Probabilistic Completion Time in Project Scheduling
Abstract
There are two common used methods to find the minimum completion time for a project scheduling. These methods are Critical Path Method (CPM) and Program Evaluation Review Technique (PERT). In CPM, a network diagram, which is Activity on Node (AON), is drawn and the slack time for every activity is calculated such that the project’s critical path could be found. It is important that the critical path can suggest the shortest possible completion time. On the other hand, PERT concerns on uncertainty and risk in a project. It has three time estimates, which are optimistic, pessimistic and most likely, and all the time estimates mentioned follows the beta distribution. Besides, the probability in completing the project within certain duration is calculated by using the standard normal distribution. As the risk cannot be avoided in a project, it is important to keep track on any changes and to minimize the completion time for a project. Both of the methods are used to calculate the shortest possible completion time, slack and critical path. The difference between these methods is CPM has only one determined time estimate, while PERT has three time estimates, which shows the uncertainty in the duration of an activity in a project. For illustration, the data used for the construction of a three-room house was studied. The results show that the minimum completion time for the project is 44 days with a success probability 0.91. In conclusion, CPM and PERT are practical tool in the project scheduling.
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Introduction
Project scheduling is a complicated process of planning, scheduling and controlling a progressing event. The problem that deals with a project is always related to risk, which its occurrence will affect the project objective, scope, time, budget and quality [1]. Since variability is unavoidable, a project manager shall determine the risk and uncertainty before executing a project. A good estimation of project completion time is one of the solutions in diminishing uncertainty. On this basis, the project manager will be able to gauge the uncertainty and quickly adapt to any problem that might occur. The project manager should also figure out the shortest completion time in order to minimize the cost incurred. By virtue of this, two popular methods, which are critical path method (CPM) and program evaluation review technique (PERT), are applied to find the shortest completion time with consideration of risk factors and uncertainty [2]. Duration on a critical path is the possible shortest time to complete critical activities, and any delay of a critical activity will cause the impact on the project completion. Thus, critical path, which is having the least amount of scheduling flexibility, is identified by using the network diagram, that is, Activity on Node (AON) [3]. The probability of completing a project by certain time is calculated by using the standard normal distribution. Here, SAS University Edition is employed for the calculation.
The rest of the paper is organized as follows. In Section 2, the problem of scheduling for a project is described, where the activities and the corresponding time estimates are presented. In Section 3, the methods used, which are CPM and PERT, are clearly discussed. The forward and backward passes are considered in calculating the slack time such that the critical path of the activities could be determined. In Section 4, Gantt chart and network diagram AON are shown. The results show the critical path and the probabilities of the certain duration are given. Finally, some concluding remarks are made.
Conclusion
In this paper, the probabilistic completion time of a project scheduling was discussed. The minimum possible completion time for the project mentioned is 44 days with the probability of 0.91. Uncertainty in the project can be minimized by applying CPM and PERT. The project manager will be able to cope with these methods as they know the use of these two approaches. CPM is more suitable for construction process as the project has fairly accurate in the time estimation. However, if it is dealing with large and high capital construction project, PERT would be a better choice. For the future usage, it is more challenging if it is including the cost in the project and taking the real data from the real-world implementing projects. This suggestion would be more practical if the knowledge can be applied in more challenging environment and increasing the value of the study.