How many types of critical activities exist? A conjecture in need of proof

摘要

The Precedence Diagramming Method (PDM) is the prevalent scheduling technique used for temporal planning of projects. Critical paths require special attention during the course of planning as their lengths define the project duration. However, increasing/decreasing the duration of an activity on the critical path does not necessarily results in a longer/shorter project duration. Responses of the critical path in a PDM network for small changes of the duration of a critical activity can be classified into six categories, while nine different possible categories exist in theory. The modeling capabilities of PDM recently have been extended by the introduction of a) point-to-point relations, b) continuous relations, and c) non-linear activity (production-time) functions. The paper presents the following conjecture that needs a proof: The number of existing types of critical activities remains six when using the recently developed precedence relations and non-linear production-time functions for activities. The theory of the different types of critical activities is briefly discussed and the mathematical model of the generalized PDM technique is presented. An additional feature presented in the paper beyond defining the conjecture is the introduction of influence lines for project duration that have never been used in project management before. Influence lines can be of great help in understanding the nature of critical activities. Papers providing solutions or confuting this conjecture will be honored with the CCC 2017 award.