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A review of synchronization problems in parts-to-picker warehouses
Abstract
Triggered by the great success of e-commerce, today’s warehouses more and more evolve to fully-automated fulfillment factories. Many of them follow the parts-to-picker paradigm and employ shelf-lifting mobile robots or conveyors to deliver stock keeping units (SKUs) to stationary pickers operating in picking workstations. This paper aims to structure and review the family of synchronization problems that arise in this environment: If multiple orders demanding the same SKU can be serviced jointly, then a more efficient picking process and a relief of the bin supply system can be achieved. This paper classifies the family of slightly varying synchronization problems arising with different workstation setups in alternative warehouses. This classification scheme is applied to analyze computational complexity, to systematically quantify the gains of alternative workstation setups, and to benchmark the performance gains of synchronization with those of other well-established decision tasks. Our results show that the right workstation setup can greatly improve throughput performance, so that the gains of synchronization can outreach those promised by other well-researched decision tasks.
... Specifically, most of the existing studies on storage assignment in traditional picker-to-parts order picking systems aimed to minimize the total travel distance of human pickers or minimize the overall order picking time [23]. However, minimizing the number of pod visits can be the main optimization objective in RMFS [5,37,39]. Jiang et al. [37] justified the objective from two aspects: the number of pod visits directly reflects the movement of robots, and a reduced number of pod visits can decrease the size of the required robot fleet. ...
... However, they all have in common that the storage bins or moveable racks are transported to the picking workstations by automated devices such as autonomous mobile robots, shuttles, and conveyors. Then, the human picker in the workstation picks items from bins or racks into the corresponding customer bins [39]. Thus, the findings of this study can also be applied to some other parts-to-picker warehouses, such as some automated storage and retrieval systems (ASRS). ...
... 4) Although the trend toward automated processes is continuing and robots are becoming increasingly intelligent, the human advantage cannot be completely replaced. In the foreseeable future, many technical problems in robot picking are still expected to occur; not all of them can be resolved, and human pickers will remain an integral part of order picking [39,54]. Furthermore, human pickers are the bottleneck resource in parts-to-picker systems. ...
This study examines the item storage assignment problem in robotic mobile fulfillment systems (RMFSs), that determines the assignment of items to pods. Unlike previous studies on this problem that generally considered an empty warehouse, the current study addresses the problem in RMFSs with nonempty pods. The problem is formulated as a mixed-integer program with the goal of maximizing the correlation degree among items. On the basis of the characteristics of the problem, an adaptive large neighborhood search (ALNS) heuristic is designed for the solution. Numerical results show that the gap between the ALNS heuristic and the Gurobi solver is less than 0.32% in small-scale instances. In medium- and large-scale instances, the ALNS heuristic improves the objective value by at least 10% compared with the methods in literature, and it outperforms commonly used storage assignment policies for traditional warehouses (e.g., random, dedicated, and class-based storage) by more than 30%. The ALNS heuristic can also be applied to the special case where the initial state of the warehouse is empty. The computational study of the ALNS heuristic in all instances shows that it can effectively solve this problem by providing high-quality solutions and has good scalability.
... for synchronization in an ergonomic picking workstation with a capacity for a single SKU bin at a time and two parallel customer bins [14]. ...
... Boysen Nils et al. classified the family of slightly varying synchronization problems in parts-to-picker systems during the following years. They demonstrated that the correct workstation setup can enhance throughput performance [14]. It is necessary to conduct research to determine whether order structures advocate integrating, separating, or combining warehousing systems when dealing with high-volume-low-mix retail orders and low-volume-high-mix online orders. ...
Research and development on a global scale have been conducted on overhead hoist transportation systems (OHTSs) in recent years. The majority of these systems are utilized in manufacturing facilities that are either semiautomated or fully automated. By using stochastic models to evaluate medication distribution and product delivery processes in automated delivery systems, hospitals can reduce patient waiting times and drug response times. Warehouses are being transformed into fully automated fulfillment factories by using conveyors and shelf-lifting mobile robots, which reduce waiting times and improve efficiency. Modern warehouses are increasingly becoming fully automated fulfillment facilities as a response to the significant development of e-commerce. A significant number of organizations are using mobile robots or conveyor systems to transport shelves. The parts-to-picker model is used to transport stock-keeping units (SKUs) to stationary pickers at picking workstations. The aim of this study is to analyze and organize the relationship between transportation system families. They are utilized in various fields, such as warehouses, hospitals, airports, cross-dockings, etc. Furthermore, this study categorizes a range of synchronization issues that arise from minor variations in workstation configurations within different warehouse settings. Next, we identify a multistation ATS (automatic transportation system) that switches lines to different stations by using overhead conveyors and active line-switching devices. Vietnam’s automated freight problem can be solved with this potential solution. Our study’s findings suggest that enhancing the workstation layout can significantly enhance throughput performance. As a result, the benefits of synchronization can surpass those provided by other well-studied decision tasks.
... Warehouses have always been essential components of supply chains. The growth and development of both online and offline commerce have facilitated the evolution of increasing retail system needs into highly sophisticated order fulfillment centers today [1]. A greater emphasis has been placed on warehousing systems as a consequence of the integration of supply chain management with approaches such as just-in-time. ...
Background: In today’s business world, where competition lies between supply chains, customer expectations are changing dynamically. Effective order picking in warehouses has become a top concern given expectations for rapid delivery, a larger product range, and continuous support. Methods: In this study, it is aimed to find a simultaneous solution to the problems of picker routing and order batching, which have an important place in order picking. A genetic algorithm-based solution with group-based coding is proposed to minimize the travel time of pickers. Results: A new set of equations for rectangular warehousing systems with three or more blocks (multi-blocks) is presented to directly determine the shortest distances between order points. It is found that the proposed solution methodology gives better results than traditional approaches. Conclusions: The study is expected to contribute to the improvement of order picking, which is the most costly and repetitive activity in warehouses, within the scope of practical and academic applications.
... In the context of optimizing the order picking process, Boysen, Schwerdfeger, and Stephan (2023) have demonstrated that the synchronization of order and tote sequences significantly influence order picking efficiency, reducing over 30% tote deliveries. However, it presents a formidable challenge due to the complex relationship between two sequences (Zhuang et al. 2022). ...
