An autonomous-steerable-vehicle storage and retrieval system is a new storage conception, which has high space utilization and can dispatch its equipments flexibly. To achieve efficient and low-cost operations, the equipment dispatch and task assignment should be designed according to the requirements of the warehouse. In this paper, the inbound and outbound processes of the autonomous-steerable-vehicle storage and retrieval system are modeled as queue networks, which include several service centers. The equipments in each service center are dispatched to ensure the steady state of the system. A fuzzy controller based on the expected time of handling palletized units is designed, which can assign the palletized units to the optimal lifters in inbound and outbound process. In this method, the number of forklift can be reduced due to the reduction of the handling distance in the inbound and outbound processes, so that it decreases the operation cost and heightens the operation efficiency. At last, an example simulation of inbound process is shown to verify the validness of the method in the task assignment.