Robotic Mobile Fulfillment System Research Articles

Warehouse layout optimization for fishbone robotic mobile fulfillment systems

The rapid development of electronic commerce has increased demands for order fulfillment efficiency, making this a crucial challenge for warehouse systems. The study proposes a novel fishbone robotic mobile fulfillment system (FRMFS) to optimize warehouse layout and enhance the picking efficiency of automated warehouse systems, such as robotic mobile fulfillment systems (RMFS). Through the construction and analysis of mathematical models, the research demonstrates that FRMFS can significantly reduce the travel distance of robots when compared to traditional RMFS. This leads to an improvement in the overall picking efficiency of the warehouse system. The study also examines the impact of warehouse parameters, cross-aisle angles, and the number of picking stations on system operational efficiency. Simulation experiments confirm that FRMFS can reduce picking distances by 18%–28% compared to traditional RMFS. This makes it particularly suitable for complex warehouse systems with high requirements for operational response time and system throughput. Furthermore, the study introduces a point-based layout design method for picking stations in FRMFS, demonstrating its efficiency as a heuristic approach. This research presents a scientific analysis framework and model support for the operational design and optimization of FRMFS, offering valuable insights for management practices.

The role of energy consumption in robotic mobile fulfillment systems: Performance evaluation and operating policies with dynamic priority

The robotic mobile fulfillment system (RMFS), with wide application in warehousing and logistics, requires many robots powered by electricity, which significantly impacts energy consumption. This paper investigates the energy consumption in the RMFS under a classic e-business environment, which classifies the orders into regular orders and expedited orders. We evaluate the impact of three dynamic priority policies (the earliest deadline first policy, waiting time-dependent policy, and weighted waiting time first policy) on throughput time and energy consumption. This paper proposes multi-class semi-open queuing network models (SOQN) with dynamic priority policies to investigate energy consumption. We validate the accuracy of the analytical models by simulation models. This paper makes the following contributions: (1) In methodology, we propose new methods to solve the SOQN with dynamic priority policies. (2) In operational planning and control, we are among the earliest to investigate the impact of dynamic priority policies on order throughput time and energy consumption in an RMFS. (3) In design optimization, we propose a decision tool to optimize the robot number for realizing the required throughput time with minimal energy consumption. Our model can also decide the optimal warehouse shape to minimize energy consumption. (4) In system analysis, we estimate the energy consumption per transaction in an RMFS, providing logistics managers insights into energy saving of warehouses.

A dynamic programming algorithm for order picking in robotic mobile fulfillment systems

AbstractThe 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.

Optimizing Robotic Mobile Fulfillment Systems for Order Picking Based on Deep Reinforcement Learning.

Robotic Mobile Fulfillment Systems (RMFSs) face challenges in handling large-scale orders and navigating complex environments, frequently encountering a series of intricate decision-making problems, such as order allocation, shelf selection, and robot scheduling. To address these challenges, this paper integrates Deep Reinforcement Learning (DRL) technology into an RMFS, to meet the needs of efficient order processing and system stability. This study focuses on three key stages of RMFSs: order allocation and sorting, shelf selection, and coordinated robot scheduling. For each stage, mathematical models are established and the corresponding solutions are proposed. Unlike traditional methods, DRL technology is introduced to solve these problems, utilizing a Genetic Algorithm and Ant Colony Optimization to handle decision making related to large-scale orders. Through simulation experiments, performance indicators-such as shelf access frequency and the total processing time of the RMFS-are evaluated. The experimental results demonstrate that, compared to traditional methods, our algorithms excel in handling large-scale orders, showcasing exceptional superiority, capable of completing approximately 110 tasks within an hour. Future research should focus on integrated decision-making modeling for each stage of RMFSs and designing efficient heuristic algorithms for large-scale problems, to further enhance system performance and efficiency.

