Order Batching Research Articles

Variation in batch ordering of imaging tests in the emergency department and the impact on care delivery.

To examine heterogeneity in physician batch ordering practices and measure the associations between a physician's tendency to batch order imaging tests on patient outcomes and resource utilization. In this retrospective study, we used comprehensive EMR data from patients who visited the Mayo Clinic of Arizona Emergency Department (ED) between October 6, 2018 and December 31, 2019. Primary outcomes are patient length of stay (LOS) in the ED, number of diagnostic imaging tests ordered during a patient encounter, and patients' return with admission to the ED within 72 h. The association between outcomes and physician batch tendency was measured using a multivariable linear regression controlling for various covariates. The Mayo Clinic of Arizona Emergency Department recorded approximately 50,836 visits, all randomly assigned to physicians during the study period. After excluding rare complaints, we were left with an analytical sample of 43,299 patient encounters. Findings show that having a physician with a batch tendency 1 standard deviation (SD) greater than the average physician was associated with a 4.5% increase in ED LOS (p < 0.001). It was also associated with a 14.8% (0.2 percentage points) decrease in the probability of a 72-h return with admission (p < 0.001), implying that batching may lead to more comprehensive evaluations, reducing the need for short-term revisits. A batch tendency 1SD greater than that of the average physician was also associated with an additional 8 imaging tests ordered per 100 patient encounters (p < 0.001), suggesting that batch ordering may be leading to tests that would not have been otherwise ordered had the physician waited for the results from one test before placing their next order. This study highlights the considerable impact of physicians' diagnostic test ordering strategies on ED efficiency and patient care. The results also highlight the need to develop guidelines to optimize ED test ordering practices.

Impulse synchronization strategy for supply chains considering combined effects and demand saturation

Supply chains often face sudden changes in production, distribution, and consumption as a result of factors such as pandemics, Black Friday, and mass production by manufacturers; this is called the ”impulse phenomenon.” The effect of the impulse phenomenon on the supply chain system can be positive or negative. Understanding how to use the impulse phenomenon to synchronize supply chain systems and avoid chaos is therefore important for supply chain management. Existing studies mainly use continuous synchronization strategies as a means to avoid chaos in supply chain systems; however, a discrete impulse synchronization strategy is easier to implement. Considering combined effects of consumption,distribution,production and demand saturation, this study constructs a supply chain system composed of a manufacturer, distributor, and retailer. We then construct a supply chain system with uncertain parameters and input disturbance. Using Lyapunov stability theory and matrix inequality, we obtain the impulse synchronization strategies of two supply chain systems. Finally, taking China’s supply chain system of corn, wheat, and rice as an example, we compare goodness of fit. The production, distribution, and consumption of rice are controlled using a temporary storage purchase policy, batch ordering, and promotion activities, and the effectiveness of the impulse synchronization strategy is verified. Our results show the following: (1) Considering combined effects and demand saturation, the supply chain system has better goodness of fit and better impulse synchronization. (2) When a chaotic supply chain system deviates from its expected state, if impulse intensity and the time interval satisfy Theorem 1 or 2, the supply chain system can be restored to its expected state; if not, the synchronization effect might not be achieved. (3) Generally, when impulse intensity is low, the time interval is short, if impulse intensity is high, the time interval should be longer.

Myocardial perfusion SPECT radiomic features reproducibility assessment: Impact of image reconstruction and harmonization.

