Order Retrieval in a Compact Storage System with Side Access

Growing demand for sustainable logistics and higher space utilization, driven by e-commerce and urbanization, increases the need for storage systems that are efficient in time, energy and space. Compact storage systems aim to maximize space utilization in limited storage areas and are therefore particularly suited in densely-populated urban areas where space is scarce. In this paper, we examine a recently introduced compact storage system in which uniformly shaped bins are stacked directly on top of each other, eliminating the need for aisles used to handle materials. Target bins are retrieved in a fully automated process by first lifting all other bins that block access, creating a tunnel for a robot to enter the storage area from the side and to retrieve the target bin via the tunnel. While this process enables fast retrieval, it requires substantial lifting effort and, consequently, energy. Smart retrieval strategies can reduce this energy expenditure. From an operational perspective, we investigate how retrievals can be optimized with respect to energy consumption. We formulate the retrieval problem in a mathematical framework. We show that the problem is strongly NP-complete and derive structural insights. Building on these insights, we propose two exact methods: a mixed-integer programming (MIP) formulation and a dynamic programming algorithm, along with a simple greedy algorithm that yields near-instant solutions. Numerical experiments reveal that dynamic programming consistently outperforms state-of-the-art MIP solvers in small to medium sized instances, while the greedy algorithm delivers satisfactory performance, especially when exact methods become computationally impractical.