Retrieval scheduling in crane-based 3D automated retrieval and storage systems with shuttles

Retrieval task scheduling has been extensively studied for 2D automated retrieval and storage systems (AS/RS). A good schedule can significantly reduce the makespan for finishing a given group of retrieval tasks. However, the task scheduling problem has never been studied for crane-based 3D AS/RS with shuttle-based depth movement mechanisms (DMMs), which has become increasingly popular in practice. This study considered how to schedule a group of retrieval requests in a crane-based 3D AS/RS with shuttle-based DMMs with the objective to minimize the makespan. A mixed-integer programing model was developed to represent the problem, and the problem was proven to be NP-hard. Four heuristics were investigated for their computational performance. First-Come-First-Serve is the current practice while the Percentage Priority to Shuttle Reallocation with the Shortest Leg rule was developed based on the existing rule for scheduling storage and retrieval tasks in 3D AS/RS with conveyor-based DMMs. The Genetic Algorithm, which is popular for 2D systems, was adapted to deal with the 3D system. The Lowest-Waiting-Time-First heuristic was proposed based on the optimality condition of the scheduling problem and was demonstrated to outperform the other three algorithms in terms of solution quality and computational time. Further numerical results revealed insights for improving 3D AS/RS productivity. When the number of retrieval tasks is small (e.g., when a short planning horizon is adopted for high responsiveness), having more shuttles can improve the system performance. When there are many tasks to schedule, for example, in a situation with a long planning horizon, using a crane with higher speed rather than adding more shuttles can improve system efficiency more.