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Zoning strategies for human–robot collaborative picking
Abstract
During the last decade, several retailers have started to combine traditional store deliveries with the fulfillment of online sales to consumers from omni‐channel warehouses, which are increasingly being automated. A popular option is to use autonomous mobile robots (AMRs) in collaboration with human pickers. In this approach, the pickers' unproductive walking time can be reduced even further by zoning the storage system, where the pickers stay within their zone periphery and robots transport order totes between the zones. However, the robotic systems' optimal zoning strategy is unclear: few zones are particularly good for large store orders, while many zones are particularly good for small online orders. We study the effect of no zoning (NZ) and progressive zoning strategies on throughput capacity for balanced zone configurations with both fixed and dynamic order profiles. We first develop queuing network models to estimate pick throughput capacity that correspond to a given number of AMRs and picking with a fixed number of zones. We demonstrate that the throughput capacity is dependent on the chosen zoning strategy. However, the magnitude of the gains achieved is influenced by the size of the orders being processed. We also show that using a dynamic switching strategy has little effect on throughput performance. In contrast, a fixed switching strategy benefiting from changes in the order profile has the potential to increase throughput performance by 17% compared to the NZ strategy, albeit at a higher robot cost.
... They propose an MILP model to minimize total travel distance and design a polynomial-time routing algorithm to solve it. Azadeh et al. (2023) study a similar system but then using stochastic modeling for arrivals and travel times. Additionally, Ž ulj et al. (2022) study an AMR-assisted picker-to-parts system by partitioning the warehouse into disjoint zones and assigning an order picker to each zone. ...
... When the number of pickers is four, the proper speed of AMRs is about 1.3 m/s. Storage space zoning is an important strategy in warehouse operations management to reduce makespan (see Azadeh, de Koster, and Roy 2023). A zoning strategy divides the warehouse into a certain number of disjoint zones (e.g., two or four), and the four pickers are evenly assigned to these zones; each picker is allowed to move only inside the picker's assigned zone. ...
... The results in Figure 7 also imply that, for the current order pattern, more zones yield a larger makespan. This aligns with insights by Azadeh, de Koster, and Roy (2023) and seems intuitive because setting fewer zones means a larger solution space for the problem, which improves the solved results. ...
Autonomous mobile robots (AMRs) can support human pickers in warehouse picking operations by reducing picker walking distance and increasing the warehouse’s throughput. AMR-assisted order picking is becoming popular as it can be conveniently implemented in conventional warehouses. This study proposes an integrated optimization model for scheduling the operations in AMR-assisted picker-to-parts warehouse systems. The model aims to minimize the makespan of all picking operations for a batch of orders by assigning batched orders to AMRs, selecting storage racks for AMRs and pickers to visit, and determining the routes of the AMRs and the pickers. A column- and row-generation algorithm is designed to solve the model using synchronization constraints between AMRs and pickers. Numerical experiments are conducted to validate the applicability of our proposed algorithm in a warehouse that handles 16,000 orders per day. Our algorithm can solve small-scale instances to optimality. Our algorithm can also obtain better solutions in less time than a column generation (CG)–based method. Extensive experiments are conducted to derive managerial insights.
Funding: This research was supported by the National Natural Science Foundation of China [Grants 72025103, 72394360, 72394362, 72401179, 72361137001, and 72371221], the Project of Science and Technology Commission of Shanghai Municipality China [Grant 23JC1402200], and the Research Grants Council of the Hong Kong Special Administrative Region, China (Project number HKSAR RGC TRS T32-707/22-N).
Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2024.0800 .
... We uniformize the decision epochs by applying the uniformization technique of Lippman (1975). Therefore, the system can be described as an event-based discrete-time MDP with process completions and order arrivals as events (Azadeh et al. 2023). ...
... The robot speed is set at 1.3 m/s. The cost of a postponed order in an e-commerce environment is estimated at e20 per order (Azadeh et al. 2023). If a parcel finds a full buffer at an input station upon arrival, we assume it misses the truck Transportation Science, Articles in Advance, pp. ...
Robotic sorting systems (RSSs) use mobile robots to sort items by destination. An RSS pairs high accuracy and flexible capacity sorting with the advantages of a flexible layout. This is why several express parcel and e-commerce retail companies, who face heavy demand fluctuations, have implemented these systems. To cope with fluctuating demand, temporal robot congestion, and high sorting speed requirements, workload balancing strategies such as dynamic robot routing and destination reassignment may be of benefit. We investigate the effect of a dynamic robot routing policy using a Markov decision process (MDP) model and dynamic destination assignment using a mixed integer programming (MIP) model. To obtain the MDP model parameters, we first model the system as a semiopen queuing network (SOQN) that accounts for robot movement dynamics and network congestion. Then, we construct the MIP model to find a destination reassignment scheme that minimizes the workload imbalance. With inputs from the SOQN and MIP models, the Markov decision process minimizes parcel waiting and postponement costs and helps to find a good heuristic robot routing policy to reduce congestion. We show that the heuristic dynamic routing policy is near optimal in small-scale systems and outperforms benchmark policies in large-scale realistic scenarios. Dynamic destination reassignment also has positive effects on the throughput capacity in highly loaded systems. Together, in our case company, they improve the throughput capacity by 35%. Simultaneously, the effect of dynamic routing exceeds that of dynamic destination reassignment, suggesting that managers should focus more on dynamic robot routing than dynamic destination reassignment to mitigate temporal congestion.
Funding: This work was supported by The Fundamental Research Funds for the Central Universities [Grant WK2040000094] and the National Natural Science Foundation of China [Grants 71921001 and 72091215/72091210].
Supplemental Material: The online appendices are available at https://doi.org/10.1287/trsc.2023.0458 .
... Another potential approach is an implementation of a fixed allocation of drivers to yard areas with the aim of reducing the driving time to the receiving semitrailer, and, therefore, the time to process a task. This approach represents an adaptation of the zoning concept from warehouses (Azadeh et al., 2023;Yu and Ramanathan, 2009). ...
