Investigation of Critical Activities in a Network with Point-to-point Relations

Recently developed point-to-point relations have greatly extended the modeling capability of the Precedence Diagram Method. These relations can connect any inner (and extreme) points of the related activities. Furthermore, the definition of multiple relations is allowed between the same two activities. These features make point-to-point relations suitable for modeling overlapping activities more easily and with greater precision than it was possible before. However, there is a lot of work ahead. Although both proper mathematical modeling, and the algorithm that handles both minimal and maximal relations are available, re-investigation of well-known definitions for float, critical path, critical path metrics, classification of critical activities etc. are still missing. This paper deals with the investigation of the critical path. It describes the ways in which an activity can be part of the critical path. Collecting the possible cases provides the opportunity for classifying critical activities. The main result of the paper is that it provides a method for determining the type of the critical activity based on the relationships going in and out of the activity.