Growing demand for sustainable logistics and higher space utilization, driven by e-commerce and urbanization, increases the need for storage systems that are both energy- and space-efficient. 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 and then accessing the target bin from the side of the system by a dedicated robot. Consequently, retrieving a bin can require substantial lifting effort, and thus energy. However, this energy can be reduced through smart retrieval strategies. From an operational perspective, we investigate how retrievals can be optimized with respect to energy consumption. We model the retrieval problem within 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, practitioner-oriented 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.

翻译：电子商务和城市化推动了对可持续物流和更高空间利用率的需求增长，从而增加了对节能和空间高效存储系统的需求。紧凑存储系统旨在最大化有限存储区域的空间利用率，因此特别适用于空间稀缺的人口密集城市地区。本文研究了一种最近引入的紧凑存储系统，其中统一形状的货箱直接堆叠在彼此之上，消除了用于处理物料的通道需求。目标货箱通过全自动流程进行检索：首先提升所有阻碍访问的其他货箱，然后由专用机器人从系统侧面访问目标货箱。因此，检索一个货箱可能需要大量的提升工作和能量消耗。然而，通过智能检索策略可以降低这种能量消耗。从运营角度出发，我们研究了如何优化检索以降低能耗。我们在数学框架内对检索问题进行了建模。我们证明了该问题是强NP完全的，并推导了结构特性。基于这些见解，我们提出了两种精确方法：混合整数规划（MIP）公式和动态规划算法，以及一种面向实践者的简单贪心算法，该算法能提供近乎即时的解决方案。数值实验表明，在中小规模实例中，动态规划算法始终优于最先进的MIP求解器，而贪心算法则能提供令人满意的性能，尤其是在精确方法计算上变得不切实际时。