In this blog post, we’ll explore the concept of CPM (Critical Path Method)—a schedule management technique widely used in the construction industry—as well as how to create a schedule chart, the principles of forward and backward scheduling, the meaning of the critical path, and practical applications through examples.

The Importance of Schedule Management

In the construction industry, adhering to and shortening the construction schedule (the period during which construction is carried out) is of utmost importance. The construction schedule is directly linked to a construction company’s profitability, and its importance grows significantly, especially for large-scale construction projects. If a building cannot begin operations by the scheduled date, the client and the operator may suffer substantial economic losses, and liquidated damages are often incurred depending on the contract terms. As modern construction projects are trending toward longer durations, larger scales, and greater complexity, the likelihood of schedule delays is also increasing. However, attempting to meet completion deadlines at all costs can lead to various problems, such as increased construction costs or compromised quality. To prevent these issues, construction sites implement “Project Scheduling and Control” to systematically manage the construction schedule. Since shortening or delaying the construction period directly affects a company’s profit and loss, accurate project scheduling and control is an essential management element on construction sites.

What is the difference between CPM and PERT?

Various techniques are used in project scheduling and control. Representative techniques include CPM (Critical Path Method) and PERT (Program Evaluation and Review Technique).
CPM is a technique for planning and managing the entire project based on the sequence of tasks and the time required for each task. Traditionally, the AOA (Activity on Arrow) method was used, in which tasks were represented by arrows connecting time points; subsequently, the AON (Activity on Node) method, which represents tasks as individual nodes, has also become widely used.
In contrast, PERT is a technique designed for projects where task durations are variable and uncertain. It probabilistically analyzes the duration of each task to calculate the project’s expected completion date and the probability of completion within a given timeframe. Therefore, it is effective for cases where it is difficult to accurately predict task durations, such as in research and development (R&D) projects or new initiatives. Conversely, since task durations can often be estimated relatively accurately in typical construction projects, CPM is the most widely used method in actual field settings.
In this blog post, we will examine the basic principles of project management through a schedule chart and network, focusing on the arrow-oriented network (AOA) method within CPM.

Components of a Schedule Chart

The following schedule chart shows the basic information for each task that makes up the project.
First, a node (Node) represents the start point (i) and end point (j) of a task. For example, the start node for Task B is 4, the end node is 6, and the task duration is 6. Additionally, you can see the precedence relationship indicating that Task A must be completed before Task B can begin. Here, the node numbers have no relation to the task durations; they are merely identification numbers used to distinguish positions within the process.
The CPM network is a graphical representation of the schedule chart in network form, based on this information. Representing the relationships between tasks as a network not only allows for an intuitive understanding of the overall process flow but also enables much more efficient schedule calculations, which will be explained later.

Meaning of ESD, EFD, LSD, and LFD

To understand CPM, it is necessary to first understand the meanings of ESD (Early Start Date), EFD (Early Finish Date), LSD (Late Start Date), and LFD (Late Finish Date). Recently, it is also common to use “Time” instead of “Date,” resulting in terms such as EST (Early Start Time), EFT (Early Finish Time), LST (Late Start Time), and LFT (Late Finish Time).
ESD refers to the earliest possible start time for a given task. In other words, since a task can only begin once all preceding tasks are complete, the ESD is the point at which all preceding tasks are finished.
By subtracting the task duration from the ESD, you can determine the Earliest Finish Date (EFD), which is the earliest possible completion date.
Conversely, the LFD refers to the latest date by which a task must be completed without affecting the overall project schedule. By subtracting the task duration from the LFD, you can determine the Latest Start Date (LSD), which is the latest possible start date for the task.
Furthermore, float refers to the amount of time that can be allocated to a single task without affecting the overall project schedule. The most commonly used measure among these is total float (TF), which represents the maximum amount of time a task can be delayed without causing a delay in the overall project duration. Generally, total float is calculated as the difference between LSD and ESD and is expressed as follows:

TF = LSD − ESD

Calculating total float makes it easy to determine how important each task is in schedule management, and it also serves as a key criterion for identifying the critical path, which will be explained later.

