Fuzzy PERT in series-parallel graphs

Abstract

This paper deals with the fuzzy project scheduling approach, where fuzzy intervals model uncertain durations of tasks. While it is easy to compute fuzzy earliest starting dates of tasks in the critical path method, the problem of determining latest starting dates and slack times is much more tricky and has never been solved in a fully satisfactory manner in the past. Here, we propose a rigorous treatment of this problem in series-parallel graphs, in the framework of possibility theory. The main difficulty lies in the fact that the variation of latest starting dates and slack times, as a function of task durations, is not straightforward to predict for general graph topologies. However, it is easier in the case of series-parallel graphs. The case of interval-valued durations is first addressed, and then extended to fuzzy intervals.

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