Retrieval sequencing in autonomous vehicle storage and retrieval systems

Autonomous vehicle storage and retrieval systems (AVS/RSs) are widely used in e-commerce warehouses due to their high throughput and flexibility. In such systems, storage and retrieval transactions are performed by lifts and vehicles. This paper focuses on the sequencing retrievals problem in an AVS/RS, which is an important problem for daily operations. We formulate this sequencing problem as a mixed-integer program to determine a retrieval sequence for the lift and the vehicles, one that minimises the makespan. A dynamic programming approach is proposed to solve the sequencing problem to optimality. However, the solution time of the dynamic programming method is exponentially increasing in the number of retrieval requests. To be more practical, we present a beam search heuristic that can solve large-sized instances in reasonable time. Computational experiments verify that near-optimal solutions can be found by the beam search heuristic. Compared to commonly used heuristics and straightforward heuristics, the beam search decreases the makespan by up to 15%. Finally, we analyse how vehicle modes impact the makespan, showing evidence that a small makespan can be achieved when considering a realistic mode of vehicles.