High performance heuristic algorithm for controlling stochastic network projects

An activity-on-arc network project of PERT type with random activity durations is considered. The progress of the project cannot be inspected and measured continuously, but only at preset inspection points. An on-line control model has to determine both inspection points and control actions to be introduced at those points to alter the progress of the project in the desired direction. On-line control is carried out to minimize the number of inspection points needed to meet the target, subject to the chance constraint. In the recently developed control models, determining the next inspection point is carried out via extensive simulation with a constant time step. This determination is based on sequential statistical analysis at each intermediate point to maximize the time span between two adjacent control points. The main shortcoming of the control algorithm is its long computational time due to the need to make numerous decisions. In this paper we present a newly developed heuristic control algorithm in which the timing of inspection points does not comprise intermediate decision making. Given a routine inspection point t_i the adjacent point t_i+1 is determined so that even if the project develops most unfavorably in the interval [t_i, t_i+1], introducing proper control action at moment t_i+1 enables the project to meet its target on time, subject to the chance constraint. The newly developed control algorithm is essentially more efficient than the step-by-step control procedures. The computational time is reduced by a factor of 25-30 while the algorithm provides better solutions than would be attained by using on-line sequential statistical analysis. Extensive experimentation has been undertaken to illustrate the comparative efficiency of the presented algorithm.