Efficient construction of “activity-on-arrow” project schedule with minumal number of fictive activities

There exist two basic types of project schedules: the “activity-on-node” schedules and “activity-on-arrow” ones. Transition from an “activity-on-arrow” schedule to the corresponding “activity-on-node” schedule is simple and unique, while the inverse transition, in general, is not unique and requires adding to the project fictive zero-time activities. We show that an “activity-on-arrow” schedule does not require zero-time activities, if lists of, so-called, supporting operations, either coincide or do not intersect. Otherwise we look for the lists being subsets of the others lists to minimize the number of zero-time activities being added to the schedule. The efficiency of the suggested method for minimization of the number of zero-time activities is verified for several important classes of test schedules, which include almost all elements met in typical projects.