Operation time and rack stability optimisation in tier-to-tier shuttle-based storage and retrieval systems with multiple retrieval locations

Tier-to-tier shuttle-based storage and retrieval systems (t-SBS/RSs) are increasingly recognised in the industry for their enhanced flexibility, reduced costs, and improved shuttle utilisation. However, the ineffectiveness of task scheduling (TSc) and retrieval location assignment (LA) schemes diminishes retrieval efficiency and compromises rack stability, thereby elevating retrieval costs and jeopardising system operational safety. Moreover, a potential conflict has been identified between total operation time and rack stability during retrieval operations. Consequently, this study proposes a joint optimisation approach for the batch retrieval TSc and LA challenges in t-SBS/RS, accommodating multiple location distributions for identical cargo types. This issue is modelled as a multi-objective optimisation problem aimed at minimising total operation time while maximising rack stability. To address this, a non-dominated sorting genetic algorithm II (NSGA-II) enhanced by a prior knowledge-based initialisation strategy was proposed. Employing a real case study, several benchmark scenarios were established to assess the effectiveness of the proposed algorithm against five other algorithms, highlighting the superiority of NSGA-II. Additionally, the effectiveness of this method is validated by comparison with classical scheduling policies. The derived Pareto fronts verify the inherent conflict between the two objectives, suggesting that a trade-off is necessary. Finally, managerial insights are offered to highlight the practical application of these findings for warehouse managers.