... The challenges of managing stochastic order fulfilment processes in warehouses have been studied extensively in the literature. There are related surveys concerning warehousing for e-commerce (Boysen et al. 2019) and brick-and-mortar retail chains (Boysen et al. 2021), as well as for the design and control of manual order picking (de Koster et al. 2007) and automated parts-to-picker systems (Boysen et al. 2023). In the following, we review the research streams on stochastic order fulfilment processes in warehouses that incorporate daily order deadlines. ...
Warehouses recently face increasing stress imposed by a volatile customer demand and increasing customer expectations in terms of ever shorter order response times. In that respect, warehouses more and more offer same-day and next-day shipment conditions. However, same-day shipment promises are challenging to fulfil, especially as the order fulfilment process operates against fixed deadlines imposed by the predefined truck departure times. As a natural mitigation strategy, warehouses set a cutoff point and offer same-day shipment only to customers that order until the cutoff point, but next-day shipment to all customers ordering thereafter. Setting an appropriate cutoff point is challenging as it affects multiple facets of the service quality, such as the order response time and the service level. In this paper, we study the design of cutoff-based shipment promises for stochastic deadline-oriented order fulfilment processes in warehouses. We present a discrete-time Markov chain model for exact steady-state performance analysis and propose two novel performance measures – α- and β-cutoff service level – for service level measurement in these systems. We numerically show the benefit of cutoff-based shipment promises. Even with a late cutoff point, there is a significant gain in the system performance. Furthermore, we find that warehouses should set the cutoff point such that it balances customer expectations in terms of service level and order response time. Finally, warehouses can improve their shipment promises when referring to β- instead of α-cutoff service level and by implementing measures reducing the utilisation and the variabilities of the order fulfilment process.
Mobile-rack warehouses have become increasingly popular in online retail due to their efficient order-picking capabilities. They adopt the parts-to-picker mode for order picking, while also introducing a new item storage assignment problem (ISAP). This problem involves determining both the categories and quantities of items assigned to each rack, with the objective of minimizing the expected number of rack movements required to fulfill orders under a given distribution. We formulate ISAP as a stochastic integer programming model and then convert it into a deterministic version using sample average approximation (SAA). To address the vast solution spaces resulting from multidimensional category-quantity correlations, we develop a parallel adaptive large neighborhood search (pALNS) algorithm featuring reduced formulations and customized operators. Experimental results demonstrate a 2.84%–38.94% reduction in rack movements compared to popular methods. Sensitivity analyses reveal that setting 20-24 bins per rack or reserving approximately 20% of rack capacity achieves a favorable balance between productivity and operational flexibility.
To this day, tasks like planning and managing warehouses remain complex. Automated storage and retrieval systems have enhanced warehousing efficiency, yet designing them optimally is still challenging, despite their importance for the efficient operation of the warehouse. This article aims to present a novel framework for automating the optimal design of vertical lift modules (VLMs), focusing on tray types, quantities, and item–tray sector assignments, based on a specified inventory list. The approach accounts for VLM’s physical, manufacturing, and ergonomic constraints to ensure a manufacturable system design. To manage computational complexity, the size of the mixed-integer problem is reduced through an exact clustering of items, sectors, and layouts. The proposed framework is tested through numerical simulations using real data from an Italian VLM manufacturer.
The order scheduling and rack sequencing problem deals with the order picking process in robotic mobile fulfillment systems: automated guided vehicles lift and transport movable storage racks to picking stations to supply items requested by customer orders which are put together in cardboard boxes on a workbench of limited capacity. To efficiently operate the station, the sequence in which racks visit the station one after another and the intervals at which customer orders are scheduled must be coordinated. We present a dynamic programming algorithm for the order scheduling and rack sequencing problem at a single picking station minimizing the number of rack visits. Despite monolithic mixed integer linear programming formulations, our approach appears to be the first combinatorial solution method for the problem in literature. A computational study demonstrates the effectiveness of the approach.
This study focuses on the problem of sequencing requests for an end-of-aisle automated storage and retrieval system (AS/RS), where each retrieved load must be returned to its earlier storage location after a worker has picked some products from the load. At the picking station, a buffer is maintained to absorb any fluctuations in speed between the worker and the storage/retrieval machine. We show that, under conditions, the problem of optimally sequencing the requests in this system with a buffer size of m loads forms a special case of the multiple Traveling Salesmen Problem (mTSP) where each salesman visits the same number of cities. Several interesting structural properties for the problem are mathematically shown. In addition, a branch-and-cut method and heuristics are proposed. Experimental results show that the proposed simulated annealing-based heuristic performs well in all circumstances, and significantly outperforms benchmark heuristics. For instances with negligible picking times for the worker, we show that this heuristic provides solutions that are on average within 1.8% from the optimal value.
The Order Processing in Picking Workstations is a real problem derived from the industry in the context of supply chain management. It looks for an efficient way to process orders arriving to a warehouse by minimizing the number of movements of goods, stored in containers in the warehouse, from their storage location to the processing zone. In this paper, we tackle this real optimization problem by providing a new Integer Linear Programming (ILP) formulation for the problem. Due to the NP-Hardness of the problem we have also designed several heuristic procedures, to find high-quality solutions in a reasonable amount of time, which is mandatory for handling real instances. Particularly, the heuristics proposed were combined into a General Variable Neighborhood Search algorithm. Finally, we have performed an extensive experimentation indicating an increased performance of our proposals (ILP and heuristic) over previous approaches in the state of the art, using both synthetic and real datasets of instances.
