Constrained Non-Renewable Resource Allocation in Metagraphs with Discrete Random Times

In this paper, it is supposed that a project can be shown as a metagraph. The duration of activities are discrete random variables with known probability function, also one kind of consumable and constrained resource is required to execute each activity of the project. Besides, the probability functions of activity durations depend on the amount of the resource allocated to it. Clearly, the amount of resource which can be allocated to each activity is limited to specific values. In this paper, it is assumed that the due date of project is known and definite. The objective of this paper is to maximize the probability of completion of stochastic metagraph before the due date of the project. As respects, solving the problem by using the analytical method is very challenging; therefore, we developed a new heuristic method including two sub-algorithms for solving the problem. Twenty examples were designed for examining the proposed algorithm.