Towards the end of the fifties methods for planning, scheduling, and control of proj- ects were developed on the basis that the evolution of a project can be associated with a special weighted directed graph, called activity network. In this association, the individual activities of the project correspond to the arcs, the so-called proj- ect events (beginning or termination of activities) correspond to the nodes, and the durations of the activities correspond to the weights of the respective arcs of the directed graph. 1) Contiguous arcs are assigned to activities which succeed one another immediately. The event corresponding to a node occurs exactly at the time at which all activities which are associated with the arcs leading into the node are terminated. After the occurrence of an event all those activities are be- gun which correspond to the arcs emanating from the respective node. This implies especially that the evolution of the project has to be uniquely determined before- hand, that every activity and every event are realized exactly once during the exe- cution of the project, and that "feedback" (corresponding to cycles in the asso- ciated network) is not permitted. Many projects, for example most R&D projects and projects in the area of production p 1 anni ng, do not sa ti sfy the foregoi ng res tri cti ons.
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