Using Trended Regression Trees for Computing Unbiased Makespan of PERT Networks

Document Type : Original Article


department of Industrial Engineering Faculty of Mechanical and Industrial Eng. Jundi-shapur Uni. of Tech. Dezful Iran



Scheduling a network of activities is a common task in project management. This paper deals with estimating the Project Completion Time in stochastic networks. Traditionally, one of the well-known tools to schedule projects consisting of activities with stochastic activity durations is Project Evaluation and Review Technique (PERT). Since PERT is known to be over-optimistic, practitioners prefer to use simulation-based methods such as Monte Carlo simulation. PERT assumes rough estimations for the mean and variance of the merge events. The completion time of merge events follows the rules of an important order stochastic known as sample maximum. We review analytic bounds and estimators for the mean and variance of sample maximum/minimum. Since no one of the currently available bounds and estimators is fit for the general case, first we develop two estimates for the mean value of sample max/min and two upper bounds for the variance of sample max/min. Then we developed a novel method named as Trended Regression Trees (TRT) to find more accurate estimates for mean and variance of sample maximum/minimum. Having more precise estimates for merge events makes it possible to estimate the project completion time with higher accuracy. Computational results are presented that confirm significant accuracy improvement in estimating the mean and variance of project completion time. We examined huge cross-validation to find the most reliable Trended Regression Trees.