In robotic mobile fulfillment systems, human pickers don’t go to the inventory area to search for and pick the ordered items. Instead, robots carry shelves (called “pods”) containing ordered items from the inventory area to picking stations. At the picking stations, pickers put ordered items into totes; then these items are transported to the packing stations. This type of warehousing system relieves the human pickers and improves the picking process. In this paper, we concentrate on decisions about the assignment of pods to stations and orders to stations to fulfill picking for each incoming customer’s order. In previous research for an RMFS with multiple picking stations, these decisions are made sequentially with heuristics. Instead, we present a new MIP-model to integrate both decision problems. To improve the system performance even more, we extend our model by splitting orders. This means parts of an order are allowed to be picked at different stations. To the best of the authors’ knowledge, this is the first publication on split orders in an RMFS. And we prove the computational complexity of our models. We analyze different performance metrics, such as pile-on, pod-station visits, robot moving distance and throughput. We compare the results of our models in different instances with the sequential method in our open-source simulation framework RAWSim-O. The integration of the decisions brings better performances, and allowing split orders further improves the performances (for example: increasing throughput by 46%). In order to reduce the computational time for a real-world application, we have proposed a heuristic.
Trolley line picking is a special warehousing system particularly suited to fulfill high-volume demands for heavy stock keeping units (SKUs). In such a system, unit loads of SKUs are positioned along a given path passed by automated trolleys, i.e., carriers hanging from a monorail or automated guided vehicles. Once a trolley reaches a requested SKU, it automatically stops and announces the requested items on a display. This is the signal for an accompanying human picker to put the demanded items onto the trolley. In this way, picking continues until, at the end of the path, the current picking order is complete and the trolley moves onward to the shipping area. Meanwhile, the picker rushes back to meet the subsequent trolley associated with the next picking order. The picking performance of the trolley line system is mainly influenced by the picker’s unproductive walking from SKU to SKU during order processing and back to the next trolley when switching to the next order. In this paper, we investigate how the storage assignment of SKUs along the path and the order sequence influence picking performance. Specifically, we explore the positive effect of duplicating SKUs and storing them at multiple positions along the path. We formulate the interdependent storage assignment and order sequencing problems and introduce a decomposition heuristic. Our computational study investigates the solution performance of this procedure and shows that SKU duplication can considerably improve picking performance.
This paper is dedicated to the cafeteria problem: given a single waiter operating multiple counters for different dishes arranged along a line and a set of customers with given subsets of dishes they desire, find a sequence of customers, which may not overtake each other, and a service schedule for the waiter, such that the makespan is minimized. This generic problem is shown to have different real-world applications in order picking with blocking restrictions. We present different heuristic and exact solution procedures for both problem parts, i.e., customer sequencing and waiter scheduling, and systematically compare these approaches. Our computational results reveal that the largest performance gains are enabled by not strictly processing order after order. Instead, the waiter should be allowed to flexibly swap between customers waiting along the line. Such a flexible service policy considerably reduces the makespan and the total walking distance of the waiter.
Our research focuses on the storage decision in a semi‐automated storage system, where the inventory is stored on mobile storage pods. In a typical system, each storage pod carries a mixture of items, and the inventory of each item is spread over multiple storage pods. These pods are transported by robotic drives to stationary stations on the boundary of the storage zone where associates conduct pick or stow operations. The storage decision is to decide to which storage location within the storage zone to return a pod upon the completion of a pick or stow operation. The storage decision has a direct impact on the total travel time, and hence the workload of the robotic drives. We develop a fluid model to analyze the performance of velocity‐based storage policies. We characterize the maximum possible improvement from applying a velocity‐based storage policy in comparison to the random storage policy. We show that class‐based storage with two or three classes can achieve most of the potential benefits and that these benefits increase with greater variation in the pod velocities. To validate the findings, we build a discrete‐time simulator with real industry data. We observe an 8% to 10% reduction in the travel distance with a 2‐class or 3‐class storage policy, depending on the parameter settings. From a sensitivity analysis we establish the robustness of the class‐based storage policies as they continue to perform well under a broad range of warehouse settings including different zoning strategies, resource utilization and space utilization levels.
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The Robotic Mobile Fulfillment Systems (RMFS) is a new type of robotized, parts-to-picker material handling system, designed especially for e-commerce warehouses. Robots bring movable shelves, called pods, to workstations where inventory is put on or removed from the pods. This paper simulates both the pick and replenishment process and studies the order assignment, pod selection and pod storage assignment problems by evaluating multiple decision rules per problem. The discrete event simulation uses realistic robot movements and keeps track of every unit of inventory on every pod. We analyze seven performance measures, e.g. throughput capacity and order due time, and find that the unit throughput is strongly correlated with the other performance measures. We vary the number of robots, the number of pick stations, the number of SKUs (stock keeping units), the order size and whether returns need processing or not. The decision rules for pick order assignment have a strong impact on the unit throughput rate. This is not the case for replenishment order assignment, pod selection and pod storage. Furthermore, for warehouses with a large number of SKUs, more robots are needed for a high unit throughput rate, even if the number of pods and the dimensions of the storage area remain the same. Lastly, processing return orders only affects the unit throughput rate for warehouse with a large number of SKUs and large pick orders.
This paper investigates the order processing in picking workstations, which are among today’s most efficient order picking devices. A workstation is continuously supplied with storage bins containing stock keeping units (SKUs) from an interconnected storage system, so that a human worker only has to repack the items into customer bins. This way of unproductive work content, e.g., travel time, is eliminated and up to 1000 picks per hour is enabled. We aim at a concerted processing of picking orders and storage bins delivered from the storage system, such that an even more efficient picking process is enabled. We formalize the resulting order processing problem and present an efficient solution procedure. Our computational results show that the automated crane of the storage system feeding the picking workstation with bins can considerably be relieved by our procedure.
The aging society in many developed countries has made an ergonomic workplace design to an important topic among researchers and practitioners alike. We investigate the workplace design for order pickers that manually collect items from the shelves of a warehouse. Specifically, we treat the storage assignment, i.e., the placement of products in shelves of different height, and zoning, i.e., the partitioning of the storage space into areas assigned to separate pickers, in the fast pick area of a warehouse. A fast pick area unifies the most fast-moving items in a compact area, so that workers are relieved from unproductive travel, but face extraordinary ergonomic risks due to the frequent repetition of picking operations. Concerning the health of (aged) workers, it is crucial to reduce such risks. Thus, we define a combined ergonomic storage assignment and zoning problem with the objective of minimizing the maximum ergonomic burden among all workers. This problem is formalized, and two construction heuristics and a tabu search procedure are proposed. Our results show that neglecting ergonomic aspects and only focusing on picking performance leads to much higher ergonomic risks of the workforce.
