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01-05 

1 

 

 

 

Article 

Critical path method utilization for optimal 

scheduling of production activities 
Ovundah King Wofuru-Nyenke  

Department of Mechanical Engineering, Faculty of Engineering, Rivers State University, Port Harcourt, Rivers State, Nigeria 

               A R T I C L E   I N F O 
 

Article history: 
Received 21 May 2024  
Received in revised form 
25 June 2024 
Accepted 20 July 2024 
 
Keywords:  
Critical path method, Production activities 
scheduling, Manufacturing engineering, Slack time 
 
*Corresponding author 
Email address: 
ovundah.wofuru-nyenke@ust.edu.ng 
 
 
DOI: 10.55670/fpll.fusus.2.3.1 
 

A B S T R A C T 
 

Critical Path Method (CPM) is a useful method for scheduling activities involved 

in a project. CPM is suitable for large and complex projects in which many tasks 

are involved and the interrelationships among these tasks must be taken into 

account. Its efficacy can easily be transferred to the optimal scheduling of 

production engineering activities in order to save time involved in the project. 

It helps in identifying the sequence of jobs that determines the earliest possible 

completion date for the project. The knowledge of the critical jobs can aid in 

eliminating the fairly common and costly practice of rushing all jobs to reduce 

the total project time. Meanwhile, rushing only the critical jobs will have the 

desired effect of decreasing the total project time. In this study, the critical path 

method was utilized in scheduling activities involved in the production of a new 

product by a metalworks manufacturing company. The project activities 

involved making an initial market study which took 25 days, developing 

promotional ideas which took 22 days, estimating promotional costs which 

took 16 days, conducting initial pricing study which took 29 days, preparing a 

detailed design which took 30 days, manufacturing prototypes which took 14 

days, making design changes which took 12 days and determination of the final 

selling price of the product which took 15 days. The critical path analysis 

revealed that the minimum allowable time and earliest possible completion 

date for the project is 96 days. This research provides a procedure for 

implementing the Critical Path Method for production activities scheduling. 

 

1. Introduction 

Production activities scheduling is very important for 

planning the sequence of tasks, allocating resources, and 

defining timelines to ensure that a production project is 

completed efficiently and on time. The key steps in scheduling 

include defining the project scope and objectives, identifying 

tasks and activities, determine task dependencies, estimating 

durations, allocating resources, developing the production 

schedule, optimizing the schedule and monitoring and 

controlling the operations. Defining the project scope and 

objectives involves identifying deliverables by clearly 

defining what the project aims to achieve and the specific 

deliverables expected at the end [1]. It also involves 

establishing clear, measurable objectives that align with the 

project goals. Identifying tasks and activities includes 

breaking down work into smaller, manageable tasks or 

activities. It also involves defining the tasks in detail, 

including what needs to be done, who will do it, and any 

necessary resources. Determining task dependencies 

involves identifying which tasks must be completed before 

others can begin. Estimating durations involves estimating 

how long each task will take to complete, using historical data, 

expert judgement or statistical methods, including making 

provisions for time buffers that have high uncertainty or risk 

[2]. Allocating resources involves assigning necessary 

resources such as people, equipment and materials to each 

task as well as identifying and addressing any resource 

constraints or limitations. Developing the schedule involves 

using scheduling tools like Gantt charts to create a visual 

timeline of the project as well as identifying key milestones 

that signify important progress points in the project [3]. 

Optimizing the schedule involves identifying the longest path 

through the network diagram that determines the shortest 

possible project duration as well as making adjustments to 

balance the schedule, considering resource availability, task 

dependencies and deadlines [4]. Monitoring and controlling 

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OKW. Nyenke /Future Sustainability                                                                                         August 2024| Volume 02 | Issue 03 | Pages 01-05 

2 

 

involves tracking progress of tasks against the schedule, 

updating the schedule and communicating to stakeholders 

about the schedule status and any changes in the schedule. 

The Critical Path Method (CPM) is a project management 

technique for identifying the critical path, which is the 

sequence of tasks that determines the minimum project 

duration. It is used in determining the sequence of activities 

that directly affects the project completion time. By 

identifying the critical path, project managers can focus on 

tasks that cannot be delayed without impacting the overall 

project schedule. The method has been utilized in several 

applications including manufacturing, construction, 

agriculture, healthcare etc [5-8]. CPM has numerous 

advantages including enhanced project planning, 

identification of critical activities that directly impact the 

project timeline, improved resource allocation to critical 

tasks, risk management since bottlenecks and delays are 

identified as well as provision of clear timelines for project 

completion, aiding in settling realistic deadlines. The 

limitations of CPM include complexity for large projects with 

many tasks and dependencies, rigidity and less flexibility for 

projects with high uncertainty or where tasks are not clearly 

defined, as well as the fact that resource limitations are not 

considered which might affect the schedule. The aim of this 

work is to utilize the CPM for scheduling activities in a 

product development project involving the manufacture of a 

new filing cabinet design considering design, promotion and 

selling price. The study provides a procedure for 

implementing the CPM project scheduling method for 

scheduling production activities in a product development 

project. 