Deep reinforcement learning driven cost minimization for batch order scheduling in robotic mobile fulfillment systems

Robotic Mobile Fulfillment Systems (RMFS) are extensively employed in modern warehouses. In the era of booming e-commerce, this parts-to-picker model significantly reduces warehouse costs and enhances operational efficiency. The primary focus of this article is on the scheduling of batch orders, which involves the simultaneous allocation of mobile robots and picking stations to orders to meet their requirements, with the aim of minimizing processing costs. While the optimization of RMFS has been extensively investigated by scholars in recent years., research on categorized storage remains limited. Furthermore, combinatorial optimization in scenarios with large orders, numerous picking stations, and multiple mobile robots presents an ongoing and significant challenge. To overcome these challenges, we introduce the Enhanced Deep Reinforcement Learning Method for Batch Order Scheduling (EDRL-OBOS), designed to minimize operational costs in RMFS. Our proposed algorithm, EDRL-OBOS, features a uniquely designed state space that encompasses the allocation of all orders, with the variable portion of the state space diminishing as the algorithm evolves. Moreover, we substitute traditional actions with heuristic rules, significantly enhancing the efficiency of the algorithm. Additionally, we establish a reward function based on a greedy algorithm, ensuring that our method surpasses conventional algorithms. As the number of episodes progresses, the EDRL-OBOS algorithm assigns picking stations and sequences of mobile robots to each order until all orders within the state space are fulfilled, subsequently determining the reward. Subsequently, all states are reset to their initial conditions, and the order allocation scheme is optimized through the learning experience from the previous episode, until convergence is reached. Ultimately, we conduct simulation experiments by varying the number of orders, picking stations, and mobile robots. The results indicate that the EDRL-OBOS algorithm achieves a maximum cost reduction of 22.89%, a minimum of 19.66%, and an average of 21.57%, across various scenarios. At the same time, the computation of our algorithms is superior to that of traditional algorithms.

A simulation-based genetic algorithm for a semi-automated warehouse scheduling problem with processing time variability

For warehouse operations, efficiently scheduling the available resources is crucial to improve the productivity and customer satisfaction. This paper proposes a simulation-based evolutionary algorithm for order scheduling and multi-robot task assignment in a robotic mobile fulfillment system. The algorithm proactively deals with the effects of the processing time variability by evaluating schedules based on both its system performance as well as its robustness under uncertain conditions. The algorithm implements an efficient resource allocation method and a variance reduction technique to reduce the overall computational burden. The experimental results show that the techniques to reduce the computational time are effective and can significantly reduce the amount of simulations required for the fitness evaluation. If a candidate schedule is allocated insufficient simulation replications it can lead to an inaccurate estimate of its long-term average performance. This could lead to an average performance loss of 7.3 %. Furthermore, the proactive scheduler is able to generate schedules that are more robust compared to deterministically generated. A reduction in the average operational cost of about 5 % can be reached, compared to a deterministically generated schedule. The paper reveals the relevance of identifying and modeling uncertainty when designing schedules in an operational system, rather than looking for optimal schedules for ideal scenarios.

Velocity-based rack storage location assignment for the unidirectional robotic mobile fulfillment system

Nowadays, the robotic mobile fulfillment system (RMFS) has been increasingly used by online retailers. Compared with traditional picker-to-parts warehouses, the racks of RMFS do not have to return to the same location after picking, thus we can dynamically change their locations, which brings great potential to efficiently fulfill orders. Aiming at minimizing the sum of rack travel distances, the key question is how to reassign a rack to an unoccupied storage location after picking items from the rack. However, the issue involves two challenges for unidirectional RMFS, one is that huge differences may exist between the classical Manhattan distance estimation and the actual distance for the unidirectional aisles in RMFS, and the other one is that we need to account for the frequency of rack moving for multi-item orders. We thus first propose closed-form formulas to optimally estimate the cycle travel distance for each rack. Then, by overcoming the repeated counting issue for multi-item orders, we propose a novel SKU (Stock Keeping Units)-correlation-based algorithm to choose high-velocity racks, which can better fulfill multi-item orders. Finally, embedding the cycle travel distance and SKU-correlation-based velocity, we propose a Velocity-based Rack Storage Location Assignment method (VRSLA) to solve the rack storage location assignment problem by assigning high-velocity racks to the nearest storage locations. Collaborating with a large online retailer in China, we demonstrate the performance of VRSLA by using both small-scale and large-scale datasets. The computational results show that VRSLA not only can achieve near-best solutions compared with an integer programming model solved by Gurobi, but also outperforms four state-of-the-art assignment methods in literature (random, velocity-based class, shortest path, and sale-based) by reducing the rack travel distance up to 43.32%. We also found that the stronger the correlation between SKUs on the racks or the larger the size of the RMFS, the shorter the rack travel distance by the proposed VRSLA method.

