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.

Multi-Agent Path Finding (MAPF) deals with the problem of finding collision-free paths for a set of agents, where each agent wants to move from its start location to its goal location on a shared graph. The paper addresses the question of how to model MAPF as a classical planning problem, specifically, how to encode various collision constraints. Several models in the PDDL modeling language are proposed and empirically compared.