In the reordering buffer management problem, a sequence of colored items arrives at a service station to be processed. Each color change between two consecutively processed items generates some cost. A reordering buffer of capacity k items can be used to preprocess the input sequence in order to decrease the number of color changes. The goal is to find a scheduling strategy that, using the reordering buffer, minimizes the number of color changes in the given sequence of items. We consider the problem in the setting of online computation with advice. In this model, the color of an item becomes known only at the time when the item enters the reordering buffer. Additionally, together with each item entering the buffer, we get a fixed number of advice bits, which can be seen as information about the future or as information about an optimal solution (or an approximation thereof) for the whole input sequence. We show that for any there is a -competitive algorithm for the problem which uses only a constant (depending on ) number of advice bits per input item. This also immediately implies a -approximation algorithm which has running time (this should be compared to the trivial optimal algorithm which has a running time of ). We complement the above result by presenting a lower bound of bits of advice per request for any 1-competitive algorithm.
Order picking (OP) activities, essential to logistics operations, are laborious and time-intensive. Humans are central actors in the OP process and determine both OP effectiveness and efficiency. Many researchers have developed models for planning OP activities and increasing the efficiencies of such systems by suggesting different warehouse layouts, OP routes or storage assignments. These studies have, however, ignored workers’ characteristics, or human factors, suggesting that they cannot be substantiated, which led to only partially realistic results. This paper proposes a conceptual framework for integrating human factors into planning models of OP activities and hypothesises that doing so improves the performance of an OP system and workers’ welfare. The framework is based on a systematic literature review that synthesises findings documented in the OP and human factors literature. The results of the paper may assist researchers and practitioners in designing OP systems by developing planning models that help in enhancing performance and reducing long-term costs caused by work-related inefficiencies.
At a cross docking terminal, inbound shipments are directly transshipped across the terminal to designated outbound trucks, so that delays and inventories are kept as low as possible. We consider an operational truck scheduling problem, where a dock door and a start time has to be assigned to each inbound truck. A set of outbound trucks is scheduled beforehand and, therefore, departure times are fixed. If a shipment is not unloaded, transshipped to the outbound gate and loaded onto the designated outbound truck before its departure we consider the shipments's value as lost profit. The objective is to minimize total lost profit. The paper at hand formalizes the resulting truck scheduling problem. We settle its computational complexity and develop heuristics in order to tackle the problem. We show the efficiency of these heuristics by means of a computational study. Last but not least, a case study is presented.
Over the last decades, many companies have offshored manufacturing activities to Asia Pacific and Eastern Europe. Since the consuming markets have not moved, this has put an increasing burden on the distribution operations of such companies. Companies have centralized warehouse operations in few, but often large facilities responsible for distributing products over a large region. Managing efficiency and effectiveness (service) is a great challenge for managers of such facilities. As a result, they feel a great need to benchmark warehouse operations, not only their own, but also their competitors'. However, assessing the performance of a distribution facility is a tricky business. Even after having visited a large number of them, it is still difficult to tell after a visit, whether this was a best-in-class operation, just above average or even relatively poor performing. Nevertheless, even short tour visits can reveal a lot of information to the trained eye. This paper proposes a method to help managers getting more information from tour visits, through a simple and rapid assessment form. The form should be filled out immediately after the visit. The evaluation has been inspired by the ideas of Gene Goodson in Harvard Business Review on rapid plant assessment (Goodson (2002) Harvard Business Review, 3-11 May). Since its development, the method has been successfully applied in several visits, with different groups of managers (with and without warehouse experience) and students.
In this paper we propose a simulation modeling approach based on aggregate process times for the performance analysis of order picking workstations in automated warehouses. The aggregate process time distribution is calculated from tote arrival and departure times. We refer to the aggregate process time as the effective process time. An aggregate model uses the effective process time distributions as input to predict tote and order flow times. Results from experimental settings show that the aggregate model accurately predicts the mean and variability of tote and order flow times. As a case study, we develop an aggregate model to predict flow times for a real, operating warehouse. The resulting flow time predictions give satisfactory accuracy for both tote and order flow times. Meaningful insights are obtained for improving the performance of the warehouse.
In the past few years, increasing numbers of automatic warehousing systems using computer-controlled stacker cranes have been installed. Our research concerns the scientific scheduling and design of these systems. There are three elements to scheduling: the assignment of multiple items to the same pallet (Pallet Assignment); the assignment of pallet loads to storage locations (Storage Assignment); and rules for sequencing storage and retrieve requests (Interleaving). This paper deals with optimal storage assignment. Results are obtained which compare the operating performance of three storage assignment rules: random assignment, which is similar to the closest-open-location rule used by many currently operating systems; full turnover-based assignment: and class-based turnover assignment. It is shown that significant reductions in crane travel time (and distance) are obtainable from turnover-based rules. These improvements can, under certain circumstances, be directly translated into increased throughput capacity for existing systems, and may be used to alter the design (e.g., size and number of racks, speed of cranes, etc.) of proposed systems in order to achieve a more desirable system balance between throughput and storage capacity.
Due to demanding service levels in e‐commerce order fulfillment, modeling and analysis of integrated storage and order picking processes in warehouses deserve special attention. The upstream storage system can have a significant impact on the performance of the downstream order picking process. With a particular focus on multiline e‐commerce orders, we develop an analytical modeling framework for integrated analysis of upstream (shuttle‐based storage and retrieval system) and downstream (pick system) networks. To capture the consolidation delays in fulfilling multiline orders, the downstream pick system is modeled with a closed queuing network that includes synchronization nodes. The configuration of the synchronization station is adapted to model the variety of order profiles handled at the pick station. For the downstream closed queuing network, we propose a decomposition‐based solution methodology that results in good solution accuracy. The resulting semi‐open queuing network (SOQN) of the integrated system is analyzed using the matrix‐geometric method (MGM). To improve the accuracy of analytical estimates of the measures, we propose a hybrid simulation/analytical framework, where the performance measures of complex subnetworks are obtained from simulation. We also develop a detailed simulation model of the physical system for validating the analytical and hybrid estimates of the performance measures. The results from experiments indicate that the hybrid simulation/analytical approach reduces the error in the throughput time estimates to 3% from 18% obtained from the analytical model. Then, we investigate the effect of the upstream network configuration (such as the number of storage aisles) and the downstream network configuration (such as the mixed vs. dedicated picking, CONWIP control for orders, order batching) on the order throughput times. Our analysis provides a threshold on the maximum numbers of allowable orders (CONWIP control) and number of aisles beyond which the improvement in average throughput time of the integrated system is marginal. Numerical experiments with high‐order arrivals also highlight that mixed picking in the downstream network can result in significant throughput time reduction in comparison to dedicated picking.
