Comparison of Approaches for Calculating the Probability of a Project Completion

Abstract

The paper deals with a comparison of two different approaches (PERT method and Monte Carlo method) for calculation of the probability of a project completion. The PERT method is commonly used in a project management; the Monte Carlo is used less. The base assumption of authors can be expressed: The difference between the results obtained by the Monte Carlo method and PERT method is not significant with increasing number of simulations (iterations). For this reason, the hypothesis was formulated: There is no statistically significant difference between the calculated probabilities, i.e. both approaches are identical from application’s point of view. The case study describes a model of a project, which is shown by a network chart. This chart contains 18 nodes and 18 real activities and 6 fiction’s activities. Each activity is expressed by three time estimates, i.e. pessimistic, most likely and optimistic time. The planned date of completion of the project was selected at 200 time units and it was calculating the probability of completion of the project by PERT method and Monte Carlo method. Time duration of each project activity by the Monte Carlo method is successively obtained for 10, 100, 300, 500, 1000, 5000 and 10000 simulations. The calculated probabilities of project completion were compared using statistical hypothesis testing. The hypothesis was rejected for all simulations. It follows that there is difference between the approaches from application’s point of view.The paper deals with a comparison of two different approaches (PERT method and Monte Carlo method) for calculation of the probability of a project completion. The PERT method is commonly used in a project management; the Monte Carlo is used less. The base assumption of authors can be expressed: The difference between the results obtained by the Monte Carlo method and PERT method is not significant with increasing number of simulations (iterations). For this reason, the hypothesis was formulated: There is no statistically significant difference between the calculated probabilities, i.e. both approaches are identical from application’s point of view. The case study describes a model of a project, which is shown by a network chart. This chart contains 18 nodes and 18 real activities and 6 fiction’s activities. Each activity is expressed by three time estimates, i.e. pessimistic, most likely and optimistic time. The planned date of completion of the project was selected at 200 time units and it was calculating the probability of completion of the project by PERT method and Monte Carlo method. Time duration of each project activity by the Monte Carlo method is successively obtained for 10, 100, 300, 500, 1000, 5000 and 10000 simulations. The calculated probabilities of project completion were compared using statistical hypothesis testing. The hypothesis was rejected for all simulations. It follows that there is difference between the approaches from application’s point of view.