A rule for slack allocation proportional to the duration in a PERT network

In this paper, we define a new rule for the resolution of the slack allocation problem in a PERT network. This problem exists of allocating existing extra time in some paths among the activities belonging to those paths. The allocation rule that we propose assigns extra time to the activities proportionally to their durations in such a way that no path duration exceeds the completion time of the whole project. This time allocation enables us to make a schedule for the PERT project under study. We give two characterizations of the rule and we compare it with others that have been previously defined in the literature.