Dynamic order batching in bucket brigade order picking systems with consecutive batch windows and non-identical pickers

The blocking mitigation mechanism contained in a batching and sequencing model improves order picking performance in bucket brigade order picking systems by adjusting the batch formation in a given batch window. The batch formation of a given batch window affects the transition to the next batch window and limits the batch formation’s structure in the next window. In addition, imbalance in picker capability increases the variation of batch formation while mitigating blocking delay. Our paper proposes a dynamic indexed batching model to smooth the transition between consecutive batch windows and give a better approximation of non-identical pickers’ capability. We develop a mixed integer programming solution for a dynamic indexed batching model in a bucket brigade order picking system (DIBMB). Simulation experiments show that the DIBMB smooths the transition between batch windows as measured in the delay experienced by the first batch in each batch window. Comparisons to the available batching models show that under DIBMB, the blocking delay gradually increases throughout the sequence of batches.     

Common-use check-in counter reassignments with a variable number of service lines and variable length of time window

In the real world, there are a number of common factors that can cause perturbations at check-in counters, such as an airport closure, a temporary power failure, crashing of the counter computer, baggage conveyor belt malfunctions, and so on, forcing the airport authority to reassign flights to new check-in counters. In this study, we develop a model and a solution method to solve common-use check-in counter reassignment problems with a variable number of service lines and a variable length of time window. To test how well the proposed model and the solution method can be applied to the real world, we perform numerical tests based on a hypothetical incident in relation to a Taiwan airport’s operations. The test results show that the model and solution would be useful for the airport authority in actual operations.     

Storage assignment and order batching problem in Kiva mobile fulfilment system

This article studies the storage assignment and order batching problem in the Kiva mobile fulfilment system. The storage assignment model aims to decide which product to put in which pod to maximize the product similarity and the order batching model aims to minimize the number of visits of pods. To solve the order batching problem, a heuristic is proposed, where a batch schedule is initialized with the objective of maximizing the order association or minimizing order alienation and improved by variable neighbourhood search. Computational experiments are conducted to verify the performance of the proposed model and algorithm.     

Effective bullwhip metrics for multi-echelon distribution systems under order batching policies with cyclic demand

A large number of problems in a distribution supply chain require that decisions are made in the presence of the bullwhip effect phenomenon. The impact of the order batching policies on the bullwhip effect is analysed in this paper, when cycle demand on a multi-echelon supply chain operating is considered. While investigating which bullwhip effect metrics are more adequate to measure the bullwhip effect in these type of systems, the optimal reordering plan that minimises the operation costs of the overall system is calculated. A Mixed Integer Linear Programming (MILP) model is developed that takes into account an inventory and distribution system formed by multiple warehouses and retailers with lateral transshipments. The bullwhip effect is measured through four metrics: the echelon average inventory; the echelon inventory variance ratio; the echelon average order; and the echelon order rate variance ratio. As conclusion the inventory metrics suggest that (i) using batching policy reduces instability; (ii) batching may reduce in general order variance if using larger batches and (iii) cycle demand length has no major impact in the bullwhip effect. A motivational example and a real word case study are used and tested.     

基于时间延迟的订单分批策略研究

将延迟制造思想引入到配送中心拣货作业中，提出基于时间延迟的动态时窗分批策略。该策略能消除目前拣货系统存在的等待时间和块状需求(闲忙不均)现象，保证拣货系统运行的连续性和均衡性，极大地提高了拣货系统的运行效率，并利用计算机实现该策略。     

基于NSGA-Ⅱ算法的分区拣选优化

电商背景下的客户订单呈现出多品种、小批量、高频次等特点,给仓库拣选工作带来很大的挑战。为提高拣选效率,在订单完全拆分的分批策略和组合优化的行走策略下,设计了以总服务时间最小、分区工作量平衡度最优和二次分拣效率最高的多目标分区拣选模型。由于3个目标函数之间存在矛盾,设计了NSGA-II算法对多目标优化模型进行求解。通过数值实验,与传统的不拆分订单的分区拣选系统对比,发现在订单批量环境为[1,4]时,分别使总服务时间减少了43.88%,平衡度改善了84.61%,并分析了区域个数、订单总数和订单批量环境对系统效率的影响。     