A reinforcement learning-based hyper-heuristic for AGV task assignment and route planning in parts-to-picker warehouses

Globally, e-commerce warehouses have begun implementing robotic mobile fulfillment systems (RMFS), which can improve order-picking efficiency by using automated guided vehicles (AGVs) to realize operations from parts to pickers. AGVs depart from their initial points, move to a target rack position, and subsequently transport racks to picking stations. The AGVs return the racks to their original positions after the workers pick them up. When all tasks are completed, the AGVs return to their starting point. In this context, the main challenge is the task assignment and route planning of multiple AGVs to minimize travel times. We formulate a mixed-integer linear programming (MILP) model with valid inequalities to solve small problem instances optimally. We introduce a reinforcement learning (RL)-based hyper-heuristic (HH) framework to solve large instances to near-optimality. A typical HH framework comprises two levels: high-level heuristics (HLH) and low-level heuristics (LLH). The framework starts from an initial solution and improves iteratively through LLHs, while the HLH invokes a selection strategy and an acceptance criterion to generate a new solution. We propose a novel selection strategy based on the improved Multi-Armed Bandits algorithm called Co-SLMAB and Exponential Monte Carlo with counters (EMCQ) as the acceptance criterion. The corresponding collision avoidance rules are then formulated for different conflicts to construct a conflict-free traveling route for AGVs. Besides testing the proposed framework’s effectiveness in real-life warehouse layouts, we perform extensive computational experiments and a thorough sensitivity analysis. The results show that (i) the proposed valid inequalities aid in obtaining better lower bounds and significantly speed up the solution process; (ii) the Co-SLMAB-HH framework is quite competitive compared to CPLEX, outperforming the other tested hyper-heuristics and the problem-specific heuristic regarding convergence and computation time; and (iii) a pool of LLHs consisting of a wide range of different operators is advantageous over a limited set of simple operators while solving problems using hyper-heuristics.

Improving order picking efficiency through storage assignment optimization in robotic mobile fulfillment systems

The order picking efficiency in robotic mobile fulfillment systems is not only determined by the order and rack processing sequences, but also by the product distribution on the racks. In this paper, we focus on long-term planning based on historical order data to identify the optimal distribution of SKUs on racks for order picking operation improvement. This product distribution problem is formulated as an integer linear program, with the goal of minimizing rack movements required to fulfill orders. We develop a solution procedure that takes into account both the affinity and frequency of products in the orders, as well as the corresponding performance of the order and rack sequencing. We evaluate the performance of the proposed method through comparisons with the theoretical optimal solution on manually generated small instances and with existing heuristic solutions on a large real-world order dataset provided by a major e-commerce company, demonstrating a significant improvement from using our algorithm.

Storage Location Assignment for Improving Human–Robot Collaborative Order-Picking Efficiency in Robotic Mobile Fulfillment Systems

The robotic mobile fulfillment (RMF) system is a parts-to-picker warehousing system and a sustainable technology used in human–robot collaborative order picking. Storage location assignment (SLA) tactically benefits order-picking efficiency. Most studies focus on the retrieval efficiency of robots to solve SLA problems. To further consider the crucial role played by human pickers in RMF systems, especially in the context that the sustainable performance of human workers should be paid attention to in human–robot collaboration, we solve the SLA problem by aiming to improve human–robot collaborative order-picking efficiency. This study specifically makes decisions on assigning multiple items of various products to the slots of pods in the RMF system, in which human behavioral factors are taken into account. To obtain the solution in one mathematical model, we propose the heuristic algorithm under a two-stage optimization method. The results show that assigning correlated products to pods improves the retrieval efficiency of robots compared to class-based assignment. We also find that assigning items of each product to slots of pods, considering behavioral factors, benefits the operation efficiency of human pickers compared to random assignment. Improving human–robot collaborative order-picking efficiency and increasing the capacity usage of pods benefits sustainable warehousing management.

