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Negative weights in network time model


Time does not go backward. A negative duration, such as “time period” at first sight is difficult to interpret. Previous network techniques (CPM/PERT/PDM) did not support negative parameters and/or loops (potentially necessitating recursive calculations) in the model because of the limited computing and data storage capabilities of early computers. Monsieur Roy and John Fondahl implicitly introduced negative weights into network techniques to represent activities with fixed or estimated durations (MPM/PDM). Subsequently, the introduction of negative lead and/or lag times by software developers (IBM) apparently overcome the limitation of not allowing negative time parameters in time model. Referring to general digraph (Event on Node) representation where activities are represented by pairs of nodes and pairwise relative time restrictions are represented by weighted arrows, we can release most restraints in constructing the graph structure (incorporating the dynamic model of the inner logic of time plan), and a surprisingly flexible and handy network model can be developed that provides all the advantages of the abovementioned techniques. This paper aims to review the theoretical possibilities and technical interpretations (and use) of negative weights in network time models and discuss approximately 20 types of time-based restrictions among the activities of construction projects. We focus on pure relative time models, without considering other restrictions (such as calendar data, time-cost trade-off, resource allocation or other constraints).


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Correspondence to Zoltán A. Vattai.

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This work was supported by the Hungarian National Research, Development and Innovation Fund (TUDFO/51757/2019-ITM, Thematic Excellence Program). Open access funding provided by Budapest University of Technology and Economics.

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Vattai, Z.A., Mályusz, L. Negative weights in network time model. Front. Eng. Manag. 9, 268–280 (2022).

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  • graph technique
  • network technique
  • construction management
  • scheduling