Purpose
The use of digital platforms is continuously increasing. This naturally entails various risks and opportunities. However, these risks and opportunities have not yet been studied in the context of team familiarity and task prioritisation. Therefore, this paper evaluates how team familiarity and task prioritisation affect both task-acceptance and task-processing time within a digital platform utilising a broadcast mechanism in a logistical context. Hence, our findings contribute to a deeper understanding of the relationship between digital platforms and intra-organisational team dynamics.
Design/methodology/approach
This study investigated a real-world observational dataset from an intra-organisational digital work platform utilised to organise shunting tasks in yard management. We tested our hypotheses by applying a linear mixed-effects model to our dataset encompassing 146,446 yard transport missions completed between January 2022 and April 2023.
Findings
Our study shows that high levels of team familiarity were associated with shorter task-processing times on a digital platform with a broadcast mechanism as explained by the transactive memory system theory. For task prioritisation, higher same-month high-priority task specialisation also resulted in shorter task-processing times, which is supported by the self-determination and social loafing theories. Same-month high-priority task specialization refers to the drivers on the yard who have repeatedly executed tasks with the same high priority within a month. Conversely, higher team familiarity levels led to longer task-acceptance times, based on the learning curve and nudge theories. Similarly, higher same-day high-priority task specialisation correlated with longer task-acceptance times due to the habitual effect.
Originality/value
First, our research contributes to the limited research in the field of yard management through its empirical investigation of social interaction and real-world operational-level processes for driver teams focused on shunting transport. Second, prior research in the context of digital platforms has focused on the individual level, while our research is dedicated to the team level, which highlights the communication and social interaction of drivers with other operators in the warehouse. Third, we discuss the relationship between social interaction and informal communication along with their implications for the success of digital platforms.
... Factors such as product weight, pick density, and travel distance influence the effectiveness of these systems, with robots being especially beneficial when travel distances are less than 5 meters. To date, we have identified studies focusing on warehouse layouts [21], zoning strategies [22], order batching and batch sequencing [23], and routing strategies [24] based on the concept of AMR-assisted order picking. Moreover, some studies combine different planning aspects to achieve greater flexibility in planning (combining order batching and routing strategies in [25]). ...
... AGVs are different from other robotic systems because they are meant for horizontal transportation tasks, making them appropriate for larger warehouses (Scholz et al., 2017). On the contrary, RMFS have a varied robotic solutions sphere, as they stand to optimize order fulfillment operations, as seen in instances of picking robots and AMR (Azadeh et al., 2023). This paper focuses on the deployment of AGVs in a human leading scenario within a warehouse environment characterized by nonperishable goods, serving high-volume, low-mix retail operations. ...
... Factors such as product weight, pick density, and travel distance influence the effectiveness of these systems, with robots being especially beneficial when travel distances are less than 5 meters. To date, we have identified studies focusing on warehouse layouts [21], zoning strategies [22], order batching and batch sequencing [23], and routing strategies [24] based on the concept of AMR-assisted order picking. Moreover, some studies combine different planning aspects to achieve greater flexibility in planning (combining order batching and routing strategies in [25]). ...
This study investigates the impact of integrating autonomous mobile robots (AMRs) into order picking, with a particular focus on how age influence human performance. Our research employs a multimethod approach, combining descriptive statistics, ANOVA, and post-experiment survey data analysis to evaluate the effects of AMR-assisted picking compared to manual cart picking. The results demonstrate that AMRs significantly reduce order-picking times (OPTs) and variability in performance across both age groups, with the older group showing an OPT improvement of 23.68%, and the younger group 29.40%. The ANOVA revealed that age significantly influenced OPTs. Additionally, the survey data indicated that participants perceived AMRs as simple to use and collaborative, with a strong positive correlation between AMR positioning and collaboration experience. These findings highlight the benefits of AMRs in enhancing efficiency and consistency in warehouse operations. The study underscores the importance of considering human factors in the design and implementation of robotic systems, paving the way for a human-centric Industry 5.0. Future research should attempt to achieve empirical data from real industrial operations, with the focus on larger sample sizes and the long-term effects of AMR integration on job satisfaction and overall performance.
... AMRs can work collaboratively with human operators, enhancing the productivity of warehouse operations. For example, in the case of Locus Robotics, their AMRs are known for working alongside human pickers to increase picking efficiency [126]. AMRs can optimize routes, avoid obstacles, and seamlessly integrate into existing warehouse management systems. ...
Intelligent robotics has the potential to revolutionize various industries by amplifying output, streamlining operations, and enriching customer interactions. This systematic literature review aims to analyze emerging technologies and trends in intelligent robotics, addressing key research questions, identifying challenges and opportunities, and proposing the best practices for responsible and beneficial integration into various sectors. Our research uncovers the significant improvements brought by intelligent robotics across industries such as manufacturing, logistics, tourism, agriculture, healthcare, and construction. The main results indicate the importance of focusing on human–robot collaboration, ethical considerations, sustainable practices, and addressing industry-specific challenges to harness the opportunities presented by intelligent robotics fully. The implications and future directions of intelligent robotics involve addressing both challenges and potential risks, maximizing benefits, and ensuring responsible implementation. The continuous improvement and refinement of existing technology will shape human life and industries, driving innovation and advancements in intelligent robotics.
Order batching plays a pivotal role in enhancing order fulfillment efficiency within both manual and robotic warehousing systems. Rare attention has been devoted to the impact of future incoming orders on online order batching. This study addresses this gap by exploring the potential benefits of reserving suitable orders when upcoming orders share similarities with existing orders in the order pool. Specifically, we investigate the online order batching problem with predictive order reservation, employing the Ensemble Learning method, to predict similarities between current and future orders. Our proposed approach involves deliberate reservation of certain orders upon arrival, deferring their batching to a subsequent period for additional efficiency gains. To operationalize this predictive order reservation, we develop an algorithmic framework that comprehensively addresses online order batching, encompassing batching, sequencing, and assignment. Experimental results, conducted on real data from an e-commerce warehouse, demonstrate the superiority of our proposed approach over fixed and variable time-window online batching algorithms in terms of order turnover time, with improvements of up to 6.1%. Notably, the benefits are more pronounced when the order arrival rate aligns with the available picking resources.
