Abstract:

With the rapid advancement and widespread adoption of E-commerce， online shopping has become an integral component of modern life. However， the unique characteristics of online orders pose significant challenges to warehouse operational efficiency. A primary concern is the heightened consumer demand for timely deliveries， particularly with the increasing prevalence of next-day and same-day delivery services， which substantially amplify delivery complexities. Additionally， the sheer volume of daily orders， each typically comprising multiple stock-keeping units （SKUs）， coupled with the overlap of SKUs across different orders， further complicates the process. Moreover， real-time orders often originate from diverse geographic regions， introducing additional logistical challenges. These factors collectively exert considerable pressure on the order picking and delivery systems of E-commerce enterprises. According to Statista， during 2020–2021， over 4.5% of Amazon orders experienced delays. In traditional picker-to-parts systems， pickers spend approximately 60% of their time traveling within the warehouse. To enhance efficiency and reduce operational costs， E-commerce platforms have increasingly adopted automated order picking systems， such as parts-to-picker systems or robotic mobile fulfillment systems （RMFS）， exemplified by Amazon’s Kiva system and JD.com’s Ground wolf system. Motivated by these operational challenges， this study focuses on optimizing decision-making processes in intelligent warehouses with delivery deadlines to minimize total order tardiness.

Key operational challenges include order assignment， order sequencing， and rack visit sequencing. （i） Order assignment： In warehouses with multiple parallel picking stations， balancing workloads and optimizing efficiency across stations is critical due to variations in order sizes， SKU compositions， and delivery due dates. （ii） Order sequencing： Orders arrive with varying due dates， necessitating prioritization of urgent orders to reduce the likelihood of tardiness. （iii） Rack visit sequencing： Adjacent orders at a picking station may share common SKUs， enabling simultaneous retrieval. However， since each rack carries only one type of SKU， determining the optimal sequence for retrieving SKUs—equivalent to sequencing rack visits—becomes a pivotal issue.

To address these challenges， this study formulates a mixed-integer programming model aimed at minimizing total order tardiness in parts-to-picker systems with delivery due dates. Leveraging the model’s characteristics， an improved knowledge-guided fruit fly optimization algorithm （IKGFOA） is proposed to determine optimal order allocation and sequencing schedules. The algorithm incorporates heuristic rules to accelerate solution convergence and introduces a knowledge-guided search mechanism to balance local and global search capabilities， thereby enhancing the rationality of order assignment and sequencing decisions. Additionally， a shortest waiting time （SWT） rule is designed to optimize order picking and rack visit sequences at each picking station.

The feasibility of the proposed model and the effectiveness of the algorithm are validated through numerical experiments. Small-scale experiments demonstrate that the IKGFOA-SWT algorithm achieves solutions comparable to those obtained by CPLEX under certain conditions. Large-scale experiments further confirm the algorithm’s superiority over the commonly used first-come-first-served （FCFS） strategy in real-world applications. The model and algorithms developed in this study provide E-commerce enterprises with scientifically robust decision-making tools， emphasizing the importance of incorporating delivery due dates into operational optimization strategies to minimize order tardiness in intelligent warehouses.

Key words: “parts-to-picker” order picking, delivery due dates, knowledge-guided, fruit fly optimization algorithm, heuristic algorithm