Stochastic customer order scheduling with setup times to minimize expected cycle time

Short cycle time of customer orders is crucial for companies to achieve mass customization and quick response. However, the complicated and stochastic environment, especially the exist of setup times, makes it extremely challenging to optimize the efficiency of a system. In this study, stochastic customer orders are scheduled to minimize their expect cycle time with the consideration of setup times. Customer orders arrive dynamically, and each order requires multiple product types with random workloads. These workloads will be assigned to a set of unrelated parallel machines to be processed. Particularly, for each machine, setup times are required whenever there is a product type changeover, and the lengthes are both machine- and product type-dependent. This paper intends to minimize the long-run expected order cycle time by proper policies including workload allocation and type sequencing. The impacts of product type sequence and workload variance are evaluated through theoretical study and several analytical properties are developed. With the help of these properties, three scheduling algorithms are proposed, and a lower bound is derived to evaluate the proposed algorithms. Computational experiment is conducted to demonstrate the effectiveness of the lower bound and the algorithms under various circumstances, and several important managerial insights are also provided.     

基于动态时间窗的泊车系统路径规划研究

针对智能立体停车库中自动导引运输车(automated guided vehicle,AGV)存取车路径规划问题,采用分时利用策略,将Dijkstra算法和时间窗法有效结合,提出了一种基于动态时间窗的泊车系统路径规划方法。首先,通过引入优先级策略为接收任务的AGV设定优先级;其次,采用Dijkstra算法,按照任务优先级高低次序,依次为接受任务的AGV规划出最短可行路径;最后,在已知AGV可行路径基础上,通过对可行路径各路段的时间窗进行初始化、实时更新以及实时排布处理,实现多AGV的无冲突路径规划。为验证所提方法的可行性和有效性,以4台AGV同时工作的智能立体停车库为实例进行仿真测试。结果显示:所提出的路径规划方法不仅有效解决了目前多AGV路径规划柔性差、易出现死锁、碰撞冲突等问题,而且可在有效解决路径冲突的前提下,为接受任务的AGV规划出一条时间最短的优化路径。所提方法具有较好的鲁棒性和柔性,有效提高了智能立体停车系统整体运行效率,降低了存取车等待时间。     

The use of bucket brigades in zone order picking systems

As the transactions through electronic commerce and TV home shopping increase, the warehouses often receive a large amount of small orders to be picked within tight time windows. One of the important warehousing activities is order picking, the process of retrieving a number of items from warehouse storage to meet a number of independent customer orders. This paper examines a new order picking method, bucket brigade order picking (BB picking). Bucket brigade is a way of coordinating workers who progressively perform a set of operations on a flow line. In the BB picking system, a worker performs operations on an order until the next worker downstream takes it over; then goes back to the previous worker upstream to take over a new order. We discuss distinct characteristics in order picking systems when bucket brigades are applied. We identify some efficiency losses under the BB picking and present a new BB picking protocol to improve the performance of order picking systems. The new BB picking is compared with the existing BB picking and zone picking through simulation experiments.     

基于遗传算法的配送中心订单拣选优化问题研究

针对分区拣选与自动循环分拣线相结合的分拣系统中的订单分批问题开展研究。提出延迟订单数量最少、平均延迟时间最小的多目标订单分批排序模型,应用VNS算法进行求解,采用被动分波缓解分拣线堵塞。案例分析结果表明,订单到达率λ=5时,先到先服务指派规则下联合拣选和分拣的分批策略与仅考虑拣选的订单分批策略相比,在延迟订单数量、平均延迟时间上优化率分别为88.8%和80.4%,固定优先级指派规则下,两项指标优化率达到100%,证明当前条件下联合拣选和分拣的分批策略对减少订单履行延迟具有较好的效果。最后,通过讨论订单到达率和交付通道数量的敏感度分析,进一步推广实验结果,给出参数选择的依据。

