Order Retrieval in Compact Storage Systems

2025-10-15

AI Summary

This paper addresses the energy consumption optimization problem for cargo-bin retrieval in high-density urban environments under a channel-free, fully stacked compact automated storage and retrieval system (AS/RS). We first formulate a rigorous mathematical model and prove the problem’s strong NP-hardness. To solve it, we propose three complementary approaches: (i) a state-compression-based dynamic programming (DP) algorithm, (ii) an exact mixed-integer programming (MIP) formulation, and (iii) a real-time greedy heuristic tailored for low-latency operation. Numerical experiments demonstrate that the DP method significantly outperforms state-of-the-art MIP solvers on small-to-medium instances, while the greedy heuristic delivers high-quality near-optimal solutions within milliseconds on large-scale instances—substantially reducing lifting energy consumption. To the best of our knowledge, this work establishes the first theoretically sound and practically implementable optimization framework for retrieval energy minimization in compact AS/RS architectures.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments

Abstract

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.

Problem

• Optimizing energy consumption in compact storage bin retrieval
• Developing efficient algorithms for NP-complete retrieval optimization
• Enhancing automated storage systems through smart operational strategies

Innovation

• Automated bin retrieval using lifting mechanism
• Mathematical modeling for energy optimization
• Dynamic programming outperforms MIP solvers