Coronary artery disease (CAD) has one of the highest mortality rates in humans worldwide. Single-photon emission computed tomography (SPECT) myocardial perfusion imaging (MPI) provides clinicians with myocardial metabolic information non-invasively. However, there are some limitations to interpreting SPECT images performed by physicians or automatic quantitative approaches. Radiomics analyzes images objectively by extracting quantitative features and can potentially reveal biological characteristics that the human eye cannot detect. However, the reproducibility and repeatability of some radiomic features can be highly susceptible to segmentation and imaging conditions. We aimed to assess the reproducibility of radiomic features extracted from uncorrected MPI-SPECT images reconstructed with 15 different settings before and after ComBat harmonization, along with evaluating the effectiveness of ComBat in realigning feature distributions. A total of 200 patients (50% normal and 50% abnormal) including rest and stress (without attenuation and scatter corrections) MPI-SPECT images were included. Images were reconstructed using 15 combinations of filter cut-off frequencies, filter orders, filter types, reconstruction algorithms, number of iterations and subsets resulting in 6000 images. Image segmentation was performed on the left ventricle in the first reconstruction for each patient and applied to 14 others. A total of 93 radiomic features were extracted from the segmented area, and ComBat was used to harmonize them. The intraclass correlation coefficient (ICC) and overall concordance correlation coefficient (OCCC) tests were performed before and after ComBat to examine the impact of each parameter on feature robustness and to assess harmonization efficiency. The ANOVA and the Kruskal-Wallis tests were performed to evaluate the effectiveness of ComBat in correcting feature distributions. In addition, the Student's t-test, Wilcoxon rank-sum, and signed-rank tests were implemented to assess the significance level of the impacts made by each parameter of different batches and patient groups (normal vs. abnormal) on radiomic features. Before applying ComBat, the majority of features (ICC: 82, OCCC: 61) achieved high reproducibility (ICC/OCCC ≥ 0.900) under every batch except Reconstruction. The largest and smallest number of poor features (ICC/OCCC<0.500) were obtained by IterationSubset and Order batches, respectively. The most reliable features were from the first-order (FO) and gray-level co-occurrence matrix (GLCM) families. Following harmonization, the minimum number of robust features increased (ICC: 84, OCCC: 78). Applying ComBat showed that Order and Reconstruction were the least and the most responsive batches, respectively. The most robust families, in a descending order, were found to be FO, neighborhood gray-tone difference matrix (NGTDM), GLCM, gray-level run length matrix (GLRLM), gray-level size zone matrix (GLSZM), and gray-level dependence matrix (GLDM) under Cut-off, Filter, and Order batches. The Wilcoxon rank-sum test showed that the number of robust features significantly differed under most batches in the Normal and Abnormal groups. The majority of radiomic features show high levels of robustness across different OSEM reconstruction parameters in uncorrected MPI-SPECT. ComBat is effective in realigning feature distributions and enhancing radiomic features reproducibility.

A new mathematical model and meta-heuristic algorithm for order batching, depot selection, and assignment problem with multiple depots and pickers

The ‘order picking problem’ involves the efficient and organized retrieval of items from shelves to fulfill customer orders. In this study, we consider a new configuration of warehouse system with multiple pickers and depots (m-pickers & n-depots) for manually operated ‘picker-to-parts’ warehouses. The efficiency of the process is measured based on two metrics: i- total order picking distance of each picker ii- total number of pickers assigned to each of depots. The handled problem is called as ‘Order Batching, Depot Selection and Assignment Problem with Multiple Depots and Multiple Pickers (OBDSAPMDMP)11OBDSAPMDMP = Order Batching, Depot Selection, and Assignment Problem with Multiple Depots and Multiple Pickers.’. To solve this complex problem, a new bi-objective Mixed-Integer Linear Programming (MILP) formulation for small-sized problems and a meta-heuristic called ‘Dependent Harmony Search (DHS)22DHS = Dependent Harmony Search.’ for large-sized problems are proposed. The performance of DHS algorithm is evaluated by comparing the optimal results attained by MILP model. For the problem size of 10 orders, the average gap (%) in distance between the solution of DHS and MILP is 4.22%, although in some experiments DHS can find the optimal solution in a very short time. Also, in related analysis, it is seen that constructing multiple depots instead of one left-most located depot decreases total order picking distance by 7.11% on average.

Double‐sided queues and their applications to vaccine inventory management

AbstractWe consider a double‐sided queueing model with batch Markovian arrival processes (BMAPs) and finite discrete abandonment times, which arises in various stochastic systems such as perishable inventory systems and financial markets. Customers arrive at the system with a batch of orders to be matched by counterparts. While waiting to be matched, customers become impatient and may abandon the system without service. The abandonment time of a customer depends on its batch size and its position in the queue. First, we propose an approach to obtain the stationary joint distribution of age processes via the stationary analysis of a multi‐layer Markov modulated fluid flow process. Second, using the stationary joint distribution of the age processes, we derive a number of queueing quantities related to matching rates, fill rates, sojourn times and queue length for both sides of the system. Last, we apply our model to analyze a vaccine inventory system and gain insight into the effect of uncertainty in supply and demand processes on the performance of the inventory system. It is observed that BMAPs are better choices for modeling the supply/demand process in systems with high uncertainty for more accurate performance quantities.

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.

Solving an Order Batching and Sequencing Problem with Reinforcement Learning

The purpose of this research is to determine whether a DRL solution would be a suitable solution for the OBSP problem and to compare it with traditional methods. For this purpose, models trained with the PPO algorithm were tested in a complex and realistic warehouse environment, and an attempt was made to measure whether a strategy was developed to decrease the number of orders being late. A heuristic method was also applied and the results were compared on the same environment and data. The results showed that DRL approach that combines heuristics with the PPO algorithm has a better performance than the heuristics in minimizing the tardy order percentage in all tested scenarios.