     

Oscillator with non-integer order nonlinearity and time variable parameters

In this paper, the vibrations of the oscillator with nonlinearity of integer or non-integer order and with mass variable parameters are considered. New appreciative analytical procedures are developed: first, based on the generating solution that is the exact analytic solution of the system with constant parameters and the second, based on the approximate solution in the form of a trigonometric function with exact period of vibration of the system with constant parameters. For the both methods, the assumed trial solutions represent the perturbed versions of the solutions of the equations with constant parameters, where the amplitude and phase of vibration are supposed to be time variable. The amplitude and phase functions are determined using the averaging procedure over the period of vibration. The obtained approximate analytic solutions are compared with numerical ones. It is shown that the developed methods are accurate for the monotone slow time variable systems. The example of mass variable oscillator is considered. The influence of mass variation, small linear viscous damping and of the reactive force is investigated, too.     

The choice of the optimum frequency band in correlation measurements of variable time delay

Algorithms for choosing the optimum bandwidth and integration interval T when constructing the cross-correlation function of signals from moving objects are proposed. The fundamental features of the behavior of the optimum interval T and the optimum frequency band as a function of the parameters of motion of the object are considered. Translated from Izmeritel’naya Tekhnika, No. 12, pp. 34–40, December, 2008.     

Dynamic order acceptance and scheduling problem with sequence-dependent setup time

This paper studies the order acceptance and scheduling problem under a single machine environment when the orders come stochastically during the planning horizon and a sequence-dependent setup time is required between the processing of different types of orders. The objective is to maximise the expected revenue subject to the due date constraints. The problem is formulated as a stochastic dynamic programming model. A rule based on the opportunity cost of the remaining system capacity for the current system state is proposed to make the order acceptance decisions. The remaining system capacity is estimated by a heuristic which generates a good schedule for the accepted orders. Its opportunity cost is estimated by both mathematical programme and greedy heuristic. Computational experiments show that the profit generated by the integrated dynamic programming decision model is much higher than the widely used first-come-first-accept policy in industries and the benefit increases with the length of planning horizon, the arrival rate and the length of lead time. Acceptance decision based on mathematical programming outperforms greedy heuristic by about 7% and its computational time is short. It also shows that the quality of the solutions generated by the opportunity cost based order acceptance rule is satisfactory.     

Managing warehouse efficiency and worker discomfort through enhanced storage assignment decisions

Humans are at the heart of crucial processes in warehouses. Besides the common economic goal of minimising cycle times, we therefore add in this paper the human well-being goal of minimising workers’ discomfort in the context of order picking. We propose a methodology for identifying the most suitable storage location solutions with respect to both goals. The first step in our methodology is to build data-driven empirical models for estimating cycle times and workers’ discomfort. The second step of the methodology entails the use of these empirically grounded models to formulate a bi-objective assignment problem for assigning products to storage locations. The developed methodology is subsequently tested on two actual warehouses. The results of these practical tests show that clear trade-offs exist and that optimising only for discomfort can be costly in terms of cycle time. Based on the results, we provide practical guidelines for taking storage assignment decisions that simultaneously address discomfort and travel distance considerations.     

Optimal order picker routing in a conventional warehouse with two blocks and arbitrary starting and ending points of a tour

This paper investigates manual order picking, where workers travel through the warehouse to retrieve requested items from shelves. To minimise the completion time of orders, researchers have developed various routing procedures that guide order pickers through the warehouse. The paper at hand contributes to this stream of research and proposes an optimal order picker routing policy for a conventional warehouse with two blocks and arbitrary starting and ending points of a tour. The procedure proposed in this paper extends an earlier work of Löffler et al. (2018. Picker routing in AGV-assisted order picking systems, Working Paper, DPO-01/2018, Deutsche Post Chair-Optimization of Distribution Networks, RWTH Aachen University, 2018) by applying the concepts of Ratliff and Rosenthal (1983. “Order-picking in a Rectangular Warehouse: a Solvable Case of the Traveling Salesman Problem.” Operations Research 31 (3): 507–521) and Roodbergen and de Koster (2001a. “Routing Order Pickers in a Warehouse with a Middle Aisle.” European Journal of Operational Research 133 (1): 32–43) that used graph theory and dynamic programming for finding an optimal picker route. We also propose a routing heuristic, denoted S*-shape, for conventional two-block warehouses with arbitrary starting and ending points of a tour. In computational experiments, we compare the average order picking tour length in a conventional warehouse with a single block to the case of a conventional warehouse with two blocks to assess the impact of the middle cross aisle on the performance of the warehouse. Furthermore, we evaluate the performance of the S*-shape heuristic by comparing it to the exact algorithm proposed in this study.     

