Temporal Networks with Alternatives: Complexity and Model

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Temporal Networks play an important role in solving planning problems and they are also used, though not as frequently, when solving scheduling problems. In this paper we propose an extension of temporal networks by parallel and alternative branching. This extension supports modelling of alternative paths in the network; in particular, it is motivated by modelling alternative process routes in manufacturing scheduling. We show that deciding which nodes can be consistently included in this extended temporal network is an NP-complete problem. The ideas are presented using precedence networks, but we also show how they can be extended to simple temporal networks.