Integrated process planning and scheduling (IPPS) can take advantage of the complementary attributes of process planning and shop scheduling to obtain better production schemes and process routes improving the whole performance of the manufacturing system. Additional consideration of the shop logistics system including task assignment of automated guided vehicles (AGVs) can improve shop productivity while ensuring the smooth running of the whole manufacturing system. This paper investigates an IPPS problem considering AGV transportation task (IPPS_T). Compared with the original IPPS, IPPS_T addresses not only the process selection, operation sequencing, and machine selection but also the transportation task assignment of the AGVs. Therefore, it is much more difficult than the IPPS problem which has already been proven to be NP-hard. The paper proposes an integrated encoding method to improve the integration of the manufacturing system by representing the process route, shop scheduling scheme, and transportation task assignment plan simultaneously in one individual. This paper designs an improved genetic algorithm (IGA) combining a critical path-based neighborhood searching strategy which can ensure the effectiveness of local search on both AGVs and machines. The numerical experiments with different numbers of AGVs are conducted on the open instances which are extended from the well-known Kim benchmark. The results obtained by the IGA show significant advantages proving the effectiveness of the proposed encoding method and critical path-searching strategy.