What is a “dummy” task?

To understand project scheduling, it is also necessary to understand the concept of a “dummy” task. A dummy task does not represent an actual task but is a hypothetical task used in a network diagram to clearly express the sequence of tasks. In other words, it is a nominal task used to prevent overlapping connections between tasks and to accurately represent logical sequences.
If you look at the following schedule chart, you’ll see that the durations for tasks d1 and d2 are both shown as 0; these are dummy tasks. Although they are not actual tasks performed in a construction project, they are necessary elements for correctly constructing the network and play a particularly important role in arrow-line networks (AOA). Understanding this concept makes it easier to grasp the structure of a CPM network.

How is a CPM network calculated?

An arrow-line network (AOA) is constructed by connecting each point in the process with arrows. The numbered circles represent nodes, which denote the start or end points of an activity. The arrows connecting the nodes each represent a single activity.
By representing the relationships between activities in this network format, scheduling information such as ESD, EFD, LSD, LFD, and TF can be systematically calculated.
First, a forward pass is performed to calculate the ESD and EFD for each activity. Since the first activity starts at 0—the project start date—its ESD is 0. Adding the activity duration to this value yields the EFD.
The ESD of subsequent activities is equal to the EFD of the latest-completing activity among all its predecessors. If there are multiple predecessors, the largest EFD value is used as the ESD for the new activity. This is because the next activity cannot begin until all predecessors are completed.
By repeating this process until the final activity of the project, the ESD and EFD for all activities can be calculated. For the final task, the EFD and LFD have the same value, and the backward pass is performed based on this.
The backward pass is the process of calculating the LSD and LFD starting from the final task of the project. The LFD of the final task is the same as the EFD of the final task determined in the forward pass. Thereafter, the LFD for each task is determined as the smallest LSD among the successor tasks that have that task as a predecessor. This is because if even one of the successor tasks cannot start late, the current task must also be completed in accordance with that schedule.
Once the LFD is determined, the LSD can be calculated by subtracting the task duration. By repeating these calculations all the way back to the project’s first task, you can determine the LSD and LFD for every task.
Finally, the total float (TF) for each task is calculated by subtracting the ESD from the LSD, which allows us to determine how much leeway each task has within the schedule.

Meaning of the Critical Path

In CPM, the ultimate goal is to determine the total project duration using the critical path.
The critical path refers to the path with the longest total duration among the various paths connecting the project’s first task to its last task. Therefore, the total duration of the critical path is equivalent to the overall project duration.
The critical path can be identified by connecting tasks with a total float (TF) of 0 in sequence. If the project proceeds as planned, tasks with a positive total float will not affect the overall project duration even if they are slightly delayed within a certain range. On the other hand, tasks with a Total Float (TF) of 0 must begin immediately upon completion of the preceding task and must be completed within the planned duration. Otherwise, the entire construction schedule will be delayed accordingly.
In other words, all tasks that directly affect the total construction duration are located on the Critical Path. Therefore, if the duration of these tasks can be shortened, the total construction duration can be reduced; conversely, if they take longer than expected, the total construction duration will be delayed accordingly.
In the example presented in this blog post, A → B → d1 → F → G → I corresponds to the Critical Path, and since the LFD of the final task, I, is 25, the total project duration is calculated as 25 days.

The CPM Calculation Process Using a Sample Schedule

To better understand the principles of CPM, let’s examine a simple sample schedule. In this blog post, the construction process has been simplified into foundation work, structural work 1, structural work 2, concrete work 1, concrete work 2, mechanical and electrical work, and finishing work to create the schedule. Based on this, a CPM network was constructed, and to more easily explain the principles of forward and backward calculations, we will examine each calculation process separately.

How is forward calculation performed?

