Integrating transportation decisions into Integrated Process Planning and Shop Scheduling (IPPS) enables tighter coordination between machining operations and material handling, leading to more efficient production schedules. However, most existing IPPS studies assume homogeneous or unlimited transportation resources, and thus overlook the practical scheduling complexity introduced by heterogeneous and capacity-limited automated guided vehicle (AGV) fleets. This study proposes an IPPS model with a heterogeneous AGV transportation system (IPPSHT), in which process route selection, operation sequencing, machine assignment, and AGV allocation are jointly optimized under functional compatibility constraints between AGVs and machines. To solve the resulting bi-objective problem of minimizing makespan and total energy consumption across machining and transportation stages, we develop a high-performance memetic algorithm that combines tailored encoding/decoding, dominance-based selection, and problem-aware local improvement. Extensive experiments on 60 benchmark instances and an engineering case study demonstrate that the proposed method consistently outperforms three representative multi-objective evolutionary algorithms in terms of solution quality and statistical significance, indicating its effectiveness for complex manufacturing settings with heterogeneous material-handling resources.