• Wolfram Wiesemann
Part of the Advances in Computational Management Science book series (AICM, volume 11)


We define a temporal network as a directed, acyclic graph G=(V,E) whose nodes \(V = \left \{1,\ldots,n\right \}\) represent the network tasks and whose arcs EV ×V describe the temporal precedences between the tasks. This convention is known as activity-on-node notation; an alternative activity-on-arc notation is discussed in [DH02]. In our notation, an arc (i,j)∈E signalizes that task j must not be started before task i has been completed. For ease of exposition, we assume that 1∈V represents the unique source and nV the unique sink of the network. This can always be achieved by introducing dummy nodes and/or arcs. We assume that the processing of each task requires a nonnegative amount of time. Depending on the problem under consideration, the tasks may also give rise to cash flows. Positive cash flows denote cash inflows (e.g., received payments), whereas negative cash flows represent cash outflows (e.g., accrued costs). Figure 1.1 illustrates a temporal network with cash flows.


Cash Flow Project Schedule Temporal Network Task Duration Network Task 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of ComputingImperial College LondonLondonUK

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