The autonomous shuttle and stacker crane (AC/SC) warehousing system, as a new automated deep-lane unit load storage/retrieval system, has been becoming more popular, especially for batch order fulfilment because of its high flexibility, low operational cost and improved storage capacity. This system consists of a shuttle sub-system that controls motion along the x-axis and a stacker crane sub-system that controls motion along the y-axis and z-axis. The combination of shuttles and a stacker crane performs storage and retrieval tasks. Modelling the parallel motion is an important design tool that can be used to calculate the optimal number of shuttles for a given configuration of the warehousing system. In this study, shuttle movements from one lane to another are inserted into the stock-keeping unit (SKU) task queue, and convert such that they are consistent with the retrieval tasks. The tasks are then grouped according to their starting lane, and converted to an assembly-line parallel job problem by analysing the operating mode with the objectives of minimising the total working time of the stacker crane and the wasted shuttle time. A time sequence mathematical model based on the motion of the shuttles and stacker crane is proposed, and an improved Pareto-optimal elitist non-dominated sorting genetic algorithm is used to solve this multi-objective optimization problem. The model is validated via a simulation study, and via a real-world warehousing case study. We go on to describe guidelines for the layout and configuration of AS/SC warehousing systems, including the optimal number of shuttles and number of x-axis storage cells of lanes, which can improve efficiency and minimise both capital investment and operating costs.
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