependencies may lead to rework and project delay. But not all of the dependencies are hard; some of them are soft or preferential. They are not required by the work logic but set by choice, reflecting one’s experience and preferences in scheduling. For example, we may decide to write a piece of software code, test it, write another piece, test it, and so forth. Dependencies may also be dictated by availability of key resources. If two activities require the same resources, one will have to follow the
THE CRITICAL PATH METHOD DIAGRAM 157 other. Once the dependencies are established, they can be recorded, as we have done in Figure 6.3.
Assign Resources and Estimate Activity Duration
The age-old rule of scheduling is that people and material resources get the work done. As a result, it is logical to estimate an activity’s duration by identifying resources necessary to successfully complete it. Consider, for example, 100 hours of work from a business analyst. This is the work (effort) time, which in the case of mature work technologies is calculated by dividing the amount of work by the production norms.8 With the information that the analyst splits her work time between this and three more projects, and knowing the company’s work calendar (50 hours per week only; no work on Saturdays and Sundays), she may need eight weeks to get it done.
This is the calendar time. Write the calendar time in the fourth column of the table in Figure 6.3.
Draft a CPM Diagram
Each activity is drawn on the network diagram as a circle or rectangle, with identifying symbols and duration within the circle or per convention chosen. This format is called AON (activity-on-node). Later in this chapter, we discuss another format of drawing net- work diagrams, AOA (activity-on-arrow). To pursue the AON format, indicate sequence dependencies by arrows connecting each circle (activity) with its immediate successors, with arrows pointing to the latter. For convenience, connect all circles without predeces- sors into a circle denoted “Start.” Similarly, connect all circles without successors into a circle marked “Finish.”
Identify the Critical Path
Normally, the diagram shows a number of different paths from Start to Finish, defined as sequences of dependent activities. To calculate the time to pass through a path, add up the times for all activities in the path. The critical path is the longest path (in time) from Start to Finish. It indicates the minimum time necessary to complete the entire project. Essentially, the critical path is the bottleneck route, and the highest priority set of activities to manage.
There is another way to calculate the critical path: using the forward/backward pass procedure.9 While adding up activity times is simpler for smaller projects, it is too cumbersome and difficult for larger projects. Rather, the large projects use the pass procedure. Say, for example, you have the start date for a project. Then, for each activity there exists an earliest start time (ES). Assuming that the time to finish the activity ist, then its earliest finish time (EF) is ES+t. Figure 6.4 shows how to go through the forward pass to calculate ES and EF for each activity. The process, from left to right, is as follows:
■ ES is the largest (or latest) EF of any immediate predecessors.
■ EF is ES+time to complete the activity (t).
c, 10
b, 5
e, 10 f, 20
g, 10 h, 0
d, 15 a, 0
10 0
10 0
20 10
20 10
40 20
40 20
50 40
50 40
50 50
50 50
25 10
40 25 0 5
10 5 10
0 10 0
Key
Activity Name a, 0
Activity Duration
Critical
Path 2040
40 20 Early Start (ES)
Late Start (LS)
Early Finish (EF) Late Finish (LF) Backward Pass: Right to Left
Determine Late Finish & Late Start Forward Pass: Left to Right
Determine Early Start & Early Finish
Figure 6.4: Forward and Backward Pass
Suppose now that you want to finish the project by the time that is equal to the EF for the project. If so, you can define the concept of late finish (LF), or the latest time that the project can be finished, without delaying the total project beyond EF. Thus, LF is equal to EF.
Similarly, you can define late start (LS) as LF−t, wheretis the activity time. Building on these concepts, we can go through the backward pass, from right to left, to calculate for each activity (see Figure 6.4):
■ LF is the smallest (or earliest) LS of any of immediate successors.
■ LS is LF – Time to complete the activity (t).
Now that the forward/backward pass is finished, note that Figure 6.4 indicates that in some activities, early start is equal to late start, while in some it is not. The difference between an activity’s early and late start (or between early and late finish) is calledtotal float. Total float is the maximum amount of time you can delay an activity beyond its early start without delaying the project completion time.Free floatis another kind of float equal to the amount of time you can delay an activity without delaying the early start of any activity immediately following it. While an activity with the positive total float may or may not have free float, the latter never exceeds the former. The formula to calculate free float is the difference between the activity’s EF and the earliest of the ES of all of its immediate successors.
THE CRITICAL PATH METHOD DIAGRAM 159
In our example in Figure 6.4, activitiesbanddhave free float of 5 days and 15, respec- tively, while all other activities have zero free float. Activities on the critical path have zero total float and are calledcritical activities. They are shown in Figure 6.4, with thick arrows connecting critical activities on the only critical path. It is, however, legitimate to have multiple critical paths, a common situation in fast-tracking projects.
An activity with zero total float has a fixed scheduled start time, meaning that ES=LS.
Consequently, to delay the start time is to delay the whole project, which is why such activities are calledcritical.
In contrast, activities with positive total float offer some flexibility. For example, we can relieve peak loads in a project by shifting activities on the peak days to their late starts. That won’t impact project completion time. But this flexibility may vanish quickly. Consider a path with a very small total float, which we callnear-critical path,the second-highest priority to pay attention to. If we let an activity on the near-critical path slip, its small total float may be gone and it becomes critical path. In case of the free float, we can delay the activity start by an amount equal to (or less than) the free float without affecting the start times or float of succeeding activities.
Review and Refine
Look closely at the drafted diagram and ask the following questions:
■ Has any important activity been left out of the schedule?
■ Is the activity sequencing logical?
■ Are durations of activities reasonable?
■ Is the project schedule time-constrained or resource-constrained? (See “Time- or Resource-Constrained? Or Both?”)
Time- or Resource-Constrained? Or Both?
