Introduction

Abstract

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 E⊆V ×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 n∈V 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.