Trucks carrying just-in-time parts for assembly plants need to be processed on the factory premises in a speedy manner to guarantee smooth operations, improve supply chain performance, and avoid demurrages. Traditionally, plant managers and logistics providers have long been dissatisfied with extensive waiting times and severe on-site congestion. In this context, we tackle the problem of scheduling a set of trucks arriving at an assembly plant to deliver parts to specific dock doors on the factory premises. Trucks must visit a given set of doors, and they have individual arrival and due dates. They should be scheduled such that the total weighted tardiness is minimal. We propose a mixed-integer programming model and develop bounding procedures and heuristics, which are shown to perform well in a computational study, yielding small optimality gaps in under a minute of runtime. Our tests also reveal that door assignment and time window management have a substantial impact on on-premise congestion.