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In this paper, we develop an approach to optimally allocate a limited nonrenewable resource among the activities of a project, represented by a PERT-Type Network (PTN). The project needs to be completed within some specified due date. The objective is to maximize the probability of project completion on time. The duration of each activity is an arbitrary discrete random variable and also depends on the amount of consumable resource allocated to it. On the basis of the structure of networks, they are categorized as either reducible or irreducible. For each network structure, an analytical algorithm is presented. Through some examples, the algorithms are illustrated  

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... 

This paper is concerned with the study of the constant due-date assignment policy in repetitive projects, where the activity durations are exponentially distributed random variables. It is then extended to the case where activity durations follow generalized Erlang distributions. The main feature of this research over the classical PERT networks is that the projects are generated according to a renewal process and share the same facilities. Our approach is first to obtain the project completion time distribution, for each generated project, by constructing a proper continuous-time Markov chain, and then to compute the optimal constant lead time for each particular project. The repetitive...