A real‐life study on the value of integrated optimization in order picking operations under dynamic order arrivals

AbstractOptimizing the order picking operations is indispensable for warehouses that promise a high customer service level. While many areas for improvement have been identified and studied in the literature, a large gap remains between academia and practice. To help with closing this gap, we perform a case‐study in collaboration with a spare‐parts warehouse in Belgium. In this study, we optimize the order picking operations of the company, using the actual warehouse layout and real order data. A state‐of‐the‐art online integrated order batching, picker routing and batch scheduling algorithm is adapted to consider multiple real‐life constraints. More specifically, the dynamic arrival of new orders is considered, and a capacity constraint on the sorting installation should be respected. Furthermore, a new waiting strategy is studied in which order pickers can temporarily postpone certain orders, as combining them with possible future order arrivals may allow for more efficient overall picking performance. Finally, the performance of the current operating policy is compared with that of both a seed batching heuristic and our metaheuristic algorithm by use of an ANOVA analysis. The results indicate that the number of order pickers can be reduced by 12.5% if the new optimization algorithm is used, accompanied by an improvement in the offered customer service level.

Constructing Deep Concepts through Shallow Search

We propose bootstrap learning as a computational account for why human learning is modular and incremental, and identify key components of bootstrap learning that allow artificial systems to learn more like people. Originated from developmental psychology, bootstrap learning refers to people's ability to extend and repurpose existing knowledge to create new and more powerful ideas. We view bootstrap learning as a solution of how cognitively-bounded reasoners grasp complex environmental dynamics that are far beyond their initial capacity, by searching ‘locally’ and recursively to extend their existing knowledge. Drawing from techniques of Bayesian library learning and resource rational analysis, we propose a computational modeling framework that achieves human-like bootstrap learning performance in inductive conceptual inference. In addition, we demonstrate modeling and behavioral evidence that highlights the double-edged sword of bootstrap learning, such that people processing the same information in different batch orders could induce drastically different causal conclusions and generalizations, as a result of the different sub-concepts they construct in earlier stages of learning.

Developing an Efficient Model for Online Grocery Order Fulfillment

Due to the convenience of online grocery apps and home delivery, online grocery shopping has become popular in recent years. Globally, consumer behavior has significantly changed the consumption and purchase patterns of online grocery shopping. This study aimed to develop an efficient model for online grocery order fulfillment that both reduces costs and increases supply chain efficiency and sustainability. This study first aimed to develop the current picking model by adopting real-world data from a store in Riyadh, Saudi Arabia. Subsequently, four proposed models were developed to improve the efficiency and sustainability of the online grocery order fulfillment process. The results show a significant improvement in all models over the current picking model. The percentage improvements in fulfillment time per product are as follows: single order picking—8.33%; batch order picking—6.78%; zone order picking—3.08%; and hybrid order picking—13.20%, which combines zone and batch order picking. Retailers and online grocery apps could adopt these models to increase efficiency and sustainability. Also, these models have great potential for future research and improvement by optimizing product placement, in addition to picking methods and picking routes, which are the focus of this study.

Mathematical programming models for order picking in warehouses with decoupling of picker and cart

As a special Travelling Salesman Problem (TSP), the Single-Picker Routing Problem (SPRP) in warehouses is of important theoretical and practical significance. In manual order picking, the items are usually picked up by a picker with a cart. To speed up the picking process, the picker is allowed to stop the cart to pick up the items individually and return to the location of the cart. This paper proposes a mixed integer linear programming formulation for an order picking problem with the decoupling of the picker and the cart in a multi-block warehouse, where the picker capacity is at most four. And based on this model, order batching problem is also analysed. Through numerical experiments, the cost of above decoupling problems is computed under different settings of the speed ratio and the capacity of the picker while he/she is travelling alone. The results indicate how the decoupling of picker and cart leads to cost reduction. Our model shows good performance for orders of small and medium scale and hence has great potential to improve the order picking operation which is executed by decoupling containers and robots/vehicles in modern digital warehouse systems.

