Optimal constrained non-renewable resource allocation in PERT networks with discrete activity times

In this paper, we develop an approach to optimally allocate a limited nonrenewable resourceamong the activities of a project, represented by a pert-type network (ptn). the project needs tobe completed within some specified due date. the objective is to maximize the probability of projectcompletion on time. the duration of each activity is an arbitrary discrete random variable and also dependson the amount of consumable resource allocated to it. on the basis of the structure of networks, theyare categorized as either reducible or irreducible. for each network structure, an analytical algorithm ispresented. through some examples, the algorithms are illustrated.