Warehouse automation is increasingly adopted to manage throughput fluctuations in e‐commerce order fulfillment. This work develops queuing network models and solution methodologies for performance analysis of a stock‐to‐picker system that connects an upstream automated storage system to a downstream pick station. We focus on the pick station process, quantifying the throughput differences between a pick station that employs a static versus dynamic batching strategy. We consider a waveless order release environment where the item totes are requested from the storage system only when an order arrives. We capture throughput performance in this environment for single as well as multi‐line orders with/without item commonality by developing closed‐queuing network models. The consolidation of multiple product‐lines for a multi‐line order is modeled using fork–join synchronization stations within the closed queuing network. For analyzing such queuing networks, we develop a network‐decomposition based solution methodology. We validate the models using a simulation model of the upstream storage and downstream order‐picking system. We find that in waveless order release environment, dynamic batching always outperforms static batching in terms of system throughput. However, for single‐line orders, the percentage gain in the throughput (by implementing dynamic batching) decreases for smaller item tote inter‐arrival times. For multi‐line orders, dynamic batching increases the system throughput by 37–43%. We also analyze the effect of batch size on the throughput performance. The results indicate that the system throughput increases with an increase in the batch size under both batching policies. But, the marginal benefit reduces as we increase the batch size.
In this paper we investigate the problem of simultaneously allocating orders and mobile storage racks to static pickers. Here storage racks are allocated to pickers to enable them to pick all of the products for the orders that have been allocated to them. Problems of the type considered here arise in facilities operating as robotic mobile fulfilment systems. We present a formulation of the problem of allocating orders and racks to pickers as an integer program and discuss the complexity of the problem. We present two heuristics (matheuristics) for the problem, one using partial integer optimisation, that are directly based upon our formulation. We also consider the problem of how to sequence the racks for presentation at each individual picker and formulate this problem as an integer program. We prove that, subject to certain conditions being satisfied, a feasible rack sequence for all orders can be produced by focusing on just a subset of the orders to be dealt with by the picker. Computational results are presented, both for order and rack allocation, and for rack sequencing, for randomly generated test problems (that are made publicly available) involving up to 1000 products, 200 orders, 500 racks and 10 pickers.
Warehouses are an inevitable component in any supply chain and a vividly investigated object of research. Much attention, however, is absorbed by warehousing systems dedicated to the special needs of online retailers in the business-to-consumer segment. Due to the ever increasing sales volumes of e-commerce this focus seems self-evident, but a much larger fraction of retail sales are still realized by traditional brick-and-mortar stores. The special needs of warehouses servicing these stores are focused in this paper. While e-commerce warehouses face low-volume-high-mix picking orders, because private households tend to order just a few pieces per order from a large assortment, distribution centers of retail chains rather have to process high-volume-low-mix orders. We elaborate the basic requirements within both business segments and identify suited warehousing systems for brick-and-mortar stores (e.g., fully-automated case picking). The setup of each identified warehousing system is described, elementary decision problems are discussed, and the existing literature is surveyed. Furthermore, we identify future research needs.
The robotic mobile fulfillment system (MFS) is widely used for automating storage pick and pack activities in e-commerce distribution centers. In this system, the items are stored on movable storage shelves, also known as inventory pods, and brought to the order pick stations by robotic drive units. We develop stylized performance evaluation models to analyze both order picking and replenishment processes in a mobile fulfillment system storage zone, based on multi-class closed queueing network models. To analyze robot assignment strategies for multiple storage zones, we develop a two-stage stochastic model. For a single storage zone, we compare dedicated and pooled robot systems for pod retrieval and replenishment. For multiple storage zones, we also analyze the effect of assigning robots to least congested zones on system throughput in comparison to random zone assignment. The models are validated using detailed simulations. For single zones, the expected throughput time for order picking reduces to one-third of its initial value by using pooled robots instead of dedicated robots; however, the expected replenishment time estimate increases up to three times. For multiple zones, we find that robots that are assigned to storage zones with dedicated and shortest queues provide a greater throughput than robots assigned at random to the zones.
In many warehouses shuttle-based technologies have replaced the traditional AS/R system based storage technologies. The impact these systems have on downstream order picking performance is largely unknown. To study the interactions between upstream storage and downstream picking systems, we develop a novel analytical model for integrated storage and order picking systems. The resulting semi-open queuing model is solved using the matrix-geometric method. Using the queuing network model, we are able to study the effect of storage system technology on order throughput times, and the effect of the picking station input buffer size on order picking performance. Further, we analyze the effect of a constant work-in-process (CONWIP) control for orders on system performance. Our results indicate that using SBS/R instead of AS/R-based storage systems yields investment cost savings (i.e., fewer aisles in the storage area and fewer picking stations), paired with a lower total throughput time at a given order arrival rate. Numerical studies show how the total throughput time, first, benefits and then becomes stable by increasing the input buffer size at the picking stations. Retrieving item tote at the storage system in advance with respect to the picker availability is also advantageous, especially in the SBS/R system.
Scattered storage is a storage assignment strategy where single items are isolated and distributed all around the shelves of a warehouse. This way, the probability of always having some items per stock-keeping units close-by is increased, which is intended to reduce the unproductive walking time during order picking. Scattered storage is especially suited if each order line demands just a few items, so that it is mainly applied by business-to-consumer online retailers. This paper formulates a storage assignment problem supporting the scattered storage strategy. We provide and test suited solution procedures and investigate important managerial aspects, such as the frequency with which refilling the shelves should be executed.