Additional effort estimation due to ergonomic conditions in order picking systems

Within a warehouse, the picking activity often relies on human operators. Therefore, when designing and evaluating a manual picking system, it is important to consider that, besides the high flexibility the pickers are able to warrant, they inevitably require an additional effort due to their ergonomic working conditions. In this paper, the authors propose a new model to consider such additional effort, starting from the concepts of human availability and rest allowance. The new method allows the evaluation of the current configuration of a certain warehouse, considering two different operative situations (directly employed operators and indirectly employed ones). Moreover, it makes it possible to estimate and to understand the benefits that can be achieved by introducing some ergonomic improvements. The proposed procedure has also been applied to a real industrial case study.     

Production control policy for tandem workstations with constant service times and queue time constraints

Queue time constraints are commonly imposed to ensure product quality in contemporary production systems. We study the performance of two single stations with deterministic service times and a predetermined time window in between, where both stations suffer time-based pre-emptive breakdowns. To improve productivity, achieving higher capacity and lower rework rate are the two main objectives. While higher capacity requires a higher work-in-process (WIP)-level threshold, a lower rework rate requires a smaller one. To quantify the trade-off between the two objectives, an analytical model is derived. The model is then used to derive the WIP-level threshold control policy for a time-constrained system. We also show that system capacity diminishes with the decrease in WIP-level thresholds.     

Particle swarm optimization for the multi-period cross-docking distribution problem with time windows

Cross-docking has emerged as a new technique in supply chain management to replace the warehouse concept in the retail industry. This paper proposes a multi-period cross-docking distribution problem that consists of manufacturers, cross-docks and customers. This model is formulated for cases that consider multiple products, consolidation of customer orders and time windows that are available in multiple periods. The objective function is to minimise the total cost, which includes transportation cost, inventory cost and penalty cost. The penalty cost arises when demand remains in each period that cannot be satisfied. To deal with the complexity of the problem, an algorithm is developed based on particle swarm optimisation (PSO) with multiple social learning terms, GLNPSO, with two solution representations. The solution representations are a one-period solution representation (OP-SR) and a multi-period solution representation (MP-SR). The GLNPSO-based algorithm performs well in solving this problem. Moreover, both representations are proven effective when comparing the solution quality and computational time with those results obtained from CPLEX. In terms of quality, the MP-SR solution is better than the OP-SR solution for both stable and fluctuating demand instances. However, MP-SR requires more computational effort than OP-SR.     

Picklist generation algorithm with order-consolidation consideration for split-case module-based fulfilment centres

This paper serves as an initial study on order-consolidating time for a module-based order-picking system. In this system, items are stored in modules, and order picking is performed in waves that comprise more than one customer order. Picked items from multiple modules are conveyed to the packaging department for sortation based on customer orders. The order-consolidating time is the main focus as well as the performance measure in this paper. Order-consolidating time is the time difference between the arrival time of the first and the last item at the packaging department that belong to the same customer order. We proposed a heuristic control strategy, namely a pick-list generation algorithm, which will reduce the order-consolidating time. We named our proposed algorithm the push algorithm, which is an improvement algorithm. The push algorithm is compared with the basic algorithm to evaluate its performance. This comparison is extended under different environment settings to provide a robust conclusion. The experimental results indicate that the proposed algorithm consistently out-performs the basic algorithm in every tested environment with at least 17% improvement.