On Completion Times of Networks of Concurrent and Sequential Tasks

The problem of determining the time to complete multiple tasks that may proceed concurrently, sequentially, or both is considered. In the solution offered, each individual task completion time may be described with a number, interval, or distribution function. In the case of distribution functions, two task completion times might be independent random variables, as when the tasks are performed in different environments and proceed independently. Alternatively, completion times might be positively correlated, as when both depend on the quality of management and proceed within the same managerial environment, or they could be negatively correlated, as when resource sharing means that faster completion of one implies slower completion of the other. Finally, various factors might interact to make completion times dependent in a way that is difficult to characterize accurately. The solution offered avoids assuming that individual task completion times are independent or have any other dependency relationship. One application of the results is in project management, as in the context of PERT (Program Evaluation and Review Technique) diagrams.