Note to Practitioners
—This paper was motivated by the practical problem of predictively reserving orders to improve the holistic efficiency of online batch picking in e-commerce warehouses. Existing approaches generally have assumed that warehouse management system (WMS) releases all orders in the order pool to generate the order batch and not considered the potential benefits of order reservation. This paper proposes a new online order batching approach with order reservation using machine learning. The proposed approach could bring many benefits to practitioners. Firstly, the proposed algorithm could improve the quality of order batch and could easily be embedded in the existing WMS without interference to current operation process. Secondly, the proposed algorithm framework could be easily re-configured to cover diverse scenarios of operation strategy combination and used to evaluate the performance of different methods. Thirdly, the proposed online order batching approach with order reservation using machine learning can be used to various order picking systems including manual order picking system, human-robot collaborative order picking system and robotic order picking system. In future research, we will address the order reservation mechanism considering different objective functions, such as minimizing tardy orders or variance of order turnover time and explore its applicable scenarios.
Manual order picking, the process of retrieving stock keeping units from their storage location to fulfil customer orders, is one of the most labour-intensive and costly activity in modern supply chains. To improve the outcome of order picking systems, automated and robotized components are increasingly introduced creating hybrid order picking systems where humans and machines jointly work together. This study focuses on the application of a hybrid picker-to-parts order picking system, in which human operators collaborate with Automated Mobile Robots (AMRs). In this paper a warehouse with a two-blocks layout is investigated. The main contributions are new mathematical models for the optimization of picking operations and synchronizations. Two alternative implementations for an AMR system are considered. In the first one handover locations, where pickers load AMRs are shared between pairs of opposite sub-aisles, while in the second they are not. It is shown that solving the mathematical models proposed by the meaning of black-box solvers provides a viable algorithmic optimization approach that can be used in practice to derive efficient operational plannings. The experimental study presented, based on a real warehouse and real orders, finally allows to evaluate and strategically compare the two alternative implementations considered for the AMR system.
Autonomous mobile robots (AMR) are currently being introduced in many intralogistics operations, like manufacturing, warehousing, cross-docks, terminals, and hospitals. Their advanced hardware and control software allow autonomous operations in dynamic environments. Compared to an automated guided vehicle (AGV) system in which a central unit takes control of scheduling, routing, and dispatching decisions for all AGVs, AMRs can communicate and negotiate independently with other resources like machines and systems and thus decentralize the decision-making process. Decentralized decision-making allows the system to react dynamically to changes in the system state and environment. These developments have influenced the traditional methods and decision-making processes for planning and control. This study identifies and classifies research related to the planning and control of AMRs in intralogistics. We provide an extended literature review that highlights how AMR technological advances affect planning and control decisions. We contribute to the literature by introducing an AMR planning and control framework to guide managers in the decision-making process, thereby supporting them to achieve optimal performance. Finally, we propose an agenda for future research within this field.
We study Bucket Brigade (BB) production systems under the assumption of stochastic worker speeds. Our analysis provides interesting and counter-intuitive insights into realistic production environments. We analyze the following three systems: the traditional BB of Bartholdi & Eisenstein (1996), BB with overtaking allowed (BBO), and a benchmark system of parallel workers. After formulating the dynamic equations for all systems, we solve them analytically when possible and numerically in general. We identify settings in which conclusions that emerge from deterministic analysis fail to hold when speeds are stochastic, in particular relating to worker order assignment. Specifically, a fastest to slowest order with respect to expected speeds may be optimal as long as the standard deviation of the fastest worker is large enough. Significantly, in a stochastic environment the BB can improve the throughput rate compared to parallel workers, despite the fact that no blockage or starvation may occur in the latter. The BBO setting, which is relevant in a stochastic environment, and can be sometimes implemented in practice, provides an upper bound on the throughput rate of parallel workers, and is shown numerically to significantly improve upon BB.
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.
This article is protected by copyright. All rights reserved.
Order picking is one of the most time-critical processes in warehouses. We focus on the combined effects
of routing methods and storage location assignment on process performance. We present exact formulas
for the average route length under any storage location assignment for four common routing methods.
Properties of optimal solutions are derived that strongly reduce the solution space. Furthermore, we
provide a dynamic programming approach that determines storage location assignments, using the route
length formulas and optimality properties. Experiments underline the importance of the introduced
procedures by revealing storage assignment patterns that have not been described in literature before.
Order pickers and individual differences between them could have a substantial impact on picking performance, but are largely ignored in studies on order picking. This paper explores the role of individual differences in picking performance with various picking tools (pick by voice, RF-terminal picking and pick to light) and methods (parallel, zone and dynamic zone picking). A unique realistic field experiment with 101 participants (academic students, vocational students and professional pickers) is employed to investigate the influence of individual differences, especially the Big Five personality traits, on picking performance in terms of productivity and quality. The results suggest that (PbV) performs better than RF-terminal picking, and that Neuroticism, Extraversion, Conscientiousness and the age of the picker play a significant role in predicting picking performance with voice and RF-terminals. Furthermore, achieving higher productivity appears to be possible without sacrificing quality. Managers can increase picking performance by incorporating the insights in assigning the right pickers to work with a particular picking tool or method, leading to increased picking performance and reduced warehousing costs.
Stochastic dynamic programming (SDP) or Markov decision processes (MDP) are increasingly being used in ecology to find the best decisions over time and under uncertainty so that the chance of achieving an objective is maximised. To date, few programs are available to solve SDP/MDP. We present MDPtoolbox, a multi-platform set of functions to solve Markov decision problems (MATLAB, GNU Octave, Scilab and R). MDPtoolbox provides state-of-the-art and ready to use algorithms to solve a wide range of MDPs. MDPtoolbox is easy to use, freely available and has been continuously improved since 2004. We illustrate how to use MDPtoolbox on a dynamic reserve design problem.
