Picker Routing Problem Research Articles

Picker routing in scattered storage warehouses: an evaluation of solution methods based on TSP transformations

AbstractTo optimize their order fulfillment processes, many e-commerce warehouses employ a storage assignment strategy known as scattered or mixed-shelves storage. Under this approach, unit loads of homogeneous products are divided, and individual pieces are stored in various shelves throughout the warehouse. This arrangement ensures that products that appear together on unpredictable pick lists are stored in close proximity somewhere in the huge warehouses, reducing the travel distance for pickers. Despite these advancements, efficiently guiding pickers through the warehouse remains a significant planning challenge. Since the same products can be found in multiple storage positions, the traditional picker routing problem becomes more complex, as an additional selection task arises regarding which shelf to retrieve each requested product from. While previous research has developed several tailor-made solution algorithms, we demonstrate that known transformation schemes used for different variants of the well-known Traveling Salesman Problem (TSP) can be utilized to convert the single picker routing problem with scattered storage (SPRP-SS) into a classical TSP. This approach enables us to leverage the extensive array of state-of-the-art TSP solvers. The purpose of this paper is to explore the performance of these solvers when applied to solving the SPRP-SS. Through our computational study, we found that existing TSP solvers exhibit good performance, allowing near-optimal solutions to be obtained in less than a second for real-world scale SPRP-SS instances. Moreover, the efficiency of these TSP solvers remains unaffected by the number of cross aisles in the warehouse. Consequently, we exploit this flexibility to investigate the impact of cross aisles on picking performance in scattered storage warehouses.

The picker routing problem in mixed-shelves, multi-block warehouses

Unlike conventional warehouses, where the inventory of an item is concentrated on a single shelf, the inventory in mixed-shelves warehouses is broken down into units and dispersed throughout the warehouse. As a result, the locations from where items are to be retrieved must be chosen when designing the picker tour. The rare research on the picker routing problem (PRP) in mixed-shelves warehouses focuses on (and heavily exploits the properties of) 1-block warehouses, which are warehouses with only two cross aisles. Here, we tackle the more general PRP in mixed-shelves, multi-block warehouses. To solve the problem, we propose a logic-based Benders decomposition method whereby the master problem selects the locations from where each item is retrieved and the subproblem designs the associated picker tour. We introduce tailored optimality cuts and prove their validity. In addition, we propose a set of various techniques to enhance the performance of the logic-based Benders decomposition, including a lower bounding function and valid inequalities. We show the efficiency and effectiveness of the proposed method through extensive computational experiments carried out on both standard instances from the literature (for the 1-block setting) and newly generated instances (for our case). We also leverage our algorithms to generate managerial insights into the benefits of multi-block layouts and mixed-shelves policies in warehousing.

Neural Combinatorial Optimization on Heterogeneous Graphs: An Application to the Picker Routing Problem in Mixed-shelves Warehouses

Neural Combinatorial Optimization on Heterogeneous Graphs: An Application to the Picker Routing Problem in Mixed-shelves Warehouses

The single picker routing problem with scattered storage: modeling and evaluation of routing and storage policies

Despite ongoing automation efforts, most warehouses are still manually operated using a person-to-parts collection strategy. This process of collecting items of customer orders from different storage locations accounts for the majority of the operating costs of the warehouse. Hence, optimizing picker routes is an important instrument to reduce labor costs. We examine the scattered-storage variant of the single picker routing problem in a one-block parallel-aisle warehouse. With scattered storage, an article can be stored at several storage locations within the warehouse, whereas with classic storage, each article has a unique storage location. We use our recently published network-flow model with covering constraints that is based on an extension of the state space of the dynamic-programming formulation by Ratliff and Rosenthal. With modifications in the state graph, this model serves for both exact and all established heuristic routing methods for picker routing. The latter include traversal, return, largest gap, midpoint, and composite. We show that these routing policies can also be implemented through adaptations in the state space. Extensive computational studies highlight a comparison of the different routing and storage policies (in particular class-based storage policies) in the scattered storage context. Analyses demonstrate which combinations of policies are advantageous for the given warehouse layout. For class-based storage policies, we emphasize how the scattering of articles of different classes should be performed: scattering of C-articles is advantageous with reductions of up to 25%. In contrast, when articles are uniformly distributed, A-articles should be scattered.

