arXiv subjects

George Dunn

Publications and source records attributed to George Dunn.

9 recordsLinked to original sources

arXiv2026

Exact formulations for rectangular-warehouse single-picker routing with scattered storage in single-block and two-block layouts

Order picking travel dominates much of warehouse effort, and exact routing is especially valuable when storage is scattered so pick locations are not fixed in advance. We address the single picker routing problem (SPRP) and its scattered-storage variant (SPRP-SS) in single-block and two-block rectangular warehouses. We propose two mixed-integer linear programming formulations that exploit structural properties of optimal tours to simplify connectivity modelling and remove redundant edge configurations: a Configuration Connectivity model tailored to single-block layouts and an Edge Connectivity model that extends to two-block layouts. In extensive computational experiments on large randomly generated benchmark sets for single-block and two-block rectangular layouts, we compare these formulations against established MILP and network-flow baselines for SPRP and SPRP-SS and report computational gains tied to the structural restrictions. The results support using compact, solver-based exact routing models in industrial settings where dynamic programming is cumbersome to integrate, particularly for SPRP-SS and for routing subproblems embedded in larger planning or warehouse-design optimizations.

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arXiv2026

Modified Dynamic Programming Algorithms for Order Picking in Single-Block and Two-Block Rectangular Warehouses

Recent research has shown that optimal picker tours in rectangular warehouses exhibit deterministic travel patterns within each aisle, and that certain previously considered traversals are unnecessary. Using these insights, this paper proposes modifications to dynamic programming algorithms that improve computational efficiency without affecting optimality. For layouts with and without a central cross-aisle, the modifications preserve linear-time complexity in the number of aisles while reducing the number of state-action evaluations per stage. The proposed modifications reduce computational effort by factors up to 1.81, confirmed by numerical experiments. These findings are encouraging and highlight how structural refinements can yield significant improvements in practical performance of algorithms.

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arXiv2025

Double Traversals in Boundary Subaisles: Implications for Two-Block Layouts

The order picking problem seeks the shortest warehouse route that visits all required item locations. Strict conditions are known for single-block rectangular layouts under which optimal routes never require double traversals, while broader results show that double traversals serving cross-aisle connectivity can always be avoided. We strengthen these findings by proving that no double traversals are needed in the boundary subaisles, the uppermost and lowermost subaisle segments, of warehouses with at least two non-empty aisles. This yields a unified strict condition for all single-block layouts and for two-block layouts with more than one aisle. For these widely used layouts, exact methods such as dynamic programming and mathematical programming can therefore exclude the double-traversal configuration from every boundary subaisle, reducing the number of admissible edge configurations without loss of optimality.

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arXiv2025

Deterministic Structure of Vertical Configurations in Minimal Picker Tours for Rectangular Warehouses

The picker routing problem seeks the shortest tour through a warehouse that visits every item in a given pick-list and returns to the depot. For rectangular warehouses, dynamic programming algorithms solve this problem by sequentially evaluating combinations of vertical edge configurations within subaisles and horizontal edge configurations between aisles. These methods proceed through stages one after another, but how those stages relate to each other has received limited structural analysis. Building on our recent structural result for rectangular warehouses, which shows that connecting double traversals are not required to maintain tour connectivity, we prove that for rectangular warehouses of any size, the horizontal edge structure of a minimal tour subgraph uniquely determines the required vertical edge configurations. The proof uses a case analysis on horizontal degree along each aisle and at merged-segment endpoints, showing that the admissible vertical pattern in each regime is uniquely determined by Eulerian parity and by minimizing traversal length. This deterministic relationship implies that vertical configuration stages in existing dynamic programming algorithms can be replaced by a direct inference step, reducing the combinatorial complexity of the problem and providing a structural foundation for developing more efficient exact methods for warehouse layouts of any size.

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arXiv2025

Double Traversals in Optimal Picker Routes for Warehouses with Multiple Blocks

Order picking is a process that involves collecting items from their respective locations within a warehouse. There exist dynamic programming algorithms for finding the minimal picker route by considering only a limited number of options for possible travel within a subaisle. Although one such action, traversing an aisle twice, has been shown to never be required for a rectangular warehouse with two cross-aisles, this is not the case when there are more than two cross-aisles. In this work, we demonstrate that double traversals within a subaisle are not required to connect cross-aisle travel regardless of the number of cross-aisles. This result simplifies the structure of feasible tours, enabling more efficient algorithms.

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arXiv2024

A Modified Algorithm for Optimal Picker Routing in a Single Block Warehouse

The order picker routing problem involves finding the optimal tour of a warehouse that collects all the required items on a given pick list. Ratliff and Rosenthal introduced a dynamic programming algorithm for solving this problem in polynomial time by sequentially adding edges inside and between each aisle to construct a tour. We provide a method where only transitions from one aisle to the next are considered, significantly reducing the number of stages in the algorithm.

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arXiv2024

Deep Reinforcement Learning for Dynamic Order Picking in Warehouse Operations

Order picking is a pivotal operation in warehouses that directly impacts overall efficiency and profitability. This study addresses the dynamic order picking problem, a significant concern in modern warehouse management, where real-time adaptation to fluctuating order arrivals and efficient picker routing are crucial. Traditional methods, which often depend on static optimization algorithms designed around fixed order sets for the picker routing, fall short in addressing the challenges of this dynamic environment. To overcome these challenges, we propose a Deep Reinforcement Learning (DRL) framework tailored for single-block warehouses equipped with an autonomous picking device. By dynamically optimizing picker routes, our approach significantly reduces order throughput times and unfulfilled orders, particularly under high order arrival rates. We benchmark our DRL model against established algorithms, utilizing instances generated based on standard practices in the order picking literature. Experimental results demonstrate the superiority of our DRL model over benchmark algorithms. For example, at a high order arrival rate of 0.09 (i.e., 9 orders per 100 units of time on average), our approach achieves an order fulfillment rate of approximately 98%, compared to the 82% fulfillment rate observed with benchmarking algorithms. We further investigate the integration of a hyperparameter in the reward function that allows for flexible balancing between distance traveled and order completion time. Finally, we demonstrate the robustness of our DRL model on out-of-sample test instances.

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arXiv2024

Deep Reinforcement Learning for Picker Routing Problem in Warehousing

Order Picker Routing is a critical issue in Warehouse Operations Management. Due to the complexity of the problem and the need for quick solutions, suboptimal algorithms are frequently employed in practice. However, Reinforcement Learning offers an appealing alternative to traditional heuristics, potentially outperforming existing methods in terms of speed and accuracy. We introduce an attention based neural network for modeling picker tours, which is trained using Reinforcement Learning. Our method is evaluated against existing heuristics across a range of problem parameters to demonstrate its efficacy. A key advantage of our proposed method is its ability to offer an option to reduce the perceived complexity of routes.

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arXiv2021

Average-reward model-free reinforcement learning: a systematic review and literature mapping

Reinforcement learning is important part of artificial intelligence. In this paper, we review model-free reinforcement learning that utilizes the average reward optimality criterion in the infinite horizon setting. Motivated by the solo survey by Mahadevan (1996a), we provide an updated review of work in this area and extend it to cover policy-iteration and function approximation methods (in addition to the value-iteration and tabular counterparts). We present a comprehensive literature mapping. We also identify and discuss opportunities for future work.

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