In this study we consider a pick-and-sort order picking system, in which batches of orders are picked simultaneously from different (work) zones by a group of order pickers. After picking, the orders are transported by a conveyor to a next station for consolidation and packing. Packing can only occur when an order has been picked completely. For a given number of workers, each assigned to a single zone, a larger number of zones reduces pick time (since travel time reduces), but increases waiting time for completion at the packing stations, because more partial batches needing assembly arrive at the packing stations. Our aim is to determine the optimal number of zones such that the total (picking and packing) time to complete a batch is minimised. We solve this problem by optimally assigning items to pick routes in each zone. We illustrate the method with data taken from a distribution centre of one of the largest online retailers in The Netherlands.
Compact, multi-deep three-dimensional (3D), Automated Storage and Retrieval Systems (AS/RS) are becoming more common, due to new technologies, lower investment costs, time efficiency and compact size. Decision-making research on these systems is still in its infancy. This paper studies a particular compact system with rotating conveyors for the depth movement and a Storage/Retrieval (S/R) machine for the horizontal and vertical movement of unit loads. The optimal storage zone boundaries are determined for this system with two product classes: high- and low-turnover, by minimizing the expected S/R machine travel time. We formulate a mixed-integer non-linear programming model to determine the zone boundaries. A decomposition algorithm and a one-dimensional search scheme are developed to solve the model. The algorithm is complex, but the results are appealing since most of them are in closed-form and easy to apply to optimally layout the 3D AS/RS rack. The results show that the S/R machine travel time is significantly influenced by the zone dimensions, zone sizes and ABC curve skewness (presenting turnover patterns of different products). The presented results are compared with those under random storage and it is shown that significant reductions of the machine travel time are obtainable by using class-based storage.[Supplementary materials are available for this article. Go to the publisher's online edition of IIE Transactions for the following free supplemental resource: Appendix]
This paper considers routing and layout issues for parallel aisle warehouses. In such ware- houses order pickers walk or drive along the aisles to pick products from storage. They can change aisles at a number of cross aisles. These cross aisles are usually located at the front and back of the warehouse, but there can also be one or more cross aisles at positions in between. We describe a number of heuristics to determine order picking routes in a warehouse with two or more cross aisles. To analyse the performance of the heuristics, a branch-and-bound algorithm is used that generates shortest order picking routes. Performance comparisons between heuristics and the branch-and-bound algorithm are given for various warehouse layouts and order sizes. For the majority of the instances with more than two cross aisles, a newly developed heuristic appears to perform better than the existing heuristics. Furthermore, some consequences for layout are discussed. From the results it appears that the addition of cross aisles to the warehouse layout can decrease handling time of the orders by lowering average travel times. However, adding a large number of cross aisles may increase average travel times because the space occupied by the cross aisles has to be traversed as well.
Order picking, the assembly of a customer's order from items in storage, is an essential link in the supply chain and is the major cost component of warehousing. The critical issue is to simultaneously reduce the cost and increase the speed of the order picking activity. This study departs from the limited prior research that focused on either routing of workers or storage of warehoused items. The main objectives are to (1) evaluate various routing heuristics versus an optimal routine in a volume-based storage environment, (2) propose several methods of implementing volume-based storage, and (3) examine the interaction of the routing and storage policies under different operating conditions of pick list size and demand skewness. The experimental results show statistically significant differences in the mean route distance for the routing policies, storage policies, and their interactions. Further testing indicates that the choice of certain routing and storage policies in combination can result in increased picking efficiency.
The purpose of this paper is to present the main idea and rules of the bucket brigades and to analyse the modelling approaches and some real case studies reported in the literature. The bucket brigades represent a new concept of organising the flow line activities. This principle, first time implemented at Toyota, requires a considerably reduced design and supervision effort as regards the traditional assembly lines. The simple functioning protocol yields the spontaneous line balancing, due to a decentralised control strategy. So, for instance, it is no longer need to solve the Assembly Line Balancing (ALB) problem, which is NP-hard. In this paper, the main theoretical results are summed up, emphasizing the advantages and disadvantages of implementing the bucket brigades and identifying the still open problems. It seems that the bucket brigades have some strong points versus the classical solutions, including, but not limited to: decentralisation, flexibility, adaptability. This study will allow to generally concluding on some new trends in the production systems design and management.
If networks of queues satisfy certain conditions, then the equilibrium distribution for the number of jobs in the various stations has the so-called product-form. In such cases there are relatively elegant and simple computational procedures for the relevant behavioral characteristics. Quite commonly, however, the conditions are too severe and exact solution is practically impossible for larger problems.
In this paper we will consider iterative approximations for networks of queues which either don't possess product-form solutions or are so large that exact solution becomes intractable even using the product-form of the solution. The approximations are based on a mean value analysis approach and use either aggregation of some sort or decomposition. For the details of the approximations heuristic arguments are used. The approach is worked out for some problem types.
Order picking has long been identified as the most labour-intensive and costly activity for almost every warehouse; the cost of order picking is estimated to be as much as 55% of the total warehouse operating expense. Any underperformance in order picking can lead to unsatisfactory service and high operational cost for the warehouse, and consequently for the whole supply chain. In order to operate efficiently, the order-picking process needs to be robustly designed and optimally controlled. This paper gives a literature overview on typical decision problems in design and control of manual order-picking processes. We focus on optimal (internal) layout design, storage assignment methods, routing methods, order batching and zoning. The research in this area has grown rapidly recently. Still, combinations of the above areas have hardly been explored. Order-picking system developments in practice lead to promising new research directions.
This paper discusses the notion of workflow congestion in the context of material handling equipment interruptions in a manufacturing or warehousing facility. Development of a combination of probabilistic and physics-based models for workflow interruptions permits evaluation of the expected link travel time. The problem is then of routing in a way that minimizes total expected travel time. The rerouting problem is modeled as a multicommodity flow problem with link capacity design. A greedy upper bounding and Lagrangean relaxation algorithm are developed to solve this efficiently. To calibrate our modeling process we develop an object-oriented simulation model that explicitly considers various workflow interruptions. Our major finding is that rerouting traffic in a congested facility can significantly alleviate congestion delays and improve the efficiency of material movement. A managerial insight derived from this work is that rerouting is most effective in medium traffic-intensity situations.
