We develop a bicriteria model for the resource allocation problem in PERT networks, in which the total direct costs of the project as the first objective, and the mean of project completion time as the second objective are minimized. The activity durations are assumed to be independent random variables with either exponential or Erlang distributions, in which the mean of each activity duration is a non-increasing function of the amount of resource allocated to it. The direct cost of each activity is assumed to be a non-decreasing function of the amount of resource allocated to it. Finally, we use the goal attainment method to solve the related bicriteria optimal control problem numerically, by converting this problem to a related bicriteria nonlinear programming, and obtain the optimal values of the resources allocated to the activities.
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