We suggest an extension of the shifting bottleneck heuristic for complex job shops that takes the operations of automated material-handling systems (AMHS) into account. The heuristic is used within a rolling horizon approach. The job-shop environment contains parallel batching machines, machines with sequence-dependent setup times, and re-entrant process flows. Jobs are transported by an AMHS. Semiconductor wafer fabrication facilities (wafer fabs) are typical examples for manufacturing systems with these characteristics. Our primary performance measure is total weighted tardiness (TWT). The shifting bottleneck heuristic (SBH) uses a disjunctive graph to decompose the overall scheduling problem into scheduling problems for single machine groups and for transport operations. The scheduling algorithms for these scheduling problems are called subproblem solution procedures (SSPs). We consider SSPs based on dispatching rules. In this paper, we are also interested in how much we can gain in terms of TWT if we apply more sophisticated SSPs for scheduling the transport operations. We suggest a Variable Neighbourhood Search (VNS) based SSP for this situation. We conduct simulation experiments in a dynamic job-shop environment in order to assess the performance of the suggested algorithms. The integrated SBH outperforms common dispatching rules in many situations. Using near to optimal SSPs leads to improved results compared with dispatching based SSPs for the transport operations.