The joint equilibrium distribution of queue sizes in a network of queues containing N service centers and R classes of customers is derived. The equilibrium state probabilities have the general form P(S) equals Cd(S) f//1(x//1)f//2(x//2). . . f//N(x//N), where S is the state of the system, x//i is the configuration of customers at the ith service center, d(S) is a function of the state of the model, f//i is a function that depends on the type of the ith service center, and C is a normalizing constant. It is assumed that the equilibrium probabilities exist and are unique. Four types of service centers to model central processors, data channels, terminals, and routing delays are considered.
In the e-commerce era, efficient order fulfillment processes in distribution centers have become a key success factor. One novel technology to streamline these processes is robot-assisted order picking. In these systems, human order pickers are supported by autonomous mobile robots (AMRs), which carry bins for collecting picking orders, autonomously move through the warehouse, and wait in front of a shelf containing a requested stock keeping unit (SKU). Once a picker has approached a waiting AMR and placed the requested SKU into the respective bin, AMR and picker may separate and move toward other picking positions. In this way, pickers continuously move between different waiting AMRs without having to return to the depot. This paper treats the coordination of multiple AMRs and multiple pickers to minimize the makespan. We present a heuristic method for the deterministic case that can handle the requirements of large e-commerce fulfillment centers and successfully solves instances with more than one thousand picking positions. Based on the obtained solutions, the performance of our picking system is compared with the traditional warehouse setup without AMR support and to another work policy using fixed pairings of picker and AMR per order. We find that largely improved makespans can be expected. In addition, we analyze the effects of stochastic picking times, speed differences between AMRs and pickers, and a zoning strategy. The ripple effect caused by stochastic picking times, in which a single delay may cascade through a tightly synchronized schedule and deteriorate picking performance, can be effectively mitigated by separating the workforce into smaller subgroups. Another important finding is that pickers and AMR should have approximately the same travel speed because slower AMRs deteriorate system performance. Finally, zoning slightly decreases the flexibility of the system and should be used if dictated by organizational reasons.
History: This article is part of a special issue: Emerging Topics in Transportation Science and Logistics.
Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2023.1207 .
Robotisation is increasing in warehouse operations, but human employment continues to be relevant. Traditionally manual activities, such as order picking, are being re-designed into collaborative human–robot tasks. This trend exemplifies the transition towards a human-centric Industry 5.0, focusing on synergy instead of seeking human replacement. However, human workers are increasingly hard to recruit and retain. We contribute to the underrepresented literature on human factors within the domain of operations and production management research and investigate the deployment of robotic technologies alongside human workers in a sustainable way. With a unique real-effort experiment, we investigate how the manipulation of picker’s experienced levels of autonomy affects their job satisfaction and core self-evaluations, two key behavioural outcomes that determine employee turnover intentions. We establish that the introduction of human–robot collaboration positively affects job satisfaction for the contrasting collaboration dynamics of (i) gaining control (the human leading the robot) and (ii) ceding control (the human following the robot). This positive effect is larger when the human is following the robot. We additionally find that following the robot positively affects pickers’ self-esteem and that self-efficacy related to human–robot interaction benefits from the introduction of collaborative robotics, regardless of the setup dynamics.
A Robotic Mobile Fulfillment System (RMFS) is an automated parts-to-picker material handling system, in which robots carry pods with products to the order pickers. It is particularly suitable for e-commerce order fulfillment and can quickly and frequently reallocate workers and robots across the picking and replenishment processes to respond to strong demand fluctuations. More resources for the picking process means lower customer wait times, whereas more resources for the replenishment process means a higher inventory level and product availability. This paper models the RMFS as a queuing network and integrates it within a Markov decision process (MDP), that aims to allocate robots across the pick and replenishment processes during both high and low demand periods, based on the workloads in these processes. We extend existing MDP models with one resource type and one process to an MDP model for two resources types and two processes. The policies derived from the model are compared with benchmark policies from practice. The results show that the length of the peak demand phase and the height of the peak affects the optimal policy choice. In addition, policies that continually reallocate resources based on the workload outperform benchmark policies from practice. Moreover, if the number of robots is limited, continual resource reallocation can reduce costs sharply. The results show that optimal dynamic policies can reduce the cost by up to 52.18% on average compared to optimal fixed policies.
To reduce unproductive picker walking in traditional picker-to-parts warehousing systems, automated guided vehicles (AGVs) are used to support human order pickers. In an AGV-assisted order-picking system, each human order picker is accompanied by an AGV during the order-picking process. AGVs receive the picked items and, once a picking order is complete, autonomously bring the collected items to the shipping area. Meanwhile, a new AGV is requested to meet the picker at the first storage position of the next picking order. Thus, the picker does not have to return to a central depot and continuously picks order after order. This paper addresses both the routing of an AGV-assisted picker through a single-block, parallel-aisle warehouse and the sequencing of incoming orders. We present an exact polynomial time routing algorithm for the case of a given order sequence, which is an extension of the algorithm of Ratliff and Rosenthal [Ratliff HD, Rosenthal AS ( 1983 ) Order-picking in a rectangular warehouse: A solvable case of the traveling salesman problem. Oper. Res. 1(3):507–521], and a heuristic for the case in which order sequencing is part of the problem. In addition, we investigate the use of highly effective traveling salesman problem (TSP) solvers that can be applied after a transformation of both problem types into a standard TSP. The numerical studies address the performance of these methods and study the impact of AGV usage on picker travel: by using AGVs to avoid returns to the depot and by sequencing in (near-) optimal fashion, picker walking can be reduced by about 20% compared with a traditional setting. Sharing AGVs among the picker workforce enables a pooling effect so that, in larger warehouses, only about 1.5 AGVs per picker are required to avoid picker waiting.