The online appendix is available at https://doi.org/10.1287/trsc.2017.0779 .
E-commerce retailers face the challenge to assemble large numbers of time-critical picking orders each consisting of just a few order lines with low order quantities. Traditional picker-to-parts warehouses are often ill-suited for these prerequisites, so that automated warehousing systems (e.g., automated picking workstations, robots, and AGV-assisted order picking systems) are applied and organizational adaptions (e.g., mixed-shelves storage, dynamic order processing, and batching, zoning and sorting systems) are made in this branch of industry. This paper is dedicated to these warehousing systems especially suited for e-commerce retailers. We discuss suited systems, survey the relevant literature, and define future research needs.
In this paper, we present a new branch-and-price-and-cut algorithm to solve the truck-and-trailer routing problem with time windows (TTRPTW) and two real-world extensions. In all TTRPTW variants, the fleet consists of one or more trucks that may attach a trailer. Some customers are not accessible with a truck-and-trailer combination, but can however be serviced by one if the trailer is previously detached and parked at a suitable location. In the first extension, the planning horizon comprises two days and customers may be visited either on both days or only once, in which case twice the daily supply must be collected. The second extension incorporates load transfer times depending on the quantity moved from a truck to its trailer. The exact branch-and-price-and-cut algorithm for the standard variant and the two new extensions is based on a set-partitioning formulation in which columns are routes describing the movement of a truck and its associated trailer. Linear relaxations of this formulation are solved by column generation where new routes are generated with a dynamic programming labeling algorithm. The effectiveness of this pricing procedure can be attributed to the adaptation of techniques such as bidirectional labeling, the ng-neighborhood, and heuristic pricing using dynamically reduced networks and relaxed dominance. The cutting component of the branch-and-price-and-cut adds violated subset-row inequalities to strengthen the linear relaxation. Computational studies show that our algorithm outperforms existing approaches on TTRP and TTRPTW benchmark instances used in the literature.
The online appendix is available at https://doi.org/10.1287/trsc.2017.0765 .
This article studies the storage assignment and order batching problem in the Kiva mobile fulfilment system. The storage assignment model aims to decide which product to put in which pod to maximize the product similarity and the order batching model aims to minimize the number of visits of pods. To solve the order batching problem, a heuristic is proposed, where a batch schedule is initialized with the objective of maximizing the order association or minimizing order alienation and improved by variable neighbourhood search. Computational experiments are conducted to verify the performance of the proposed model and algorithm.
The vertical lift module is an automated storage and retrieval system widely used in warehouses. The performance of a warehouse with vertical lift modules is highly correlated with the efficiency of the order picking. Order batching, namely regrouping customers' orders into batches to be collected from the module, constitutes a critical decision impacting the picking efficiency. In this paper, we provide optimization models for order batching, with the objective of minimizing total completion time, that is, the time required to collect a given set of customers' orders. We first consider the case of one vertical lift module and then extend our approach to study a warehouse with several modules. We use real data from two companies operating in different sectors in order to test and validate our models. Numerical experiments show that our models perform much better than the batching method currently used by these companies. For complex cases that cannot be solved within a reasonable timeframe with Cplex, we develop a metaheuristic approach, which generally yields very good solutions in less than one minute. This paper investigates problems that are firmly grounded in practice. Our batching models and metaheuristic approach have been implemented in practice and are currently used by some companies.
Robotic compact storage and retrieval systems (RCSRS) have seen many implementations over the last few years. In such a system, the inventory items are stored in bins, organized in a grid. In each cell of the grid, a certain number of bins are stored on top of each other. Robots with transport and lifting capabilities move on the grid roof to transport bins between manual workstations and storage stacks. We estimate performance and evaluate storage policies of RCSRS, considering both dedicated and shared storage policies coupled with random and zoned storage stacks. Semi-open queuing networks (SOQNs) are built to estimate the system performance, which can handle both immediate and delayed reshuffling processes. We approximate the models by reduced SOQNs with two load-dependent service nodes and use the matrix-geometric method to solve them. Both simulations and a real case are used to validate the analytical models. Assuming a given number of stored products, our models can be used to optimize not only the length-to-width ratio of the system but also the stack height, depending on the storage strategy used. For a given inventory and optimal system configuration, we demonstrate that the dedicated storage policy outperforms the shared storage policy when the objective is to minimize dual command throughput time. However, from a cost perspective, with a maximum dual command throughput time as a constraint, we show that shared storage substantially outperforms dedicated storage. The annualized costs of dedicated storage are up to twice as large as those of shared storage, as a result of the larger number of storage positions required by dedicated storage and the relatively lower filling degree of storage stacks.
The online appendix is available at https://doi.org/10.1287/trsc.2017.0786 .
Warehouses deliver labor-intensive services to customers. Underperformance may result in high costs and unsatisfied customer demand. New market developments force warehouses to handle a large number of orders within tight time windows. To cope with this, order picking operations need to be optimized by solving a wide range of planning problems. Optimizing order picking planning problems sequentially may yield a suboptimal overall warehouse performance. Still, previous warehouse planning reviews focus on individual planning problems. This literature review differs by investigating combinations of multiple order picking planning problems. A state-of-the-art review and classification of the scientific literature investigating combinations of tactical and operational order picking planning problems in picker-to-parts systems is presented with the aim of determining how planning problems are related. Furthermore, this literature review aims to find excellent policy combinations and to provide guidelines how warehouse managers can benefit from combining planning problems, in order to design efficient order picking systems and improve customer service. Combining multiple order picking planning problems results in substantial efficiency benefits, which are required to face new market developments.
An inverse order picking system inverts the basic logic of traditional picker-to-parts systems where pickers successively visit all shelves storing requested stock keeping units (SKUs). Instead, the picker successively moves bins each containing a particular SKU along a line of multiple order bins and puts items into all bins that require the current SKU. In this setting, we aim at a synchronization between the batches of picking orders concurrently assembled and the sequence of SKUs moved along the line, such that the number of line passings to be accomplished by the picker is minimized. We formalize the resulting optimization problem, prove computational complexity, and derive suited solution procedures. In our computational study, we also address important managerial aspects, such as the sizing of the picking area that restricts the number of picking orders concurrently processed.
