On latest starting times and floats in activity networks with ill-known durations

This paper deals with fuzzy activity networks, where fuzzy intervals model uncertain durations of tasks, While it is easy to compute fuzzy earliest starting times of activities using 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 the framework of possibility theory. The main difficulty lies in the fact that the behavior of latest starting dates and slack times, as a function of task durations, is not straightforward to predict for general network 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.