Summary of Contribution: New technologies, such as automatic guided vehicles (AGVs) are currently considered as options to increase the efficiency of the order-picking process in warehouses, which is responsible for a large part of operational warehousing costs. In addition, picker-routing decisions are more and more often based on algorithmic decision support because of their relevance for decreasing unproductive picker walking time. This paper addresses both aspects and investigates routing algorithms for AGV-assisted order picking in parallel-aisle warehouses. We present a dynamic programming routine with polynomial runtime to solve the problem variant in which the sequence of picking orders is fixed. For the variant in which this sequence is a decision, we show that the problem becomes NP-hard, and we propose a greedy heuristic and investigate the use of state-of-the-art exact and heuristic traveling salesman problem solution methods to address the problem. The numerical studies demonstrate the effectiveness of the algorithms and indicate that AGV assistance promises strong improvements in the order-fulfillment process. Because of the practical relevance of AGV-assisted order picking and the presented algorithmic contributions, we believe that the paper is relevant for practitioners and researchers alike.
Efficient order fulfillment processes in warehouses are a key success factor in times of increasing global retail sales volumes and same-day deliveries. To streamline order fulfillment processes, warehouse managers frequently rely on autonomous mobile robots (AMRs). By supporting human order pickers with AMRs, unproductive picker walking time can be reduced, which is essential for increasing the performance of a traditional picker-to-parts system. We study an AMR-assisted picker-to-parts system in which the warehouse is partitioned into disjoint zones, each with one order picker assigned to it. A set of customer orders is given, each associated with a due date until which its items are to be collected. Each AMR of a given fleet is responsible for transporting the items of a single batch of customer orders from the picking area to the depot. An order picker collects those batch items that are stored in her zone and transports them to a handover location. The AMR visits the handover locations and returns to the depot after collecting all batch items. The objective is to minimize the total tardiness of all customer orders. We define the resulting problem as mixed integer program and provide an efficient heuristic solution approach. Furthermore, we investigate the influence of increasing the AMR fleet size and varying travel and walking speed ratios between AMRs and order pickers. We find that a slight increase in the speed ratio leads to a larger reduction of the total tardiness compared to increasing the AMR fleet size.
Intelligent part‐to‐picker systems are spreading across a broad range of industries as preferred solutions for agile order fulfillment, wherein mobile racks are carried by robots and moved to stations where human pickers can pick items from them. Such systems raise the challenge of designing good work schedules for human pickers; they also give rise to a new class of operational scheduling problems in human‐robot coordinated order picking systems. This work studies the problem of finding a suitable robot schedule that takes into account the schedule‐induced fluctuation of the working states of human pickers. A proposed model enables mobile racks with various workloads to be assigned to pickers, and schedule the racks that are assigned to every picker to minimize the expected total picking time. The problem is formulated as a stochastic dynamic program model. An approximate dynamic programming (ADP)‐based branch‐and‐price solution approach is used to solve this problem. The developed model is calibrated using data that were collected from a dominant e‐commerce company in China. Pickers’ working state transitions are modeled based on data obtained from this warehouse. Counter‐factual studies demonstrate that the proposed approach can solve a moderately sized problem with 50 racks in under two minutes. More importantly, the approach yields high‐quality solutions with picking times that are 10% shorter than the solutions that did not consider schedule‐induced fluctuations of pickers’ working states.
Material handling systems are progressively becoming robotized in e-commerce distribution centers. Mobile material handling solutions cut labor costs, work 24/7, and improve system efficiency. These and many other merits make them a perfect fit for e-commerce fulfillment centers. This paper presents analytical models for Last-Mile-Delivery and Meet-in-Aisle mobile solutions and compares them with traditional manual order picking. We study the potential business cases of these two warehousing mobile solutions through estimating the number of required robots and pickers under different throughput rates, pick cycle, picking area size, and storage policy scenarios. We evaluate the performance of the models through multiple analyses. A simulation model is built to evaluate the accuracy of the proposed models. Then, we design a collection of experiments to study the performance of the proposed models. The results unveil that the Last-Mile-Delivery better fits the cases with higher throughput rates, while Meet-in-Aisle is a suitable solution for facilities with large picking areas and low picks per cycle.
Many intra-logistics systems, such as automated container terminals, distribution warehouses, and cross-docks, observe parallel process flows, which involve simultaneous (parallel) operations of independent resources while processing a job. When independent resources work simultaneously to process a common job, the effective service requirement of the job is difficult to estimate. For modeling simplicity, researchers tend to assume sequential operations of the resources. In this paper, we propose an efficient modeling approach for parallel process flows using two-phase servers. We develop a closed queuing network model to estimate system performance measures. Existing solution methods can evaluate the performance of closed queuing networks that consist of two-phase servers with exponential service times only. To solve closed queuing networks with general two-phase servers, we propose new solution methods: an approximate mean value analysis and a network aggregation dis-aggregation approach. We derive insights on the accuracy of the solution methods from numerical experiments. Although both solution methods are quite accurate in estimating performance measures, the network aggregation dis-aggregation approach consistently performs best. We illustrate the proposed modeling approach for two intra-logistic systems: a container terminal with automated guided vehicles and a shuttle-based compact storage system. Results show that approximating the simultaneous operations as sequential operations underestimates the container terminal throughput on average by 28% and at maximum up to 47%. Similarly, considering sequential operations of the resources in the compact storage system results in an underestimation of the throughput capacity up to 9%.
In “Capacity Analysis of Sequential Zone Picking Systems” by van der Gaast, De Koster, Adan, and Resing, a capacity model for sequential zone picking systems is developed. These systems are popular internal transport and order-picking systems in practice. The major disadvantage of such systems is congestion and blocking under heavy use, leading to long order throughput times. To reduce blocking and congestion, most systems use the block-and-recirculate protocol to dynamically manage workload. In their paper, the various elements of the system are modeled as a multiclass block-and-recirculate queueing network with capacity constraints on subnetworks. Because of this blocking protocol, the stationary distribution of the queueing network is highly intractable. The authors propose an approximation method based on jump-over blocking that allows realistically sized systems to be efficiently analyzed and can be used in the design phase of sequential zone picking systems. The results show that the relative error in the system throughput is typically less than 1% compared with simulation.
