Negative weights in network time model

Abstract

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).

Dynamic Multiscale Information Spillover among Crude Oil Time Series

“…The net information spillover matrix for all series in a scale is mapped into an information spillover network based on network theory [ 26 , 27 , 28 , 29 ], where the node is the oil series and the weighted directed edge is the net information spillover from one series to the other.…”