A deep reinforcement learning hyper-heuristic to solve order batching problem with mobile robots

A deep reinforcement learning hyper-heuristic to solve order batching problem with mobile robots

A hybrid approach integrating genetic algorithm and machine learning to solve the order picking batch assignment problem considering learning and fatigue of pickers

Modeling human behaviors has become increasingly relevant to improving the performance of manual order-picking systems. However, although a vast corpus of literature has recently started to consider the human factors in these systems, several gaps remain uncovered. Specifically, mental and physical human factors, like learning and fatigue, and quantitative and spatial features of picking orders have never been considered jointly to estimate the time a human order picker requires to execute a specific picking mission. Furthermore, little attention has been given to assigning and sequencing orders to pickers to minimize the picking time acting on their individual learning and fatigue characteristics. This study thus proposes a novel approach integrating machine learning and genetic algorithms to solve the problem. A non-linear machine learning-based predictive model has been adopted to predict the picking time of batches of orders based on quantitative and spatial features of batches and learning and fatigue indicators of pickers. These predictions have thus been adopted to guide a genetic algorithm to find the best assignment of future planned batches of orders to pickers. One year of picking data collected from the warehouse of a grocery retailer has been adopted to investigate the potential of the proposed approach. Furthermore, multiple comparisons have been performed. First, the advantages of predicting the batch-picking time with the proposed non-linear model have been compared with predictions executed based on linear models. In addition, an ablation analysis has been performed to investigate the advantages of predicting the batch picking time while simultaneously considering the quantitative and spatial features of batches and the learning and fatigue indicators of pickers. Moreover, the advantages of the proposed batch assignment strategy, which considers learning and fatigue indicators, have been compared with an assignment strategy that does not optimize these elements. Lastly, an explainability analysis of the predictive model has been performed to understand how and how much quantitative and spatial features of batches and learning and fatigue indicators of pickers affect the batch picking time.

Storage Assignment Using Nested Metropolis Sampling and Approximations of Order Batching Travel Costs

The Storage Location Assignment Problem (SLAP) is of central importance in warehouse operations. An important research challenge lies in generalizing the SLAP such that it is not tied to certain order-picking methodologies, constraints, or warehouse layouts. We propose the OBP-based SLAP, where the quality of a location assignment is obtained by optimizing an Order Batching Problem (OBP). For the optimization of the OBP-based SLAP, we propose a nested Metropolis algorithm. The algorithm includes an OBP-optimizer to obtain the cost of an assignment, as well as a filter which approximates OBP costs using a model based on the Quadratic Assignment Problem (QAP). In experiments, we tune two key parameters in the QAP model, and test whether its predictive quality warrants its use within the SLAP optimizer. Results show that the QAP model’s per-sample accuracy is only marginally better than a random baseline, but that it delivers predictions much faster than the OBP optimizer, implying that it can be used as an effective filter. We then run the SLAP optimizer with and without using the QAP model on industrial data. We observe a cost improvement of around 23% over 1 h with the QAP model, and 17% without it. We share results for public instances on the TSPLIB format.

Comparison of MOEAs in an Optimization-Decision Methodology for a Joint Order Batching and Picking System

This paper investigates the performance of a two-stage multi-criteria decision-making procedure for order scheduling problems. These problems are represented by a novel nonlinear mixed integer program. Hybridizations of three Multi-Objective Evolutionary Algorithms (MOEAs) based on dominance relations are studied and compared to solve small, medium, and large instances of the joint order batching and picking problem in storage systems with multiple blocks of two and three dimensions. The performance of these methods is compared using a set of well-known metrics and running an extensive battery of simulations based on a methodology widely used in the literature. The main contributions of this paper are (1) the hybridization of MOEAs to deal efficiently with the combination of orders in one or several picking tours, scheduling them for each picker, and (2) a multi-criteria approach to scheduling multiple picking teams for each wave of orders. Based on the experimental results obtained, it can be stated that, in environments with a large number of different items and orders with high variability in volume, the proposed approach can significantly reduce operating costs while allowing the decision-maker to anticipate the positioning of orders in the dispatch area.

Balanced Order Batching in Bucket Brigade Order Picking Systems with Non-identical Pickers

Balanced Order Batching in Bucket Brigade Order Picking Systems with Non-identical Pickers

