Comparing the Effectiveness of PERT and CPM Techniques in a House Construction Project: A Case Study

Managing projects requiring multiple activities is one of the most challenging tasks a manager can take on. There are many factors to consider when coordinating these tasks, including setting a realistic timeline, monitoring project progress, and more [1]. Project management focuses on determining the project duration and related major tasks, and there are two main methods that have been helpful for planning and scheduling engineering projects: CPM and PERT [2].

A critical activity is defined as one in which the oldest and most recent times are the same. A project network may have more than one critical path [3]. CPM and PERT were initially created to plan construction, analyze the project, and propose related tasks. The project is accomplished by utilizing a system of interconnected and similar events to coordinate the optimal sum and period parameters [4]. So, they are handy and essential tools to manage all types of projects effectively; on the other hand, delays in the building and construction process are a global problem. Using CPM/PERT to manage construction projects facilitates the ability to supervise large projects that involve a lot of coordination of activities, which is one of the most challenging things a manager can do [5].

Structurally, planning is imperative because it determines the timing and order of several steps and the linkage between activities. People can define this critical duty and maintain control of the construction project using CPM and PERT [6, 7].

Employing cost engineering based on expertise and experience can accurately predict the time required for various tasks during project implementation by looking at previous projects. Uncertainty can also move the calendar chart. Since hesitation cannot be avoided entirely in projects [8], a technique that can reduce improbability may be needed, namely PERT. Starting from the former, PERT agrees to determine event duration estimates using three-time estimates (optimistic, almost inevitable, and adverse), taking into account the uncertainty present in the duration. These three estimates are used to calculate the expected time for the activity. The range between optimistic and pessimistic estimates is a measure of variance that allows statistical inferences about the probability of an event occurring in the project at a given time [9].

However, users may experience some advantages when applying BERT, which uses empirical distributions and requires sufficient temporal data to make estimates more accurate. Therefore, in a house building project, CPM is applied to know the critical path, and PERT is applied, where the time rate calculation equation is applied and the last start and end of the house construction project activities are calculated. The critical path will be calculated, the differences will be noted, and the results between CPM and PERT will be compared and evaluated, as well as how they differ from systematic data collection and analysis [10, 11].

Project evaluation and testing techniques are economical for planning and controlling projects [19]. PERT is one of them, the purpose of which is to study project networks, not to create schedules. In application, PERT uses three-time estimates, optimistic, most likely, and pessimistic, about dealing with duration uncertainty. Favorable time is the minimum time for an activity, most likely when an activity occurs most frequently when repeated, and pessimistic time is the maximum time for an activity. The three estimates are related in a beta probability distribution, where the parameters a and b represent the end and start points, and m is the most common value [20]. The beta distribution is used because it is unimodal (it has one peak) and not necessarily symmetric, properties that seem ideal for activity duration distributions [21].

PERT is also known as a retrospective research technique. This technique uses time as a variable in planning, organizing, coordinating, and controlling unsafe activities and performance specifications.

PERT calculations support assigning task completion time probabilities based on time for optimism (F), time for likelihood (M), and pessimistic time (S). Use PERT to determine the activity values required for the critical path to include a slack account [22, 23].

In the PERT method, activity time can have flexibility, the most common being complete floats (TF) and free floats (FF), which are the crucial route with floats with values equal to zero. That is, TF = 0 and FF = 0, which can be obtained from the equations bellow [24]:

$T F=L A_j-X_i-Z_{i j}$       (4)

$F F=X_j-X_i-Z_{i j}$         (5)

The following formula applies to the variance (V) and mean time $\left(\mu_T\right)$:

$\mu_T=\frac{F+4 M+S}{6}$       (6)

$V=\left(\frac{S-F}{6}\right)^2$         (7)

Given the parameters (α, β), it follows a beta distribution. Temporal forecasting and the probability of using the PERT completion time for construction work are also included in the calculation. The standard model for beta is as follows [25]:

$\mathrm{Z}=\frac{\left(\mathrm{X}-\sum \mu_{\mathrm{T}_{\text {critical }}}\right)}{\sqrt{\mathrm{V}_{\text {critical }}}}$       (8)

where:

X = Overall project duration (CPM).

Z = Compared with tabulated normal distribution.