In forward calculation, the ESD and EFD for each activity are calculated in sequence.
In the network below, the numbers displayed above each node represent the ESD for that activity. Since the project start date is 0, the ESD for the first activity—Foundation Work—is also 0. The duration of Foundation Work is 2, so it can be calculated as follows.

ESD = 0
EFD = 0 + 2 = 2

Since ESD represents the earliest possible start time for a task, the ESD of a subsequent task must be after the completion of all preceding tasks. Therefore, when there is only one preceding task, the EFD of that task is the ESD of the next task.
For example, Structural Work 1 cannot begin until Foundation Work is completed, so its ESD is 2.
On the other hand, the calculation method differs when there are multiple preceding tasks. For example, Finishing Work 2 cannot begin until Concrete Work 2, Equipment Installation, and Finishing Work 1 are all completed.
The completion dates for each task are as follows.

Concrete Work 2: 15 + 4 = 19
Equipment Installation: 15 + 5 = 20
Finishing Work 1: 14 + 2 = 16

Since Finishing Work 2 cannot begin until all three tasks are completed, the ESD is set to 20—the completion date of the task with the latest finish date (Finishing Work 1). Adding the task duration to this date yields the EFD.
By repeating this calculation all the way to the project’s final task, you can determine the ESD and EFD for every task.

How is backward scheduling performed?

In backward scheduling, the LFD and LSD for each task are calculated.
Backward scheduling starts with the project’s final task. The LFD of the final task is the same as the EFD of that task determined in forward scheduling. In this example, since the EFD of the final task (Finishing Work 2) is 23, the LFD is also 23.
Since the duration of Finishing Work 2 is 3, the LSD can be calculated as follows.

LFD = 23
LSD = 23 − 3 = 20

After that, the preceding tasks are calculated in reverse order. The LFD of a given task is the smallest value among the LSDs of the subsequent tasks that have that task as a predecessor.
For example, Structural Work 1 is a predecessor to Structural Work 2 and Concrete Work 1.

Structural Work 2’s LSD = 15 − 6 = 9
Concrete Work 1’s LSD = 18 − 5 = 13

Of these two values, the smaller one—9—is used as the LFD for Structural Work 1. Subtracting the duration of subsequent tasks allows you to calculate the LSD.
After calculating the LFD and LSD for all tasks using this method, you can also determine the total float for each task by applying TF = LSD − ESD.

Identifying the Critical Path Using an Example

Once all calculations are complete, you can identify the critical path by connecting the tasks with a total float (TF) of 0.
In the example in this blog post, the following tasks have a TF of 0:

Foundation Work → Structural Work 1 → Structural Work 2 → Mechanical and Electrical Work → Finishing Work 2

This path is the critical path and is indicated by a thick line on the network diagram. If any single task on this path is delayed, the entire construction period will be delayed accordingly, so these tasks must be managed with the highest priority.
Conversely, tasks with a TF greater than 0 will not affect the overall construction period even if they are delayed slightly within a certain range. Therefore, the project manager can utilize this buffer time to efficiently allocate labor and equipment and operate the entire project more stably.
In this example, the completion time of the last task is 23, so the total project duration is calculated as 23 days.

Why CPM Is Important in Project Management

The project schedule introduced in this blog post is a simple example designed to illustrate the principles of CPM, so the critical path is relatively easy to identify. However, in actual construction sites, dozens to hundreds of work items are intricately interconnected, and schedules are subject to constant changes depending on the progress of the project. In such environments, it is common to use project management software to create a network diagram and continuously analyze the critical path.
The core objective of project management is to identify the precise critical path within a complex project and to continuously compare actual progress with the planned schedule to prevent delays. Furthermore, when necessary, it is important to develop strategies to shorten the project duration—focusing on the tasks included in the critical path—to ensure the project is completed within the planned schedule.
Time is one of the most critical resources in any project, and its importance is particularly significant in construction projects. For this reason, systematic schedule management techniques such as CPM are widely used not only in the construction industry but also in various other fields, including manufacturing, the plant industry, and information technology (IT) projects, and have established themselves as core project management techniques for efficient project execution.

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