2. Methodology 

This study utilizes the CPM for scheduling activities in a 

product development project. CPM is suitable for large and 

complex projects in which many tasks are involved and the 

interrelationships among these tasks must be taken into 

account. The method is useful for determining the minimum 

time in which a production project can be completed and to 

ascertain the tasks that are likely to delay this completion, by 

identifying the most time-consuming series of tasks, which 

represent the critical path [9]. The knowledge of the critical 

jobs can aid in eliminating the fairly common and costly 

practice of rushing all jobs to reduce the total project time. 

Meanwhile, rushing only the critical jobs will have the desired 

effect of decreasing the total project time. The product 

development project involves the manufacture of a new filing 

cabinet design considering design, promotion and selling 

price. The project has been described in Table 1.  

Table 1 shows the jobs that must be performed, the 

immediate predecessor(s) for each job and the estimated time 

requirements. From Table 1, jobs with not real predecessors 

are preceded by “Start” and jobs with no real successors are 

followed by “Finish”. Both types of jobs do not require any 

time. After this phase of the CPM analysis, it is necessary to 

prepare a project graph. The project graph is useful for 

understanding the computations involved in the CPM 

analysis. The project graph is a pictorial representation of the 

jobs that make up a project and their interrelationships. In 

constructing the project graph, a rectangle is used to depict 

each job, and the rectangle will contain the letter or number 

identification of the job and the time estimated for its 

completion. From any one rectangle, arrows are drawn to all 

the immediate successor jobs. Using the project graph, the 

minimum time required to complete the project can be 

ascertained. This is usually done by enumerating the different 

routes or paths that can be followed from the start to the 

finish of the project. The minimum amount of time required 

to complete the project will be determined by the most time-

consuming sequence of jobs, which constitute the critical 

path. A project graph showing the early start and finish times 

needs to be developed as well as a project graph showing the 

late start and finish times. In developing the early start and 

finish times project graph S is the earliest possible starting 

time for the project, ES is the earliest possible starting time 

for a given job, t is the time required to complete a given job, 

EF = ES + t is the earliest possible finish time for a given job, F 

is the earliest possible finish time for the project. In 

developing the late start and finish times project graph, T is 

the target completion time for the project or the latest 

possible finish time for the project, LF is the latest possible 

finish time for a given job if the target completion time T is to 

be met, t is the time required to complete a given job and LS = 

LF – t is the latest possible starting time for a given job if the 

target completion time T is to be met. 

Table 1. Product development project description 

 

3. Results and discussion 

The results of applying the CPM methodology described 

in section two (2) is presented in this section. Two separate 

project graphs were developed for analyzing the project 

scheduling problem; the early start and finish times project 

graph as well as the late start and finish times project graph.  

The early start and finish times project graph is shown in 

Figure 1. 

Job Description 
Immediate 

Predecessors 
Required 

Time (Days) 

A Start - 0 

B 
Conduct initial 
market study 

A 25 

C 
Develop promotional 
ideas 

B 22 

D 
Estimate 
promotional costs 

C 16 

E 
Make initial pricing 
study 

B 29 

F 
Develop a detailed 
product design 

B 30 

G 
Manufacture 
prototypes 

F 14 

H 
Make necessary 
design changes 

G 12 

I 
Determine final 
selling price 

D, E, H 15 

J Finish I 0 



OKW. Nyenke /Future Sustainability                                                                                         August 2024| Volume 02 | Issue 03 | Pages 01-05 

3 

 

 

Figure 1. Early start and finish times project graph 

 

Figure 2. Late start and finish times project graph 

Figure 1 shows the earliest points in time at which each 

job can be started and finished. From Figure 1, beginning with 

the first job A, the earliest possible starting time for the 

project S is 0 days. Because the time t for job A is 0 days, its 

early finish time EF will be the starting time of 0 days plus the 

required completion time of 0 days, which yields 0 days. Next 

is job B which can be started no sooner than when its 

immediate predecessor A is finished, therefore its early start 

time ES will be equal to its immediate predecessor’s early 

finish time which was found to be 0. To obtain the early finish 

time for job B, its early start time of 0 days is taken and added 

to the 25 days required to perform the job, thereby arriving at 

an early finish time of 25 days. The early finish time of 25 days 

for job B is the early start time for its immediate successors C, 

E, and F.  