$\sum \mu_{T_{\text {critical }}}$ = Calculation of the total sum of anticipated critical values.

$V_{\text {critical }}$ = Aggregate of all variances essential task.

3.1 Methodology and data collection

The data contained therein is specific to a house-building project. For the building project, the house has 11 activities and stages; the earliest start and end times are set for each activity. The duration of each activity was determined based on the secondary data presented in Table 1 [26]. The data in this study were analyzed using CPM and PERT methods. They are collected as shown in Table 1, so the results are compared to determine the best way to determine when a home construction project will be completed. Table 1 represents the activities and phases of a home construction project, duration calculation, optimistic and pessimistic estimates (a, b) and their precursors [27].

Note: the project is a hypothetical example.

Table 1. The steps and activities involved in building a house

The network diagram in Figure 1 represents the data in Table 1.

1.png

Figure 1. Network diagram with most likely estimates (M)

3.2 Analyze data using CPM

The forward pass is calculated using Eq. (1). The time required to complete the project using CPM is 105 days, as shown in Table 2.

Table 2. Forward pass computation (CPM)

The construction project requires an entire amount of time. One hundred five days, as shown in column 5 and row 11 thereof, according to the network schematic of the forward pass calculation CPM shown in Figure 2, we have three paths to finish the project by the CPM, and using Eq. (1), the critical path is (1-2-3-5-7-8-9-11):

2.png

Figure 2. Network diagram of the front-end calculation process using the CPM

3.3 Analyze data using the PERT method

There are three-time estimates in the table [28]. This is summed up in Table 3.

A schematic of the onward pass calculation of PERT is shown in Figure 3.

It is clear to us from the method of calculating the forward pass (CPM) and the reverse pass (PERT) that the critical path includes activities with a difference between early time and late time equal to 0, as shown in Table 4.

Using PERT, we have three-time estimates; for these time estimates, the mean and variance are calculated using Eqs. (6) and (7) respectively, as shown in Table 5.

Table 3. Backward pass computation PERT method

3.png

Figure 3. Network diagram using inverse arithmetic with CPM

Table 4. The difference between late time and early time

Table 5. Mean and variance

Thus, the expected project length is calculated using the PERT method accordingly:

$\sum_{\text {critical }}=7+12+14+12+18+20+20=103$

The total variances for the critical path in the project are:

$\sum_{\text {varaince }}=1+0.444+0.111+1.778+1.778+2.778+1.361=9.25$

Then, the completion period of project X = 105 days; by applying Eq. (8), we can find that the probability of completing the home project is:

$\operatorname{prob} Z \leq\left(\frac{105-103}{\sqrt{9.25}}\right)=\operatorname{prob}[Z \leq 0.66]=0.7454$

This indicates that there is a chance of completing the project within 105 days, equal to 74.54%. There will only be a two-day difference in project completion between PERT and CPM. Thus, the critical path (CPM) and PERT methods are successful and effective when building a house. Whole floats (TF) and allowed floats (FF) are calculated using Eqs. (4) and (5) respectively, as displayed in Table 6. The critical route table above shows that the order of activities is flexible, with total floats (TF) being the most prevalent example. Moreover, floating freely (FF) is the crucial route when using floats that have values of zero. TF=0 and FF=0 in this case.

The accompanying table shows the order in which the actions of the (1-2-3-5-7-8-9-11).

Table 6. TF and FF design in PERT

3.4 Summary

This study was designed for a home-building project. Collect and analyze data using CPM and PERT. The study describes the various activities involved in the project by rolling the account forward and backward, including early events and the most recent start and end of the activity.

Using CPM and PERT methods to determine slack quantities and critical paths. According to the results, the difference in calculation methods between CPM and BERT implementation can be seen in their estimates, as shown in Table 7. The CPM method is based only on the almost certain estimate (M), while the study using PERT is based on the optimistic estimate (A), the almost certain estimate (M), and the doubtful estimate (B).

However, PERT calculations support the possibilities of reporting task completion times based on three-period estimates. Furthermore, the research shows that the total CPM days to completion is 105 days, the total number of PERT days is 103 days, the probability of completing a home construction project is 74.54%, and the time for project completion is very important.

The difference was very important in terms of reducing costs and saving time.

Table 7. Compare results between CPM and PERT