Joint green dynamic order batching and picker routing problem using PSO with global worst experience

With the increasing importance of various countries’ initiatives on reducing carbon emissions (e.g., carbon border adjustment mechanism, CBAM), intelligent order picking systems have assisted electronic retailers in realizing a green supply chain. Previous studies on picker routing operations focused on adopting offline static customer order information to carry out operational decisions. However, in practice, the customer order information is updated dynamically; and high-efficiency warehouse layouts have been increasingly concerned. Therefore, this study creates a mixed-integer programming model for minimizing both the total carbon footprint and the total penalty cost for delayed orders in the joint order batching and picker routing problem with dynamic arriving orders and shipping time constraints in a high-efficiency fishbone warehouse layout. To solve this complex problem, a particle swarm optimization algorithm that integrates the swarm’s previous global and local worst experiences and a migration mechanism is further proposed to increase solution quality and computing efficiency. In addition, a three-dimensional space for the warehouse floorplan and shipping time constraints is designed to divide orders into batches to address the constraints. Theoretical analysis of this algorithm is conducted, and experimental analysis shows that this algorithm finds superior solutions than current practical strategies, to offer a valuable reference for carbon emission reduction in greening warehousing.

Learning-Aided Iterated Local Search Algorithm for Integrated Order Batching, Picker Assignment, Batch Sequencing, and Picker Routing Problem

Learning-Aided Iterated Local Search Algorithm for Integrated Order Batching, Picker Assignment, Batch Sequencing, and Picker Routing Problem

A memetic algorithm with fuzzy-based population control for the joint order batching and picker routing problem

The joint order batching and picker routing problem (JOBPRP) is a combinatorial optimization problem that occurs during in the order-picking operation of warehouse management. It consists of simultaneous assignment of customer orders to batches and routing of picking operations in the batches such that the total travel distance is minimized. In this paper, we develop a memetic algorithm with fuzzy-based population control (MA-FPC) to solve the JOBPRP. MA-FPC takes advantage of the hierarchical nature of the problem to design a batch exchange crossover (BEX) operator and a two-level local improvement procedure. BEX transfers complete batches from parent solutions to offsprings. Local improvement systematically employs a combined heuristic and exact routing approach to solve the picker routing problem. Furthermore, fuzzy-based population control is used to dynamically regulate population diversity during the search, which removes individuals from or adds individuals to the population. In numerical experiments, MA-FPC significantly outperforms state-of-the-art point-based and population-based algorithms developed for the order batching problem and JOBPRP with respect to solution quality in reasonable running times. Our algorithm improves the previous best-known solutions for 57 of the 64 benchmark instances.

Learning efficient in-store picking strategies to reduce customer encounters in omnichannel retail

Omnichannel retailers are reinventing stores to meet the growing demand of the online channel. Several retailers now use stores as supporting distribution centers to offer quicker Buy-Online-Pickup-In-Store (BOPS) and Ship-From-Store (SFS) services. They resort to in-store picking to serve online orders using existing assets. However, in-store picking operations require picker carts traveling through store aisles, competing for store space, and possibly harming the offline customer experience. To learn picking policies that acknowledge interactions between pickers and offline customers, we formalize a new problem called Dynamic In-store Picker Routing Problem (diPRP). This problem considers a picker that tries to pick online orders (seeking) while minimizing customer encounters (hiding) – preserving the offline customer experience. We model the problem as a Markov Decision Process (MDP) and solve it using a hybrid solution approach comprising mathematical programming and reinforcement learning components. Computational experiments on synthetic instances suggest that the algorithm converges to efficient policies. We apply our solution approach in the context of a large European retailer to assess the proposed policies regarding the number of orders picked and customers encountered. The learned policies are also tested in six different retail settings, demonstrating the flexibility of the proposed approach. Our work suggests that retailers should be able to scale the in-store picking of online orders without jeopardizing the experience of offline customers. The policies learned using the proposed solution approach reduced the number of customer encounters by up to 50%, compared to policies solely focused on picking orders. Thus, to pursue omnichannel strategies that adequately trade-off operational efficiency and customer experience, retailers cannot rely on actual simplistic picking strategies, such as choosing the shortest possible route.