Optimal resource allocation and routing in robotic mobile fulfillment systems

This paper addresses a combinatorial optimization problem in the context of a robotic mobile fulfillment system deployed in a warehouse that consists of movable racks, a picker, and a fleet of mobile robots. The objective is to efficiently prepare a set of orders with specified due dates by bringing the racks to a picking station in a sequential manner, where the picker selects the required products for the open orders, namely the orders that are being processed simultaneously. The picking station has a limited capacity for processing of open orders. Our goal is to minimize the total travel times of the robots and the delays in fulfilling orders. To achieve this, several decision variables need to be determined, including order sequencing, rack allocation, rack scheduling, and mobile robot routing. We formulate the problem as a mixed integer programming model and devise a heuristic algorithm grounded in decomposition principles to address the problem across two distinct phases. Additionally, we introduce two variable neighborhood search (VNS) algorithms tailored to resolve each respective phase within the aforementioned heuristic framework. The performance of the proposed solution approaches is evaluated and compared using two sets of randomly generated test instances, encompassing small-size and large-size instances. Furthermore, we conduct an analysis to examine the influence of key parameters on the objective function value.

Joint Optimization of Item and Pod Storage Assignment Problems with Picking Aisles’ Workload Balance in Robotic Mobile Fulfillment Systems

The item and pod storage assignment problems, two critical issues at the strategic level in robotic mobile fulfillment systems, have a strong correlation and should be studied together. Moreover, the workload balance in each picking aisle needs to be considered in the storage assignment problems to avoid robots’ congestion within picking aisles. Motivated by these, the joint optimization of item and pod storage assignment problems (J-IPSAP) with picking aisles’ workload balance is studied. The mixed integer programming model of the J-IPSAP with the workload balance constraint is formulated to minimize the robots’ movement distance. The improved genetic algorithm (IGA) with the decentralized pod storage assignment strategy is designed to solve the J-IPSAP model. The experimental results show that the IGA can obtain high-quality solutions when compared with Gurobi and the two-stage heuristic algorithms. The robots’ movement distance is smallest when the width-to-length ratio of the storage area is close to 1, and the robots’ movement distance will increase with more stringent workload balance constraints.

Capacitated Vehicle Routing Problem with Pickup and Delivery in Robotic Mobile Fulfillment Systems

Capacitated Vehicle Routing Problem with Pickup and Delivery in Robotic Mobile Fulfillment Systems

Breaking the Limit on the Number of Robots Through the Conflict-Free Scheduling in Robotic Mobile Fulfillment Systems

Breaking the Limit on the Number of Robots Through the Conflict-Free Scheduling in Robotic Mobile Fulfillment Systems

Item Storage Assignment Problem in Robotic Mobile Fulfillment Systems With Nonempty Pods

Item Storage Assignment Problem in Robotic Mobile Fulfillment Systems With Nonempty Pods

Simultaneous allocation and sequencing of orders for robotic mobile fulfillment system using reinforcement learning algorithm

Robotic Mobile Fulfillment Systems (RMFS) can benefit large e-commerce warehouse operations significantly. To fulfill the orders received, RMFS deploys mobile robots to carry shelves back and forth from the storage area to the picking station. Order allocation and sequencing for mobile robots is a complex yet critical task as it influences the distance traveled by mobile robots in fulfilling the orders, i.e., appropriately allocating and sequencing the orders. In this paper, a Simultaneous Allocation and Sequencing of Orders Reinforcement Learning (SASORL) algorithm is proposed to minimize the distance traveled by mobile robots. Unlike existing methods, the SASORL algorithm optimizes order allocation and sequencing concurrently, significantly reducing mobile robot travel distance. The proposed SASORL algorithm encompasses three sets, namely state, action, and reward/penalty. The state set comprises the orders fulfilled, whereas the action set contains the orders yet to be fulfilled. The distance traveled by the mobile robot as a result of the orders allocated and sequenced is taken as the penalty for the proposed SASORL algorithm. As the proposed SASORL algorithm simultaneously allocates and sequences the orders to the mobile robots, the action set depletes, the state set enlarges, and the penalty updates until the action set becomes null. Each episode restarts with the learned experience of the prior episodes, and after completing a few episodes, the SASORL algorithm is capable of generating an optimal order allocation and sequence that commits the minimum travel distance to the mobile robots. SASORL algorithm is superior to widely adopted soft computing techniques when orders are randomly distributed. This superiority is evidenced by a 26% reduction in the maximum distance traveled by all mobile robots, a 54% reduction in the standard deviation of the distance traveled by the mobile robots, and a marginal increase of 7% in the total distance traveled by all mobile robots. Moreover, the SASORL algorithm outperforms soft computing techniques by 44% in terms of computation time.

