In many real-life high-variety make-to-order shops, jobs are physically transported from one station to another, and transportation capacity may constrain order progress on the shop floor. Yet, the material handling literature on vehicle assignment rules remains largely inconclusive on which rule to apply, and it neglects order release control. Similarly, and despite the importance of material handling, its impact is widely neglected in the order release literature. In response, this study assesses the combined performance effect of vehicle assignment, order release and dispatching rules. It uses discrete event simulation. Results show that assigning a vehicle to the station with the largest outgoing queue leads to the best performance. This simple vehicle assignment rule has been largely neglected in the literature since the 1980s. In contrast, the two rules that have received the most attention in the literature -the shortest distance and first-come-first-served rules -lead to the worst performance. Meanwhile, order release has a direct detrimental performance effect in pure job shops with material handling constraints. This identifies an important contingency factor so far neglected in the literature that assesses the applicability of order release. More specifically, the use of order release should be restricted to general flow shops with more directed routings since, in these contexts, it can reduce throughput times without jeopardizing tardiness performance.