A new approach to the joint order batching and picker routing problem with alternative locations

Abstract Accepted by: M. Zied Babai The clustered and generalized vehicle routing problem (CGVRP) extends the well-known vehicle routing problem by grouping the demand points into multiple distinct zones, and within each zone, further separation is made by forming clusters. The objective of the CGVRP is to determine the optimal routes for a fleet of vehicles dispatched from a depot, visiting all zones within each cluster. This requires making two simultaneous optimization decisions. Firstly, each zone must be visited by exactly one node, and secondly, all zones within a cluster must be visited by the same vehicle. In this paper, we introduce two mixed-integer linear programming formulations for the CGVRP, aimed at solving a joint order batching and picker routing problem with alternative locations in a warehouse environment featuring mixed-shelves configuration. Both formulations are tested on three scenarios of randomly generated small- and medium-sized instances. Additionally, we propose a general rule approach for calculating a cost matrix in a rectangular environment. The results demonstrate the effectiveness of the proposed mathematical formulations in efficiently solving problems with up to 180 nodes.

Solving Location Assignment and Order Picker-Routing Problems in Warehouse Management

One of the critical warehousing processes is the order-picking process. This activity consists of retrieving items from their storage locations to fulfill the demand specified in the pick lists. Therefore, the storage location assignment affects the picking time and, consequently, reduces the operating costs of the warehouse. This work presents two alternative mixed-integer linear models and an adaptive multi-start heuristic (AMH) for solving the integrated storage location and picker-routing problem. The problem considers a warehouse with a general layout and precedence constraints for picking according to the products weight. Experimental work confirms the efficiency of the proposed reformulations since we found out a total of 334 tested instances and optimal solutions for 51 new cases and 62 new feasible solutions. The proposed AMH improved more than 29% of the best-known solutions and required an average execution time of 117 s. Consequently, our proposed algorithm is an attractive decision-making tool to achieve efficiency when solving practical situations in a warehouse.

A Three-Stage model for Clustering, Storage, and joint online order batching and picker routing Problems: Heuristic algorithms

The online shopping center is an electronic commerce where customer orders arrive over time. The joint online order batching and picker routing is essential for managing online shopping, as it allows for the retrieval of products from storage locations as order arrival timings become known. Meanwhile, the picker routing performance is substantially affected by the product allocation to storage locations, whereas the success of the storage assignment depends on the product grouping. In order to handle such a system, this study offers a novel three-stage model, the first stage of which aims to classify products according to various available capacity levels to maximize similarity measures among products. The second stage determines the assignments of the obtained classes to carriers and storage locations in a multi-block 3D warehouse to minimize the total transportation costs and the energy costs of carriers. The third stage provides a joint online order batching and picker routing model in a picker-to-parts system to minimize completion time in the 3D warehouse. Since learning effects affect the search and pick times, and pickers’ horizontal and vertical velocities are dissimilar, these crucial factors are considered for calculating travel time of pickers. In addition, two efficient heuristic algorithms are proposed to solve the developed models in the first two stages, and an effective online 2-competitive heuristic algorithm is developed to solve the proposed model in the third stage. Moreover, a broad range of numerical experiments illustrates the validity and applicability of the proposed models and solution approaches. What is more, a competitive analysis evaluates the effectiveness of the proposed online heuristic algorithm. The results reveal that the developed hierarchical framework can provide high-quality solutions in a reasonable time and reduce the total cost and makespan by 35.65% and 12.48% on average, respectively.