Iterated-local-search-based chaotic differential evolution algorithm for hybrid-load part feeding scheduling optimization in mixed-model assembly lines

PurposeDriven by sustainable production, mobile robots are introduced as a new clean-energy material handling tool for mixed-model assembly lines (MMALs), which reduces energy consumption and lineside inventory of workstations (LSI). Nevertheless, the previous part feeding scheduling method was designed for conventional material handling tools without considering the flexible spatial layout of the robotic mobile fulfillment system (RMFS). To fill this gap, this paper focuses on a greening mobile robot part feeding scheduling problem with Just-In-Time (JIT) considerations, where the layout and number of pods can be adjusted.Design/methodology/approachA novel hybrid-load pod (HL-pod) and mobile robot are proposed to carry out part feeding tasks between material supermarkets and assembly lines. A bi-objective mixed-integer programming model is formulated to minimize both total energy consumption and LSI, aligning with environmental and sustainable JIT goals. Due to the NP-hard nature of the proposed problem, a chaotic differential evolution algorithm for multi-objective optimization based on iterated local search (CDEMIL) algorithm is presented. The effectiveness of the proposed algorithm is verified by dealing with the HL-pod-based greening part feeding scheduling problem in different problem scales and compared to two benchmark algorithms. Managerial insights analyses are conducted to implement the HL-pod strategy.FindingsThe CDEMIL algorithm's ability to produce Pareto fronts for different problem scales confirms its effectiveness and feasibility. Computational results show that the proposed algorithm outperforms the other two compared algorithms regarding solution quality and convergence speed. Additionally, the results indicate that the HL-pod performs better than adopting a single type of pod.Originality/valueThis study proposes an innovative solution to the scheduling problem for efficient JIT part feeding using RMFS and HL-pods in automobile MMALs. It considers both the layout and number of pods, ensuring a sustainable and environmental-friendly approach to production.

A bi-level optimization approach for joint rack sequencing and storage assignment in robotic mobile fulfillment systems

A bi-level optimization approach for joint rack sequencing and storage assignment in robotic mobile fulfillment systems

A cyber-physical robotic mobile fulfillment system in smart manufacturing: The simulation aspect

A cyber-physical robotic mobile fulfillment system in smart manufacturing: The simulation aspect

How to Deploy Robotic Mobile Fulfillment Systems

Many warehouses involved in e-commerce order fulfillment use robotic mobile fulfillment systems. Because demand and variability can be high, scheduling orders, robots, and storage pods in interaction with manual workstations are critical to obtaining high performance. Simultaneously, the scheduling problem is extremely complicated because of interactions between decisions, many of which must be taken timely because of short planning horizons and a constantly changing environment. This paper models all such scheduling decisions in combination to minimize order fulfillment time. We propose two decision methods for the above scheduling problem. The models batch the orders using different batching methods and assign orders and batches to pods and workstations in sequence and robots to jobs. Order picking and stock replenishment operations are included in the models. We conduct numerical experiments based on a real-world case to validate the efficacy and efficiency of the model and algorithm. Instances with 14 workstations, 400 orders, 300 stock-keeping units (SKUs), 160 pods, and 160 robots can be solved to near optimality within four minutes. Our methods can be applied to large instances, for example, using a rolling horizon. Because our model can be solved relatively fast, it can be used to take managerial decisions and obtain executive insights. Our results show that making integrated decisions, even when done heuristically, is more beneficial than sequential, isolated optimization. We also find that positioning pick stations close together along one of the system’s long sides is efficient. The replenishment stations can be grouped along another side. Another finding is that SKU diversity per pod and SKU dispersion over pods have strong and positive impacts on the total completion time of handling order batches. Funding: This work was supported by National Natural Science Foundation of China [72025103, 72361137001, 71831008, 72071173] and the Research Grants Council of the Hong Kong Special Administrative Region, China [HKSAR RGC TRS T32-707/22-N]. Supplemental Material: The e-companion is available at https://doi.org/10.1287/trsc.2022.0265 .