 

 

 

 

 

 

The early finish time of job C is 47 days, the early start 

time for job D is the early finish time of its immediate 

predecessor job C, which is 47 days and the early finish time 

for job D is 63 days. The early finish time of job E is the early 

finish time of its predecessor plus the time taken to complete 

the job giving 54 days. The early finish time of job F is 55 days 

which is the early finish time of its predecessor plus the 30 

days taken to complete the job. From the foregoing, the early 

finish time of job G is 69 days and the early finish time of job 

H is 81 days. 

On getting to job I, it can be seen that the job has three 

immediate successor jobs, D, E and H. Moreover, jobs D, E and 

H have early finish times of 63 days, 54 days and 81 days. 

However, job I cannot be started until all three of its 

predecessor jobs are finished. Therefore, the early start time 

of job I is governed by the early finish time of job H, because 



OKW. Nyenke /Future Sustainability                                                                                         August 2024| Volume 02 | Issue 03 | Pages 01-05 

4 

 

it is the latest early finish time among the predecessor jobs. 

Therefore, the early start time of job I is 81 days. The early 

finish time of job I is the early start time plus the 15 days 

required to complete the job, giving 96 days, which is the early 

start time of job J. Finally, the early finish time of job J is the 

early start time of 96 days plus the 0 days required to 

complete the job which gives 96 days. The late start and finish 

times project graph is shown in Figure 2. 

Figure 2 shows the latest points in time at which each job 

must be started and finished if the target completion date is 

to be met. The procedure utilized in obtaining the desired late 

times is the opposite of the one followed to obtain the early 

start and finish times. Therefore, we begin with the target 

completion time for the last job and work backward until we 

reach the late start time for the first job. The target 

completion time for the project is taken to be T = 96 days. 

Given this late finish time of 96 days and a required time of 0 

days to complete job J, the late start time for this job is the 

difference between those two times, giving 96 days. 

Considering the preceding job I, the late finish time must be 

equal to the late start time of J. Therefore, the late finish time 

is 96 days, and the late start time is 96 days minus the time 

required for job I. This process continues until job B where 

there are three (3) successors to the job namely C, E and F. 

These successors have late start times of 43 days, 52 days and 

25 days, respectively, therefore the late finish time of job B 

will be governed by the late start time of job F. This is because 

it is the earliest and more demanding late start time. 

Consequently, the late start times for jobs A and B become 0. 

Table 2 shows the determination of slack times for the 

production project. From Table 2, the slack time column 

contains the slack time in days for each job. This time is the 

difference between the late start time and the early start 

times for a job or between the late finish time and the early 

finish times for the job. The slack times represent the total 

allowable delay in the completion of all the jobs. Therefore, 

the minimum allowable time for the project is 96 days. 

Table 2. Determination of slack times 

 

 

 

4. Conclusion 

The Critical Path Method comprises of construction of 

project graphs, determination of critical path and calculation 

of job slack times. The method is useful for determining the 

probable completion dates of production projects, as well as 

developing alternative plans. It helps in identifying the 

sequence of jobs, which are the critical jobs, that determines 

the earliest possible completion date for the project. The 

knowledge of the critical jobs can aid in eliminating the fairly 

common and costly practice of rushing all jobs to reduce the 

total project time. Meanwhile, rushing only the critical jobs 

will have the desired effect of decreasing the total project 

time. The knowledge of slack times associated with each job 

in the project is useful for developing work schedules. This 

study has utilized the critical path method for scheduling 

activities involved in the production of a new product by a 

metalworks manufacturing company. The project activities 

involved making an initial market study, developing 

promotional ideas, estimating promotional costs, conducting 

initial pricing study, preparing a detailed design, 

manufacturing prototypes, making design changes and 

determination of the final selling price of the product. The 

critical path analysis revealed that the minimum allowable 

time for the project is 96 days. This research provides a 

procedure for implementing the Critical Path Method for 

production activities scheduling. Further research can 

involve the utilization of other production scheduling 

methods such as the Program Evaluation and Review 

Technique (PERT) for effective production activities 

scheduling. 

Ethical issue 

The author is aware of and comply with best practices in 
publication ethics, specifically with regard to authorship 
(avoidance of guest authorship), dual submission, 
manipulation of figures, competing interests, and compliance 
with policies on research ethics. The author adheres to 
publication requirements that the submitted work is original 
and has not been published elsewhere. 

Data availability statement 
The manuscript contains all the data. However, more data will 

be available upon request from the author. 

Conflict of interest 

The author declares no potential conflict of interest. 

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E 25 52 54 81 27 

F 25 25 55 55 0 

G 55 55 69 69 0 

H 69 69 81 81 0 

I 81 81 96 96 0 

J 96 96 96 96 0 



OKW. Nyenke /Future Sustainability                                                                                         August 2024| Volume 02 | Issue 03 | Pages 01-05 

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distributed under the terms and conditions of the Creative 

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(https://creativecommons.org/licenses/by/4.0/). 

 

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