Investigating the effect of uncertainty of the activities’ duration on project makespan with constrained resources

Project scheduling with certain data has a long history of research. Meanwhile, the use of uncertain parameters is limited to PERT technique and some innovative algorithms for calculating project completion time, which are not capable of considering all types of uncertainties. In this research, we developed some mathematical models to calculate the critical path and the activities’ float under normal conditions and time-cost trade-off.; In addition to validity check of the models, we developed an algorithm to generate extreme scenarios based on the interval values of the input parameters. The developed algorithm is able to generate the optimal interval for the values of the decision variables in the project schedule. Solving the scheduling problem of a real construction project involving more than 80 activities showed that if the input parameters of the problem were interval numbers, the values of the output decision variables of the models would often be interval numbers with a less degree of uncertainty. The spread of uncertainty and risks in the project is often linear. This means that with an optimal plan for the project schedule, most of the estimated errors and risks in the project would cause predictable behavior in uncertain decision variables especially, activities’ float.