Robotic handling systems are increasingly applied in distribution centers. They require little space, provide flexibility in managing varying demand requirements, and are able to work 24/7. This makes them particularly fit for e-commerce operations. This paper reviews new categories of automated and robotic handling systems, such as shuttle-based storage and retrieval systems, shuttle-based compact storage systems, and robotic mobile fulfillment systems. For each system, we categorize the literature in three groups: system analysis, design optimization, and operations planning and control. Our focus is to identify the research issue and operations research modeling methodology adopted to analyze the problem. We find that many new robotic systems and applications have hardly been studied in academic literature, despite their increasing use in practice. Because of unique system features (such as autonomous control, flexible layout, networked and dynamic operation), new models and methods are needed to address the design and operational control challenges for such systems, in particular, for the integration of subsystems. Integrated robotic warehouse systems will form the next category of warehouses. All vital warehouse design, planning, and control logic, such as methods to design layout, storage and order-picking system selection, storage slotting, order batching, picker routing, and picker to order assignment, will have to be revisited for new robotized warehouses.
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.
Motivated by recent technological advances in mobile robotics, this paper explores a novel approach for warehouse order picking. In particular, this work considers two types of commercially available mobile robots – one that can grasp items from a shelf (a picker) and another (a transporter) that can quickly deliver all items from the pick list to the packing station. A new vehicle routing problem is defined which seeks to minimise the time to deliver all items from a pick list to the packing station, a problem termed the pick, place, and transport vehicle routing problem. A mixed integer linear programming formulation is developed to answer three related research questions. First, what combination of picker and transport robots is required to obtain performance exceeding traditional human-based picking operations? Second, how should the composition of the robot fleet be altered to affect the greatest performance improvements? Finally, what are the impacts of warehouse layout designs when coordinated mobile robots are deployed? An extensive numerical analysis reveals that, (1) increasing the number of cross aisles decreases system performance; (2) centrally located packing stations improve system performance; and (3) the average distance from each pick location to the packing station and the average distance between pick locations are effective metrics for identifying specific fleet modifications that are likely to yield system improvements.
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 order to differentiate from competitors in terms of customer service, warehouses accept late orders while providing delivery in a quick and timely way. This trend leads to a reduced time to pick an order. The main objectives of this research are to determine which order picking planning problems are related, to explain why and how individual planning problems are related, and to identify excellent performing policy combinations in several practical situations. Previous research shows contradictory findings on which planning problems are related. This paper is the first that explicitly analyzes and statistically proves the relations between storage, batching, zoning, and routing by a full factorial ANOVA. The value of combining the four main order picking planning problems is shown with a real-life case study as well as for multiple generalized warehouse designs. The results of the study clearly indicate that warehouses can achieve significant benefits by considering storage, batching, zone picking, and routing policies simultaneously. Awareness of the influence of an individual planning problem on the overall order picking performance is required to manage warehouse operations, resulting in a reduced order pick time.
The estimation of the average travel distance in a low-level picker-to-part order picking system can be done by analytical methods in most cases. Often a uniform distribution of the access frequency over all bin locations is assumed in the storage system. This only applies if the bin location assignment is done randomly. If the access frequency of the articles is considered in the bin location assignment to reduce the average total travel distance of the picker, the access frequency over the bin locations of one aisle can be approximated by an exponential density function or any similar density function. All known calculation methods assume that the average number of orderlines per order is greater than the number of aisles of the storage system. In case of small orders this assumption is often invalid. This paper shows a new approach for calculating the average total travel distance taking into account that the average number of orderlines per order is lower than the total number of aisles in the storage system and the access frequency over the bin locations of an aisle can be approximated by any density function.
Class-based storage is widely studied in the literature and applied in practice. It divides all stored items into a number of classes according to their turnover. A class of items with higher turnover is allocated to a region closer to the warehouse depot. In the literature, it has been shown that the use of more storage classes leads to a shorter travel time for storing and retrieving items. A basic assumption in this literature is that the required storage space for all items equals their average inventory level, which is valid only if an infinite number of items can be stored in each storage region. This paper revisits class-based storage by considering each storage space to contain only a finite number of items. We develop a travel-time model and an algorithm that can be used for determining the optimal number and boundaries of storage classes in warehouses. Different from the conventional research, our findings illustrate that commonly a small number of classes is optimal. In addition, we find the travel time is fairly insensitive to the number of storage classes in a wide range around the optimum. This suggests that a manager can select a near-optimal number of storage classes in an easy way and need not be worried about the impact of storage-class reconfigurations. We validate our findings for various cases, including different ABC-demand curves, space-sharing factors, number of items, storage rack shapes, discrete storage locations, and stochastic item demand.This article is protected by copyright. All rights reserved.
We propose a simple proof of Norton's theorem for multiclass quasi-reversible networks.
At Bloemenveiling Aalsmeer (VBA), about 19 million flowers have to be distributed daily to customers in a building of 1 million m2 within a few hours. With the increasing daily number of customer orders, the congestion in the main distribution area increases. As a consequence, the makespan exceeds the available time, and flowers arrive too late at the customers. This paper investigates the concept of zoning in the distribution process, where distributors work in teams for a fixed group of customers in a specific zone of the distribution area. Customers are assigned to zones to balance workload. We show by simulation that this way of organizing the distribution process reduces congestion and leads to considerable improvements in both makespan and transaction lead time.