Picker routing optimization of storage stacker based on improved multi-objective iterative local search algorithm

<p style='text-indent:20px;'>In the process of warehouse automation, the efficient picker routing strategy is one of the key factors to improve warehouse efficiency. According to the order and the picking characteristics of the warehouse stacker, the picker routing of the stacker is regarded as the prize-collecting vehicle routing problem (PCVRP). According to the path and order for stacker picking, we designed a picker routing optimization strategy based on improved multi-objective iterative local search (IMOILS) algorithm. An elite pool strategy was set to save the high-quality solutions in the iterative process, and the nondominated solutions in the iterative evolution were stored and updated. Adding the adaptive enhanced perturbation strategy was beneficial to the current solution to escape from local optimum. In the local search procedure, to limit the excessively large search space, the epsilon constraint was adopted to limit the significant deterioration in another objective direction. The computational results showed that the proposed algorithm is superior to the comparison algorithms in the number of nondominated solutions, the hypervolume, and the spacing metric, and the stability of the algorithm is also good, which not only verifies the effectiveness of the proposed algorithm, but also provides a feasible optimization scheme for the storage stacker's picker routing problem.</p>

Solving an order batching, picker assignment, batch sequencing and picker routing problem via information integration

Modern supply chain systems require an effective scheduling scheme based on industrial information integration. Warehouses are a key part of the supply chain systems. Its efficiency can be significantly improved by making full use of the multi-dimensional information in an order-picking process. This work presents an integrated order batching, picker assignment, batch sequencing, and picker routing problem in a warehouse. Its solution is difficult due to the coupling of various information such as diversity of orders, orderliness of picking positions, and complexity of a warehouse environment. In order to obtain a high-quality solution in a reasonable time, this work proposes a hybrid iterated local search algorithm embedded with heuristic rules. In it, multiple effective perturbation moves with an evolutionary mechanism are designed to allow it to escape from a local optimal region. A perturbation strategy based on its convergence speed is presented to balance exploration and exploitation. An acceptance criterion based on the Metropolis criterion is used to improve its global search ability. Besides, a routing strategy based on Manhattan distance is proposed to evaluate the performance of the proposed method. Finally, various simulation experiments and its comparisons with several existing methods are performed to validate its advantages. The impact of information integration on system performance is also investigated.

Improved formulations of the joint order batching and picker routing problem

Order picking is the process of retrieving ordered products from storage locations in warehouses. In picker-to-parts order picking systems, two or more customer orders may be grouped and assigned to a single picker. Then routing decisions regarding the visiting sequence of items during a picking tour must be made. Won and Olafsson (2005) found that solving the integrated problem of batching and routing enables warehouse managers to organize order picking operations more efficiently compared with solving the two problems separately and sequentially. We therefore investigate the mathematical programming formulation of this integrated problem. We present several improved formulations of the problem based on the findings of Valle, Beasley, and Salles da Cunha (2017), that can significantly improve computational results. More specifically, we reconstruct the connectivity constraints and generate new cutting planes in our branch-and-cut framework. We also discuss some problem properties by studying the structure of a graphical representation of the warehouse, and we present two types of additional constraints. We also consider the no-reversal case of this problem. We present efficient formulations by building different auxiliary graphs. Finally, we present computational results for publicly available test problems for single-block and multiple-block warehouse configurations.

Intelligent Warehouse Picking Improvement Model for e-Logistics Warehouse Using Single Picker Routing Problem and Wave Picking

Abstract— The development and use of technological innovations have changed people's behavior from an industrial society to an information society. It can be seen in the increase in people's consumption patterns from trading through physical stores (offline) to trading through electronic systems, often referred to as e-commerce. Logistics services are distribution actors in the downstream line which are tasked with delivering products from the fulfillment center from e-commerce to the end customer. The uncertainty of the number of requests is the biggest challenge for logistics service players. The growth of e-commerce has also led to an increase in sales volume in e-commerce which has given rise to a new generation of warehouses that are specifically tailored to the special needs of online retailers who directly serve the demands of end-customers in the business-to-consumer (B2C) segment. Traditional warehousing systems cannot handle orders with the characteristics of many transactions but smaller sizes. In addition, warehouses that handle e-commerce are also required to have a fast process in the warehouse because shipments must be made on the same day. In this study, the author aims to perform calculations to find the optimal order picking time in the warehouse, so orders in e-commerce can be processed faster by comparing the picking process time using ordinary Single Picker Routing Problem (SPRP) and combined with the concept of wave picking using Genetic Algorithm (GA). Based on a theoretical study in this paper, the combination between SPRP and wave picking can reduce 42.28% picking time.Â