This paper treats a special parts-to-picker based order processing system, where mobile robots hoist racks and bring them directly to stationary pickers. This technological innovation – known as the Kiva system – heavily influences all traditional planning problems to be solved when operating a warehouse. We, specifically, tackle the order processing in a picking station, i.e., the batching and sequencing of picking orders and the interdependent sequencing of the racks brought to a station. We formalize the resulting decision problem and provide suited solution procedures. In a comprehensive computational study we show that an optimized order picking allows to more than halve the fleet of robots compared to simple decision rules often applied in real-world warehouses.
This paper treats an order picking system where a crane continuously relocates stock keeping units (SKUs) in a high-bay rack subdivided into the bottommost picking level and the upper reserve area. The capacity of the pick face is not large enough to store all SKUs, so that the crane has to ensure that all SKUs demanded by a current picking order are timely provided and picker idle time is avoided. We aim at a processing sequence of picking orders and a SKU switching plan, i.e., an instruction when to exchange which SKUs in the picking level, such that an unobstructed order picking is enabled. Our problem is closely related to the tool switching problem of flexible manufacturing. Here, each job requires a subset of tools to be loaded into the tool magazine (with limited capacity) of a single flexible machine. We, however, show that an alternative objective function, i.e., minimizing the maximum number of switches between any successive job pair, is better suited in the warehouse context and even better results can be obtained by a multi-objective approach. Elementary complexity proofs as well as suited solution procedures are provided and we also address managerial aspects, such as the sizing of the pick face.
This paper presents an overview of the inaugural Amazon Picking Challenge along with a summary of a survey conducted among the 26 participating teams. The challenge goal was to design an autonomous robot to pick items from a warehouse shelf. This task is currently performed by human workers, and there is hope that robots can someday help increase efficiency and throughput while lowering cost. We report on a 28-question survey posed to the teams to learn about each team's background, mechanism design, perception apparatus, planning, and control approach. We identify trends in this data, correlate it with each team's success in the competition, and discuss observations and lessons learned based on survey results and the authors' personal experiences during the challenge.
This paper models Robotic Mobile Fulfillment Systems and analyzes their performance. A Robotic Mobile Fulfillment System is an automated, parts-to-picker storage system where robots bring pods with products to a workstation. It is especially suited for e-commerce distribution centers with large assortments of small products, and with strong demand fluctuations. Its most important feature is the ability to automatically sort inventory and to adapt the warehouse layout in a short period of time. Queueing network models are developed for both single-line and multi-line orders, to analytically estimate maximum order throughput, average order cycle time, and robot utilization. These models can be used to quickly evaluate different warehouse layouts, or robot zoning strategies. Two main contributions are that the models include accurate driving behavior of robots and multi-line orders. The results show that: 1) the analytical models accurately estimate robot utilization, workstation utilization, and order cycle time 2) maximum order throughput is quite insensitive to the length-to-width ratio of the storage area and 3) maximum order throughput is affected by the location of the workstations around the storage area.
This paper focuses on the mathematical analysis of order flow times in parts-to-picker warehouses with remotely located order-picking workstations. To this end, a polling system with a new type of arrival process and service discipline is introduced as a model for an order-picking workstation. Stochastic bounds are deduced for the cycle time, which corresponds to the order flow time. These bounds are shown to be adequate and aid in setting targets for the throughput of the storage area. The paper thus complements existing literature, which mainly focuses on optimizing the operations in the storage area.
This paper addresses the scheduling of a single storage/retrieval machine (or crane) in automated storage/retrieval systems (ASRSs). A novel classification scheme is presented for precisely defining different versions of the crane scheduling problem, when varying the layout of the ASRS, the characteristics of the storage and retrieval requests, and the objective function. This classification scheme is then applied for presenting different (known and novel) exact algorithms and complexity proofs for a variety of crane scheduling problems, for reviewing the literature, and for identifying future research needs.
This paper develops a planning concept for defining repetitive delivery patterns according to which stores of a grocery retailer are supplied from a distribution center. Applying repetitive delivery patterns offers major advantages when scheduling the workforce for shelf replenishment, defining cyclic transportation routes and managing warehouse capacities. In doing so, all logistics subsystems of a retail chain, i.e., warehousing, transportation and instore logistics, are jointly scheduled. We propose a novel model to minimize total costs in all associated subsystems of a retail distribution chain. A solution approach is developed for clustering stores and selecting delivery patterns that reflects practical requirements. A broad numerical analysis demonstrates cost savings of 2.5% on average compared to a state-of-the-art approach (see [Sternbeck, M. G., & Kuhn, H. (2014). An integrative approach to determine store delivery patterns Transportation Research Part E: Logistics and Transportation Review,70(1), 205-224.]). This considerable cost reduction potential is confirmed by applying the suggested approach to a real case of a major European grocery retailer.
New types of Automated Storage and Retrieval Systems (AS/RS) able to achieve high throughput are continuously being developed and require new control polices to take full advantage of the developed system. In this paper, a dynamic storage system has been studied as developed by Vanderlande Industries, consisting of a conveyor, two non-passing lifts that share a mast, multiple transfer shuttles, and a storage rack. This study is concerned with the scheduling problem of these two lifts, i.e. which lift is going to handle which (storage or retrieval) request, and in which order. An integrated look-ahead strategy heuristic to simultaneously assign a set of pre-defined requests to the lifts and the order in which they will be handled taking into account delays caused by interference between the lifts. A practical methodology to characterize the system to identify and resolve situations where the lifts would interfere with each other is presented. Experimental results compare several priority rules to handle interference between lifts, and provide empirical evidence that the dynamic system with multiple lifts controlled by the proposed look-ahead strategy achieved average improvements of 44.34% and 35.82% in terms of total handling times (82.49% and 60.08% in terms of throughput) compared to a single lift system and to a simple rule of thumb, respectively.