Although Intel is in a constant time-to-market race with its competition, project managers in one of its divisions understand the relationship between time and resources when developing their schedules. The problem is that no matter how fast they want to complete their projects, the availability of resources is limited.
This helps classify schedules into two categories:10
1. Schedules under a time-constrained situation. The project must be fin- ished by a certain time (called the drop-dead date in Intel language), with as few resources as possible. Here, it is time, not resources, that is critical.
These are typically the highest priority projects.
2. Schedules under a resource-constrained situation. The project must be finished as fast as possible without exceeding a certain resource limit.
Here, it is resources, not time, that is critical. Projects like these are usu- ally of lower priority.
(continued)
Between these two extremes are resource-leveling projects with their medium priority. With these, once a schedule is developed, project tasks are shifted within their float allowances to provide smoother period-by-period resource utilization. As long as management clearly communicates in which category each project is, project managers face no problem—most commer- cially available software they use already have algorithms to develop schedules for any of the three situations. The trouble arrives when project managers are told their projects are time-constrained but with limited and insufficient resources. Faced with such systems constraints, they know they have to find resources on their own. So what do project managers do? They make do.
They utilize overtime, work long hours, convince team members to do the same, and navigate their way through. Most of the time they succeed. After all, Intel’s culture is all about performance.
This is the time to answer the questions and, if the answers require, to make neces- sary corrections.
If a company competes on time, a project manager must check if it is possible to reduce the project duration. The only avenue to do that is to find ways to shorten activities along the critical path. This is possible by fast tracking, or schedule crash- ing, or a combination of the two approaches.11 Note that fast-tracking or crashing noncritical activities is irrelevant, because it does not reduce the duration of the critical path. Fast-tracking means changing the hard and soft dependencies—in other words, changing the logic of the diagram by obliterating previously established dependencies and creating new ones by attempting to overlap certain activities on the critical path. In the process, neither activity durations nor resource allocations will be changed.
“Crashing” means shortening the duration of activities along the critical path with- out changing dependencies. The way to do this is by assigning more people to the activities, working overtime, using different equipment, and so on. The crucial question is whether the gains from the reduction of project duration exceed the costs of acceler- ation. For the majority of time-to-market projects the answer to the question is yes. For more details, see the Schedule Crashing section in Chapter 12.
Using the CPM Diagram
The CPM tool was originally developed for large, complex, and cross-functional projects.
This is still the primary use of CPM diagrams because it can easily deal with a large number of activities and their dependencies, directing our attention to the most criti- cal activities. However, with the dissemination of CPM knowledge, it is not unusual to also see CPM used for smaller projects.
A fine application of CPM can be found in conjunction with the Gantt chart. In short, extracting from the sizable CPM diagram activities due in the next one or two weeks, pre- senting them in the Gantt chart format, provides clear and practical partial short-term outlook schedules.
THE CRITICAL PATH METHOD DIAGRAM 161
Benefits
Having a CPM diagram helps the project manager to see the total completion time, understand the sequencing of activities, ensure resources when necessary, monitor those that are critical, and measure progress (or lack of it). This is easier to accomplish if certain rules are followed (see Tips for CPM Diagrams under “Three Don’ts for CPM Diagrams”).
The CPM diagram also offers the project manager value through its graphical struc- ture. The CPM diagram is easily explainable by means of the project network diagram that clearly charts the technological order of work. Data calculations are not difficult and can be handled readily and quickly by personal computers.
The greatest benefit to the project manager is arguably the focus on priority that the CPM diagram provides. It pinpoints attention on the small group of activities that are critical to successful project schedule completion. This focus greatly adds to higher accuracy and, later, precision of schedule control.
Three Don’ts for CPM Diagrams
1. Don’t let the CPM chart control you. It is just a schedule and won’t make a decision for you. You will.
2. Don’t consider it gospel. If there is a better way to schedule, go for it!
3. Don’t throw it aside when your project starts slipping. Review it, update, and improve, then use it again!
Tips for CPM Diagrams
■ If you need to accelerate the schedule, do it by fast-tracking and crashing.
■ Watch out! Accelerating the schedule may increase the number of critical activities. While in earlier times 10 percent of all activities were critical, in today’s fast schedules, you often see 40 percent to 50 percent of activities being critical.
■ Sprinkle major milestones over your CPM diagram. It helps you see the for- est (milestones) and the trees (activities).
■ Color-code activities performed by various resource providers in order to identify their interfaces and provide their coordination.
Variations
The CPM diagram discussed here is of the AON format. Other formats include CPM with AOA, Program Evaluation and Review Technique (PERT), and precedence diagrams. In AOA, activities are shown as arrows, and the arrows are connected by circles (or dots) that indicate sequence dependencies. In that way, all immediate predecessors of an activity lead to a circle at the beginning point of the activity arrow, while all immediate succes- sors stem from the circle at the arrowhead. Thus, a circle becomes an event, where all activities leading to the circle are completed.
The CPM diagram is very similar to the PERT diagram, but while CPM’s activity dura- tion estimate is deterministic, PERT uses a weighted average to calculate expected time of activity duration as follows:12
TE= (a+4m+b)∕6 where
a = optimistic time estimate b = pessimistic time estimate m = most likely time estimate
The PERT diagram has been used primarily in research and development projects, while CPM, which was originally developed for construction projects, has spread across other industries.
The precedence diagram is an AON network that allows for leads and lags between two activities (see the Time-Scaled Diagram section in this chapter for more details on leads and lags). This makes it easier to portray rich and complex dependencies for real-world projects, giving the precedence diagram a wider application across industries and an edge over the CPM and the PERT. These two methods allow for leads and lags only by splitting activities into subactivities, leading eventually to a significant increase in the number of activities in the network, and making it more complex and difficult to manage.