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 goat 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.

In this paper, we apply the stochastic dynamic programming to approximate the mean project completion time in dynamic Markov PERT networks. It is assumed that the activity durations are independent random variables with exponential distributions, but some social and economical problems influence the mean of activity durations. It is also assumed that the social problems evolve in accordance with the independent semi-Markov processes over the planning horizon. By using the stochastic dynamic programming, we find a dynamic path with maximum expected length from the source node to the sink node of the stochastic dynamic network. The expected value of such path can be considered as an approximation for the mean project completion time in the original dynamic PERT network.

In this paper an approach to approximate completion time distribution function (CTDF) for stochastic PERT networks is presented. This approach is made with most critical path (MCP) definition and a renewal process. In some cases, the results of this approach is better than Soroush’s algorithm that uses only MCP for computation of CTDF. Numerical examples are given and conclusions are made.

The optimal allocation of limited resource among the activities of a project, represented by a PERT-type network (PTN) is studied in this paper. The project needs to be completed within some specified period of time. The objective is to maximize the probability of project completion on time. The duration of each activity is a random variable and also depends on the amount of the consumable resource allocated to it. We develop an analytical approach consists of some algorithms to obtain the optimal solution. Then, for large and complex networks a hybrid approach is also developed by integrating conditional Monte Carlo simulation with our analytical method. The proposed approach is illustrated through some examples.

In this paper, an analytical method is developed to compute the project completion time distribution in a dynamic PERT network, where the activity durations are exponentially distributed random variables. The projects are generated according to a renewal process and share the same facilities. Thus, these projects cannot be analyzed independently. The authors' approach is to transform this dynamic PERT network into a stochastic network and. then, to obtain the project completion time distribution by constructing a proper continuous-time Markov chain. This dynamic PERT network is represented as a network of queues, where the service times represent the durations of the corresponding activities and the arrival stream to each node follows a renewal process. Finally, the proposed methodology is extended to the generalized Erlang activity durations.

In conventional PERT analyses, using beta distribution as underlying distribution for activity durations, the mean and variance of activity durations are estimated using optimistic, pessimistic, and probable estimates given by an exPERT. In order to improve these estimates, various methods have been proposed. In this paper, we propose a new model, whose estimate of the mean of activity durations is more accurate than original PERT estimates and its modifications. In addition, the proposed method does not rely on any assumptions on beta parameters.