A scheduling model and complexity proof for autonomous vehicle sequencing problem at isolated intersections

In this paper, we study the complexity of an autonomous vehicle sequencing problem under the framework of Autonomous Intersection Management (AIM). Since the objective is to schedule all approaching vehicles to pass this intersection in the shortest duration, we model the general version of this problem as a single machine scheduling problem in which jobs can be processed in parallel. Release date and chain constraint are also considered. We show that this problem is strongly NP-hard for arbitrary number of families.