Distribution centers have recently adopted Autonomous Vehicle-based Storage and Retrieval Systems (AVS/RSs) as a potential alternative to traditional automated storage and retrieval systems for processing unit-load operations. The autonomy of the vehicles in an AVS/RS provides a level of hardware sophistication, which can lead to the improvements in operation efficiency and flexibility that will be necessary in distribution centers of the future. However, in order to exploit the potential benefits of the technology, an AVS/RS must be designed using a detailed understanding of the underlying dynamics and performance trade-offs. Design decisions such as the configuration of aisles and columns, allocation of resources to zones, and vehicle assignment rules can have a significant impact on the performance of AVS/RSs. In this research, the performance impact of these design decisions is investigated using an analytical model. The system is modeled as a multi-class semi-open queuing network with class switching and a decomposition-based approach is developed to evaluate the system performance and obtain insights. Numerical studies provide various insights that could be useful in the design conceptualization of AVS/RSs.
We consider the problem of controlling M/M/c queuing systems. By providing a new definition of the time of transition, we enlarge the standard set of decision epochs and obtain a preferred version of the n-period problem in which the times between transitions are exponential random variables with constant parameter. Using this new device, we are able to utilize the inductive approach in a manner characteristic of inventory theory. The efficacy of the approach is demonstrated by successfully finding the form of an optimal policy for three distinct models that have appeared in the literature, namely, those of (i) Miller and Cramer, (ii) Crabill and Sabeti, and (iii) Low of particular note is our analysis of the Miller-Cramer model, in which we show that a policy optimal for all sufficiently small discount factors can be obtained from the usual average cost functional equation without recourse to further computation.
A classical order picking problem is the case where items have to be picked from both sides of an aisle and the picker cannot reach items on both sides without changing position. Hence the picker must cross the aisle one or more times. An efficient optimal algorithm is developed and shown to yield policies with up to 30% savings in travel time over commonly used policies. It is also shown that, for most practical aisle widths, it is significantly more efficient to pick both sides of the aisle in the same pass (a traversal policy) rather than pick one side and then pick the other side (a return policy) unless the pick densities are greater than 50%. All the algorithms presented here can be implemented in real time on a microcomputer.
"Bucket brigades" are a way of sharing work on a flow line that results in the spontaneous emergence of balance and consequent high throughput. All this happens without a work-content model or traditional assembly line balancing technology. Here we show that bucket brigades can be effective even in the presence of variability in the work content. In addition, we report confirmation at the national distribution center of a major chain retailer, which experienced a 34% increase in productivity after the workers began picking orders by bucket brigade.
In today’s competitive scenario of increasingly faster deliveries and smaller order sizes, a solution that is being used more
frequently is the pick-and-pass Order Picking System (OPS). The purpose of this study is to define a framework for the pick-and-pass
system design, by expanding previous literature on this topic. The framework aims at minimising the overall picking costs
while respecting the required service level (i.e. order throughput time), and can be easily applied to the selection stage
of OPS design. The number of zones and the number of pickers per zone are among the main project data for the framework application.
Analytical models are used to estimate the travel distance, and network queuing theory to analyse the mean order throughput.
On the basis of the proposed framework, pick-and-pass system performance is examined as a function of two typical design conditions:
order size and number of items.
KeywordsOrder picking–Pick-and-pass–Warehousing–Queuing
We consider a queuing network with M exponential service stations and with N customers. We study the behavior of a subsystem σ, which has a single node as input and a single node as output, when the subsystem parameters are varied. An “equivalent” network is constructed in which all queues except those in subsystem σ are replaced by a single composite queue. We show that for certain classes of system parameters, the behavior of subsystem σ in the equivalent network is the same as in the given network. The analogy to Norton's theorem in electrical circuit theory is demonstrated. In addition, the equivalent network analysis can be applied to open exponential networks.
We consider discrete time average cost Markov decision processes with countable state space and finite action sets. Conditions recently proposed by Borkar, Cavazos-Cadena, Weber and Stidham, and Sennott for the existence of an expected average cost optimal stationary policy are compared. The conclusion is that the Sennott conditions are the weakest. We also give an example for which the Sennott axioms hold but the others fail.
It is shown that Jackson's product form is retained for queueing networks with capacity constraints under the assumption of a ‘jump-over’ blocking protocol.
The more challenging case of transient analysis of Markov chains is investigated in Chapter 5. The chapter introduces symbolic solutions in simple cases such as small or very regular state spaces. In general, numerical techniques are more suitable and are therefore covered in detail. Uniformization and some variants thereof are introduced as the method of choice for transient analysis in most cases. Particular emphasis is given to stiffness tolerant uniformization that can be of practical relevance in many modeling scenarios where relatively rare and fast events occur concurrently. As an alternative a method for aggregation/disaggregation of stiff Markov chains is introduced for a computation of approximate transient state probabilities. The method is based on a distinction of fast recurrent and fast transient sets of states that can be aggregated with relatively small error. All steps are illustrated by a detailed example model of server breakdown and repair. In addition to numerical results an error analysis is provided as well.
This paper proposes an approximation model based on queuing network theory to analyze the impact of order batching and picking area zoning on the mean order throughput time in a pick-and-pass order picking system. The model includes the sorting process needed to sort the batch again by order. Service times at pick zones are assumed to follow general distributions. The first and second moments of service times at zones and the visiting probability of a batch of orders to a pick zone are derived. Based on this information, the mean throughput time of an arbitrary order in the order picking system is obtained. Results from a real application and simulation show that this approximation model provides acceptable accuracy for practical purposes. Furthermore, the proposed method is simple and fast and can be easily applied in the design and selection process of order picking systems.
In this paper, an approximation method is discussed for the analysis of pick-to-belt orderpicking systems. The aim of the approximation method is to provide an instrument for obtaining rapid insight in the performance of designs of pick-to-belt orderpicking systems. It can be used to evaluate the effects of changing the layout of the system, the number of picking stations, the number of pickers, the conveyor speed, the number of bins to be processed per day, the number of orderlines per bin, etc. Especially in the design phase, modeling and analysis speed is more important than accuracy. The method presented in this paper is based on Jackson network modeling and analysis. The method is fast and sufficiently accurate. The method is used by Ingenieursbureau Groenewout B.V., for early-stage evaluation of design alternatives of pick-to-belt orderpicking systems and general transportation systems.