Continuous Precedence Relations for Better Modelling Overlapping Activities

Abstract

Theoretically proper modeling of overlapping activities with traditional precedence relationships is impossible. This is due to the fact that traditional precedence relations create logic between the endpoints of activities. In contradiction, overlapping can be defined as a ‘continuous’ relation using time or location/production units between all the points of the predecessor and all the points of the successor activities. (E.g. at least 50 m safety distance is necessary between activity B and A during execution.) Recently developed point-to-point relations give a practically better solution, as they let planners form connections among as many internal points of the related activities as seemingly necessary, and all these points can be controlled during the execution phase. However, a theoretically proper solution is only available if an infinite number of point-to-point relations are used between two overlapping activities, but this is obviously impossible. The novelty of this paper is the definition of a new type of precedence relation for the Precedence Diagram Method (PDM), the so-called continuous relation. One continuous relation can be used instead of infinite point-to-point relations in order to perfectly model activity overlapping. Relation lags can be defined using either time or volume units. Another main advantage of this development is that continuous relations enable the definition of non-linear activities, while original PDM assumes continuous linear activities only.

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