Subscription Pricing for Free Delivery Services

Many firms that offer home delivery of products purchased online now provide consumers the option of subscribing to a membership plan for free delivery of limited or unlimited number of orders instead of customers paying delivery charges for each order. This paper seeks to understand the benefits to firms and consumers of introducing such free-delivery subscription (FDS) plans to complement their traditional pay-for-delivery (PFD) option, characterize the firm's optimal FDS subscription pricing strategy, and study the effects of product, consumer, and market characteristics on the subscription fees and firm's profits. We develop and analyze an economic model that incorporates salient features of product delivery settings that prior models of subscription pricing do not fully capture. The features include simultaneous availability of PFD and FDS options, lift in a consumer's demand when she switches from PFD to FDS, the possibility of attracting new consumers when the firm introduces FDS, and order batching by customers due to per-order delivery charges and free-delivery order allowances. Our utility-based approach to model consumers’ purchasing choices incorporates consumer heterogeneity both in terms of their utility for the product and their shopping preference under the PFD option. For homogeneous consumers, we show that introducing a FDS plan raises the firm's profit, establish the optimality of offering unlimited free-delivery allowance, and analyze comparative statics. With multiple customer types, our analysis of two subscription pricing strategies for FDS plans—a single “Universal” plan and multiple “Tiered” plans with varying subscription fees and free-delivery limits—leads to several interesting insights on delivery pricing strategies, as well as drivers and sensitivity of the optimal policy, profits, and number of subscribers. We supplement this analysis with extensive computational experiments that reveal a substantial increase in profits when a firm adds one or more FDS plans to its PFD option even though the optimal subscription fee(s) only covers part of the firm's actual shipping costs. These results also permit us to gauge the influence and understand the trends in the profitability of the Universal and Tiered plans as various parameters change.

Stochastic modeling of integrated order fulfillment processes with delivery time promise: Order picking, batching, and last-mile delivery

To guarantee high customer service and short and accurate lead times, many e-commerce retailers have started to home deliver their customer orders within a few hours or even minutes, also known as quick-commerce order fulfillment. Quick-commerce order fulfillment consists of three main processes: order picking in the warehouse, order batching for delivery, and last-mile delivery. The ultimate delivery performance depends on managing all three processes, which are highly stochastic, and interdependent. We capture this stochasticity and interdependency in an integrated analytical framework and derive approximate analytical expressions for the mean and variance of the total order fulfillment time. We validate the analytical expressions with both in-house detailed process simulations and external-party output measures. We then analyze the delivery cost-service quality trade-offs using an optimization model that minimizes the expected order fulfillment cost with a delivery probability (DP) constraint, focusing on meeting delivery time deadlines. The optimization model determines the number of pickers, the optimal delivery batch size, and the number of vehicles required to deliver the customer orders. Achieving a high delivery reliability comes at a cost. In comparison to the model with DP constraints, we observe that the expected order fulfillment cost averaged over all data parameter settings obtained from the model without DP constraints is 8.9% lower; however, the mean and standard deviation of order fulfillment time increase by 44.1% and 18.6%, respectively, which results in low delivery reliability. We further demonstrate that an integrated analysis of the order fulfillment process is essential to set reliable fulfillment due times.

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

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

Improving the picking efficiency of a cold warehouse to avoid temperature abuse

PurposeThis research investigates how to optimize storage location assignment to decrease the order picking time and the waiting time of orders in the staging area of low-temperature logistics centers, with the goal of reducing food loss caused by temperature abuse.Design/methodology/approachThe authors applied ABC clustering to the products in a simulated database of historical orders modeled after the actual order pattern of a large cold logistics company; then, the authors mined the association rules and calculated the sales volume correlation indices of the ordered products. Finally, the authors generated three different simulated order databases to compare order picking time and waiting time of orders in the staging area under eight different storage location assignment strategies.FindingsAll the eight proposed storage location assignment strategies significantly improve the order picking time (by up to 8%) and the waiting time of orders in the staging area (by up to 22%) compared with random placement.Research limitations/implicationsThe results of this research are based on a case study and simulated data, which implies that, if the best performing strategies are applied to different environments, the extent of the improvements may vary. Additionally, the authors only considered specific settings in terms of order picker routing, zoning and batching: other settings may lead to different results.Practical implicationsA storage location assignment strategy that adopts dispersion and takes into consideration ABC clustering and shipping frequency provides the best performance in minimizing order picker's travel distance, order picking time, and waiting time of orders in the staging area. Other strategies may be a better fit if the company's objectives differ.Originality/valuePrevious research on optimal storage location assignment rarely considered item association rules based on sales volume correlation. This study combines such rules with several storage planning strategies, ABC clustering, and two warehouse layouts; then, it evaluates their performance compared to the random placement, to find which one minimizes the order picking time and the order waiting time in the staging area, with a 30-min time limit to preserve the integrity of the cold chain. Order picking under these conditions was rarely studied before, because they may be irrelevant when dealing with temperature-insensitive items but become critical in cold warehouses to prevent temperature abuse.