Implementation of Project Evaluation and Review Technique (PERT) and Critical Path Method (CPM): A Comparative Study

The project evaluation and review technique (PERT) and critical path method (CPM) were applied in a building construction company. Different activities involved in the house construction project were described. The earliest events, latest commencement and completion of activities were determined using Forward and Backward pass computations in CPM. Critical paths were determined using both CPM and PERT. Based on the analysis, it was shown that the completion of the house project using CPM was almost the same with that of PERT such that the difference between both techniques was only one day. The probability that the house construction project could be completed in 151 days was 99.87%. This implies that the house construction project could be completed on time using both techniques. However, the results showed that the implementation of both CPM and PERT methods are effective and efficient in a house construction project.


Introduction
Project Evaluation and Review Technique (PERT) and Critical Path Method (CPM) are scheduling methods originally designed to plan a construction project and to analyse and represent the tasks involved in completing a given project by employing a network of associated and similar activities, coordinating optimum cost and time criteria [1]. According to Kelly and Walker [2], Critical Path Method (CPM) and Programme Evaluation and Review Technique (PERT) are useful tools for efficient management of all types of project such as construction, engineering, facility maintenance, research • Page 2 of 9 • ISSN: 2633-8947 | CPM and PERT allow one to identify this important task and stay on track throughout the entire construction project [4]. CPM technique is used based on the knowledge and experience of the past projects for predicting accurately the time required for various activities during the execution of the project. The company under consideration uses CPM and PERT, and hierarchy of their already completed construction project events are well defined and time of completion. Therefore, here, CPM and PERT are applied to a house construction project and the earliest events, the latest commencement and completion of activities of a house construction project is calculated. The critical path in the house construction project is also to be determined as well as evaluating the differences existing between CPM and PERT.
Section two is the brief history of the construction company used. Section three presents brief explanations of CPM, PERT and their difference. Data collection/methodology and analyses are described in Section four and five respectively. Section six gives summary and conclusion.

Brief History of the Company
Basse Engineering Construction Company is a dynamic construction company with more than twenty five years of experience in pursuing excellence in the delivery of Civil Engineering and construction services.
The Company specializes in public and private house building, maintenance, design and construction of highways and bridges, town planning and construction of modern housing units, erosion control works, underground drainage system, construction of sewage system, etc.
According to the manager, the manages scheduled construction project delivery on time to avoid delays and cost overrun. It has set construction standards in both Nigeria and outside country.
Basse Engineering Construction Company is located at No. 713 Idoro Road, Uyo Akwa Ibom State. Its distance is about 3.5 km away from Itam Junction from the East and adjacent to the new stadium Road, off Abak Road, Uyo. Their project site was established in 1994 with skilled professionals and highly experienced Engineers.
(CPM) Critical Path Method, PERT (Program Evaluation and Review Technique) and Their Differences (CPM) Critical Path Method CPM provides planned schedule to assist the project team and forms the basis for checking project schedule performance by comparing actual with planned task progress. CPM is a means of evaluating how long will each task take before one can finish the entire project Hebert, et al. However, CPM can be defined as a sequence of project network activities that add up to the longest duration. It's sequence regulates the least time possible to complete the project.
Critical Path Method assist in the management of projects in two different ways: The forward and backward pass.
The forward pass calculation is obtained with the formula below: The forward calculation moves from the initial event to the terminal event, setting the initial event at zero. i.e.,

Differences between PERT and CPM in construction projects
PERT and CMP are the two-network based project management methods that shows and exhibit the flow and sequence of activities and events. The difference between the CPM and PERT is that PERT is mainly used where the time required for completion of each of the activities is unknown whereas CPM technique bases its execution of the project on the knowledge and experience of past projects [7].