An extensible multi-block layout warehouse routing optimization model

As a special Traveling Salesman Problem, the order picking problem is theoretically challenging and practically significant. Therefore, it has received the attention of many scholars for many years. Compared with a single block layout with parallel picking aisles, the optimal solution for a multi-block layout is much more difficult to find due to the increase in cross-aisles. In this paper, two mathematical optimization formulations are proposed to deal with the multi-block layout problem. One takes the picking position as a unit, and the other takes the picking aisle as a unit. Since picking aisles are connected to each other through specific cross aisles, different picking configurations, access modes, and constraints are introduced. The distance between picking positions is divided into horizontal distance and vertical distance, forming different parts in the objective function. On this basis, two mathematical planning models for the single picker routing problem are constructed. The scale and solution time of the two models are independent of the number of cross aisles, so they have good overall performance when compared with other optimization algorithms through numerical experiments. These models can be expanded to include important features of modern inventory systems, such as scattered storage.

The min–max order picking problem in synchronised dynamic zone-picking systems

ABSTRACT In both manual and automated warehouses, a combination of efficient zoning and picker routing plays an important role in improving travel time, congestion, and system throughput. This paper considers the order picker routing problem in a dynamic and synchronised zoning environment, where the items corresponding to each customer order are picked simultaneously in multiple zones, and zones may change between different orders. The objective is to minimise the maximum time of completing the picking activities in any zone. Using a min–max type of objective not only minimises the makespan of an order picking wave, but it also helps balance the workload of the order pickers more effectively. We present a mathematical model for the optimal solution of this problem, as well as a dynamic programming approach to find the optimal solution for the case where a zone is a set of adjacent aisles. Computational experiments on randomly generated instances show that the dynamic programming approach is able to find optimal solutions in negligible computational times.

Steiner TSP based on aisle as a unit for order picking

The picker routing problem (PRP) is one of the most crucial problems in warehouse management. It is also defined as the Steiner Traveling Salesman Problem (Steiner TSP). We deal with the Steiner TSP for a low-level picker-to-parts order picking system within a multi-block warehouse, which is much more complicated to be solved compared with those in a single block layout. After a series of preprocessing, such as reducing the vertices, transforming picking aisles and limiting the connections between vertices, we construct a Steiner graph with flexible nodes based on aisle as a unit. Different picking access modes as well as restrictions on connections for picking aisles are introduced. Then, a mixed integer linear programming model for Steiner TSP based on aisle as a unit is presented. We compare the numerical computation on the benchmarks in exiting literatures. Our Steiner graph can greatly reduce the scale of vertices and arcs without losing characteristics of the original problem. And the model has good overall performance, especially in large scale cases.

Solving the picker routing problem in multi-block high-level storage systems using metaheuristics

Solving the picker routing problem in multi-block high-level storage systems using metaheuristics

The order batching problem: A state-of-the-art review

The Order Batching Problem (OBP) has received a lot of attention from researchers in recent years. Until now, this problem has been considered as a whole with different problems or it has been studied on its own, with different solution methods, in different warehouse layouts, with different data structures. The aim of this study is to provide the researchers with a general analysis for studies using the OBP. In accordance with this purpose; the OBP is analyzed by an extensive literature review that includes all relevant studies to date. This literature review is based on a specific method and the studies are grouped into specific classes. Accordingly, the most studied problem with the OBP is the Picker Routing Problem (PRP) with 17% and 51% of the studies were solved by metaheuristic algorithms. The most widely used metaheuristic algorithms are Neighborhood Search and Genetic Algorithms.