A genetic algorithm approach for the time–cost trade-off in PERT networks

We develop a multi-objective model for the time–cost trade-off problem in PERT networks with generalized Erlang distributions of activity durations, using a genetic algorithm. The mean duration of each activity is assumed to be a non-increasing function and the direct cost of each activity is assumed to be a non-decreasing function of the amount of resource allocated to it. The decision variables of the model are the allocated resource quantities. The problem is formulated as a multi-objective optimal control problem that involves four conflicting objective functions. The objective functions are the project direct cost (to be minimized), the mean of the project completion time (min), the variance of the project completion time (min), and the probability that the project completion time does not exceed a certain threshold (max). It is impossible to solve this problem optimally. Therefore, we apply a ‘Genetic Algorithm for Numerical Optimizations of Constrained Problems’ to solve this multi-objective problem using a goal attainment technique. Several factorial experiments are performed to identify appropriate genetic algorithm parameters that produce the best results within a given execution time in the three typical cases with different configurations. Finally, we compare the genetic algorithm results against the results of a discrete-time approximation method for solving the original optimal control problem.