Increasing productivity and reducing labour cost in order picking processes are two major concerns for most warehouse managers. Particularly picker-to-parts order picking methods lead to low productivity as order pickers spend much of their time travelling along the aisles. To enhance order picking process performance, an increasing number of warehouses adopt the concept of dynamic storage where only those products needed for the current order batch are dynamically stored in the pick area, thereby reducing travel time. Other products are stored in a reserve area. We analyse the stability condition for a dynamic storage system with online order arrivals and develop a mathematical model to derive the maximum throughput a DSS can achieve and the minimum number of worker hours needed to obtain this throughput, for order picking systems with a single pick station. We discuss two applications of dynamic storage in order picking systems with multiple pick stations in series. In combination with simulation modelling, we are able to demonstrate that dynamic storage can increase throughput and reduce labour cost significantly.
Automated Storage and Retrieval Systems (AS/RS) are warehousing systems that use mechanised devices to accomplish the repetitive tasks of storing and retrieving parts in racks. Since these systems represent a significant investment and considerable operating costs, their use must be as efficient as possible. AS/RS performance is the result of the interaction of many complex and stochastic subsystems. This reality creates a need for robust and efficient evaluation models. This article complements previous surveys on AS/RS by focusing on the particular research question addressed by each work and the associated assumptions used for the various models designed for evaluating AS/RS. Dynamic models based on simulation dominate the most recent literature; however, static approaches based on travel-time modelling have strongly contributed to the study of AS/RS. This review includes dynamic – simulation-based – models, but considers also steady-state (travel-time-based) models. We believe that this review may be of great help to researchers and industrial users in their search for the best modelling approach for a specific problem.
In spite of extraordinary support programs initiated by the European Union and other national authorities, the percentage of overall freight traffic moved by train is in steady decline. This development has occurred because the macroeconomic benefits of rail traffic, such as the relief of overloaded road networks and reduced environmental impacts, are counterbalanced by severe disadvantages from the perspective of the shipper, e.g., low average delivery speed and general lack of reliability. Attracting a higher share of freight traffic on rail requires freight handling in railway yards that is more efficient, which includes technical innovations as well as the development of suitable decision support systems. This paper reviews container processing in railway yards from an operations research perspective and analyzes basic decision problems for the two most important yard types: conventional rail--road and modern rail--rail transshipment yards. Furthermore, we review the relevant literature and identify open research challenges.
This paper studies two tactical level decision problems arising in transshipment hubs: berth template planning that is concerned with allocating berths and quay cranes to arriving vessels, and yard template planning that is concerned with assigning yard storage locations to vessels. These two tactical level decisions interact with each other. A mixed-integer programming model is proposed to integrate the berth template and the yard template planning with the aim to minimize the service cost that is incurred by the deviation from vessels' expected turnaround time intervals, and the operation cost that is related to the route length of transshipment container flows in yard. Moreover, a heuristic algorithm is developed for solving the problem in large-scale realistic environments. Numerical experiments are conducted to prove the necessity of the proposed model and also validate the efficiency of the proposed heuristic algorithm. For a set of real-world like instances, the heuristic algorithm can obtain good berth and yard templates within a reasonable time.
A novel design of an automated order-picking workstation processing multiple orders simultaneously is proposed to be used in warehouses with an end-of-aisle order-picking system. A typical problem at this workstation is the out-of-sequence arrival of products, assuming the workstation receives products for multiple orders simultaneously. As multiple products are present, the picking sequence at the workstation affects the system throughput. The performance of four picking policies is compared in terms of order throughput and queue length distribution under different extents of out-of-sequence arrivals. Experimental results show the capability of the workstation to handle an arbitrary extent of out-of-sequence arrival of products. Noteworthy insights for design considerations of such systems are drawn.
This paper presents a survey of vehicle routing problems with multiple synchronization constraints. These problems exhibit, in addition to the usual task covering constraints, further synchronization requirements between the vehicles, concerning spatial, temporal, and load aspects. They constitute an emerging field in vehicle routing research and are becoming a "hot" topic. The contribution of the paper is threefold: (i) It presents a classification of different types of synchronization. (ii) It discusses the central issues related to the exact and heuristic solution of such problems. (iii) It comprehensively reviews pertinent literature with respect to applications as well as successful solution approaches, and it identifies promising algorithmic avenues.
Cross-docking is a logistics strategy in which freight is unloaded from inbound vehicles and (almost) directly loaded into outbound vehicles, with little or no storage in between. This paper presents an overview of the cross-docking concept. Guidelines for the successful use and implementation of cross-docking are discussed and several characteristics are described that can be used to distinguish between different cross-dock types. In addition, this paper presents an extensive review of the existing literature about cross-docking. The discussed papers are classified based on the problem type that is tackled (ranging from more strategic or tactical to more operational problems). Based on this review, several opportunities to improve and extend the current research are indicated.
The theory of deterministic sequencing and scheduling has expanded rapidly during the past years. In this paper we survey the state of the art with respect to optimization and approximation algorithms and interpret these in terms of computational complexity theory. Special cases considered are single machine scheduling, identical, uniform and unrelated parallel machine scheduling, and open shop, flow shop and job shop scheduling. We indicate some problems for future research and include a selective bibliography.
We consider the offline sorting buffer problem. The input is a sequence of items of different types. All items must be processed one by one by a server. The server is equipped with a random-access buffer of limited capacity which can be used to rearrange items. The problem is to design a scheduling strategy that decides upon the order in which items from the buffer are sent to the server. Each type change incurs unit cost, and thus, the objective is to minimize the total number of type changes for serving the entire sequence. This problem is motivated by various applications in manufacturing processes and computer science, and it has attracted significant attention in the last few years. The main focus has been on online competitive algorithms. Surprisingly little is known on the basic offline problem. In this paper, we show that the sorting buffer problem with uniform cost is NP-hard and, thus, close one of the most fundamental questions for the offline problem. On the positive side, we give an O(1)-approximation algorithm when the scheduler is given a buffer only slightly larger than double the original size. We also sketch a fast dynamic programming algorithm for the special case of buffer size 2.
This paper gives an overview of recent research on the performance evaluation and design of carousel systems. We discuss picking strategies for problems involving one carousel, consider the throughput of the system for problems involving two carousels, give an overview of related problems in this area and present an extensive literature review. Emphasis has been given on future research directions in this area.