A multi-objective resource allocation problem in PERT networks

We develop a multi-objective model for resource allocation problem in PERT networks with exponentially or Erlang distributed activity durations, where the mean duration of each activity is a non-increasing function and the direct cost of each activity is 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 total direct costs of the project (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). The surrogate worth trade-off method is used to solve a discrete-time approximation of the original problem.