In manufacturing shops in practice, machine capacity is often constrained by more than one type of resource. Yet research mainly focusses on the effects of only one type of resource that constrains machine capacity, e.g. labour, tooling or auxiliary constraints. In response, we use simulation to assess the impact of order release, dispatching and resource assignment rules in make-to-order job shops with multiple resource constraints. The capacity wasted while a machine stands idle waiting for other resources increases with the number of constraints, and all three production planning and control functions have little impact on this waiting time. Effective production planning and control can however improve operational performance in terms of time and tardiness-related measures. In general, combining order release control with a dispatching rule that prioritises jobs for which all resources are available at dispatching and a longest queue resource assignment rule leads to the best performance. Most importantly, and rather counterintuitively, prioritising orders with the fewest missing resources worsens the performance of both the dispatching and resource assignment rule since it reduces resource utilisation during periods of high load. Results from dual resource-constrained shops are consequently not directly transferable to more complex resource-constrained shops.