Time-cost trade-off in PERT networks using a genetic algorithm

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 project completion time (min), the variance of 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 (GENOCOP) to solve this multi-objective problem, using goal attainment technique.