  We present alternative approaches to routing and scheduling in Answer Set
Programming (ASP), and explore them in the context of Multi-agent Path Finding.
The idea is to capture the flow of time in terms of partial orders rather than
time steps attached to actions and fluents. This also abolishes the need for
fixed upper bounds on the length of plans. The trade-off for this avoidance is
that (parts of) temporal trajectories must be acyclic, since multiple
occurrences of the same action or fluent cannot be distinguished anymore. While
this approach provides an interesting alternative for modeling routing, it is
without alternative for scheduling since fine-grained timings cannot be
represented in ASP in a feasible way. This is different for partial orders that
can be efficiently handled by external means such as acyclicity and difference
constraints. We formally elaborate upon this idea and present several resulting
ASP encodings. Finally, we demonstrate their effectiveness via an empirical
analysis.
