Joint optimization of storage assignment and order batching in robotic mobile fulfillment system with dynamic storage depth and surplus items

This paper studies the joint optimization of storage location assignment and order batching in robotic mobile fulfillment systems (RMFS), considering dynamic storage depth and surplus items. Firstly, a joint optimization model of storage location assignment and order batching is established. The model is divided into two stages. The first stage is the item location assignment optimization model, which is used to describe the types and quantities of items placed in each slot on each pod. The second stage is the joint optimization model of pod location assignment and order batching, which is used to describe the coordinates of each pod, the number of order batches, and the order combinations contained in each batch. Considering the vast solution space and the numerous constraints of the constructed model, a two-stage greedy variable neighborhood simulated annealing algorithm (TGVNSA) is introduced to address these challenges. Finally, numerical experiments prove that the algorithm can effectively solve the established model. TGVNSA is evaluated against two conventional methods: variable neighborhood search and adaptive genetic algorithms, focusing on metrics such as pod retrieval times, comprehensive picking costs, CPU time, and CQ value (comprehensive quality in the item location assignment). The findings demonstrate that TGVNSA boasts superior comprehensive performance. Compared with other commonly used strategies in the field such as random, classification, and optimal relevance, the method proposed in this paper demonstrates superior optimization performance, particularly when considering dynamic storage depth and surplus items. Moreover, this paper also proves that, under the same combination of strategies, the joint optimization method proposed in this paper reduces the comprehensive picking costs by 11.46% compared to the separate optimization approach.