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This paper examines calculations of the earliest and the latest possible starting times for various tasks in a project. It considers classical precedence relationships with additional complications involving lead and lag times between tasks. Since the problem of analyzing large network diagrams with complicated relationships can become computationally intractable, there is a need for a mathematical formulation for the solution of this problem that would be transparent and easy to implement. Such a solution is proposed in this paper. It involves an introduction of the fault tree models with time dependencies. Such models were recently introduced in the context of equipment safety analysis and this paper adapts these concepts in the project management field of interest.
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