A Bi-level optimization method for integrated warehouse design, storage location assignment, and order picking

This study proposes a novel bi-level optimization model for integrated warehouse planning, encompassing shelving technology selection, storage location assignment, and order picking decisions. Unlike previous studies that have largely treated these components in isolation, this research addresses the interdependencies across strategic, tactical, and operational planning horizons in a unified framework. The proposed model captures the complex interaction between layout design and real-time order fulfillment processes, ensuring a holistic optimization of warehouse performance. At the upper (leader) level, the model determines the optimal allocation of available space to three shelving technologies-wide-aisle pallet racks, narrow-aisle pallet racks, and mobile racks-based on construction costs and space utilization efficiency. These technologies differ significantly in setup costs, equipment requirements, and spatial constraints. The goal of the leader model is to minimize construction costs while meeting shelf capacity needs driven by fluctuating input/output volumes. At the lower (follower) level, the model integrates item-to-location assignment and order picking path optimization, taking into account probabilistic inbound and outbound flows over multiple periods. Product allocation to storage positions and transportation equipment is optimized with respect to equipment capacities and inventory dynamics. Additionally, the follower model includes constraints for order balancing, product placement and retrieval, vehicle loading, and sub-tour elimination in picking paths. The required shelf capacity, initially assumed as an input, is iteratively updated based on the follower's output and reintroduced to the leader level, enabling a feedback-driven optimization loop. To solve this hierarchical problem structure, an enumerative heuristic method is adopted. The leader's solution space is discretized, and for each candidate solution, the follower model is solved using GAMS. This approach enables the identification of near-optimal configurations with manageable computational effort while maintaining solution feasibility and interpretability. The innovations of this study are threefold: (1) it is among the first to integrate all three critical components of warehouse planning-shelving technology, storage location assignment, and order picking-in a bi-level structure; (2) it incorporates probabilistic modeling to account for demand uncertainty in each planning period; and (3) it proposes a practical solution methodology that balances cost, performance, and computational tractability. Numerical results show that the integrated model significantly outperforms traditional sequential approaches by reducing construction and transportation costs and improving space utilization. Sensitivity analyses confirm the robustness of the model in response to variations in demand patterns and transportation costs. The proposed framework offers warehouse designers and decision-makers a practical and data-driven tool for optimizing warehouse layout and operations under uncertainty.