Data Collection and Methodology
The data was collected from the Management unit of Basse Engineering Construction Company alongside with the planning steps involved in this house construction project.
There are 15 activities and stages for the house construction project, starting from the preparatory work/site work, to the fencing work. Each activity defines the earliest start time and earliest finish time. The duration of each activity is assigned based on the secondary data stated in Table 1, gotten from the office of the manager.
A lot of records and files for already carried out projects were shown in pictures and discs as evidence to support their experience and skills.
Data for this study are analyzed using CPM and PERT methods as explained in section 3 above. They are collected as shown in Table 1 below, where each activity is labeled with codes from A -O and from 1 -15 with activities description.
A project activity, description, duration, optimistic and pessimistic estimates (a, b) and predecessors.
Source: file in Management unit of Basse Engineering Construction Company.
The two methods of data analysis were described in section 3 above

PERT (Program Evaluation and Review Technique)
PERT is also known as Back Research Technique. This technique uses time as a variable in planning, scheduling, organising, coordinating and controlling of uncertain activities along with performance specification.
PERT computation supports assigning probabilities with task completion times in accordance with; Optimistic time (α), Most likely time (M) and, Pessimistic time (β).
Determination of the critical path from PERT requires slack calculation with activities e values known as floats.
The most common floats are the total floats (TF) and free floats (FF). The critical path is determined by the values of floats = 0. i.e., TF = 0 and FF = 0.
Total Floats and Free Floats are obtained from the equation below: That is, the slack values are also known as floats.
The mean time denoted by (µT) and variance (V) has the formula stated below: The above follows beta distribution with parameters ((α, β)).
Using PERT in time predictions, the probability of completing construction time is calculated using standard normal form of beta as shown below: Therefore the network diagram representing the data presented in Table 1 above with only most likely estimates (m) and their corresponding durations is thus (Figure 1):

Data analysis with CPM and its interpretations
The forward pass is calculated using equation (1) and is summarized in Table 2 below:   Table 2   The activities and stages for the house construction project, starting from the preparatory work/site work, to the fencing work, including duration, optimistic and pessimistic estimates (a, b) and predecessors.  Table 4 below. A network diagram is also drawn to indicate the sequence of activities of the critical path using CPM:

S/N Activity i -j Description Duration (in days) a, b (in days) Predecessor
The critical path is represented by the thick lines and arcs as shown in Figure 4 below: Network diagram is drawn in Figure 1 below to demonstrate a backward pass.

Analysis of a house construction project with PERT method
Using PERT has three times estimate from Ta-construction project takes the total duration of 151 days as shown in row 14-column 5 of the same table. Also, activity (8, 9) is dummy. The network diagram of a Forward Pass computation is shown below (Figure 2  This implies that the probability that the house construction project can be completed in 151 days is 0.9987 = 99.87%.
Hence, comparison of CPM and PERT is shown in Table 6 below: From the table, it implies that the difference between PERT and CPM in the completion of the ble 1, the mean and variances are calculated from equation (8) and (9) respectively. And this is summarized in Table 5 below for However, the expected project length is thus:     • Page 8 of 9 • ISSN: 2633-8947 | on CPM were obtained, and the earliest events, latest commencement and completion of activities were determined.
Both CPM and PERT methods were used in determining the slack values and the critical paths. Based on the findings, the difference existing between the implementation of CPM and PERT were seen on their three times estimates. Analysis of CPM was based on only the most likely estimate (m), while analysis with PERT was based on optimistic estimates (a), most likely estimates (m) and pessimistic estimates (b).
However, PERT computation supports assigning probabilities to task completion times in accordance with the three time estimates.
Furthermore, the study showed that the total completion days using CPM was 151 days, while the total days spent using PERT was 150 days with the completion probability of a house construction project 99.87%.

Conclusion
Based on the results of the analysis of this work, it can be concluded that: PERT method is more efficient than CPM method.
The implementation of CPM and PERT in the project is only just one day. Therefore, both CPM and PERT methods are effective and efficient in house construction.
Using equations (6) and (7) in section 3 above, Total Floats (TF) and Free Floats (FF) are obtained as shown in Table 7.
From the above Table,

Summary and Conclusion Summary
This work was on implementation of CPM and PERT to a house constructing project by Basse Engineering Company, Uyo, Akwa Ibom State. A descriptive study was adopted in the description of the different activities involved in the house construction project.
Secondary data were collected from a file in the management unit of Basse Engineering Constructing Company and were analyzed using CPM and PERT.