Fluid-based Slotting Optimization for Automated Order Picking System with Multiple Dispenser Types

Slotting strategy heavily influences the throughput and operational cost of automated order picking system with multiple dispenser types, which is called the complex automated order picking system （CAOPS）. Existing research either focuses on one aspect of the slotting optimization problem or only considers one part of CAOPS, such as the Low-volume Dispensers, to develop corresponding slotting strategies. In order to provide a comprehensive and systemic approach, a fluid-based slotting strategy is proposed in this paper. The configuration of CAOPS is presented with specific reference to its fast-picking and restocking subsystems. Based on extended fluid model, a nonlinear mathematical programming model is developed to determine the optimal volume allotted to each stock keeping unit （SKU） in a certain mode by minimize the restocking cost of that mode. Conclusion from the allocation model is specified for the storage modules of high-volume dispensers and low-volume dispensers. Optimal allocation of storage resources in the fast-picking area of CAOPS is then discussed with the aim of identifying the optimal space of each picking mode. The SKU assignment problem referring to the total restocking cost of CAOPS is analyzed and a greedy heuristic with low time complexity is developed according to the characteristics of CAOPS. Real life application from the tobacco industry is presented in order to exemplify the proposed slotting strategy and assess the effectiveness of the developed methodology. Entry-item-quantity （EIQ） based experiential solutions and proposed-model-based near-optimal solutions are compared. The comparison results show that the proposed strategy generates a savings of over 18% referring to the total restocking cost over one-year period. The strategy proposed in this paper, which can handle the multiple dispenser types, provides a practical quantitative slotting method for CAOPS and can help picking-system-designers make slotting decisions efficiently and effectively.

Taboo Search Algorithm for Item Assignment in Synchronized Zone Automated Order Picking System

The idle time which is part of the order fulfillment time is decided by the number of items in the zone; therefore the item assignment method affects the picking efficiency. Whereas previous studies only focus on the balance of number of kinds of items between different zones but not the number of items and the idle time in each zone. In this paper, an idle factor is proposed to measure the idle time exactly. The idle factor is proven to obey the same vary trend with the idle time, so the object of this problem can be simplified from minimizing idle time to minimizing idle factor. Based on this, the model of item assignment problem in synchronized zone automated order picking system is built. The model is a form of relaxation of parallel machine scheduling problem which had been proven to be NP-complete. To solve the model, a taboo search algorithm is proposed. The main idea of the algorithm is minimizing the greatest idle factor of zones with the 2-exchange algorithm. Finally, the simulation which applies the data collected from a tobacco distribution center is conducted to evaluate the performance of the algorithm. The result verifies the model and shows the algorithm can do a steady work to reduce idle time and the idle time can be reduced by 45.63% on average. This research proposed an approach to measure the idle time in synchronized zone automated order picking system. The approach can improve the picking efficiency significantly and can be seen as theoretical basis when optimizing the synchronized automated order picking systems.

Multiple People Picking Assignment and Routing Optimization Based on Genetic Algorithm

In order to improve the picking efficiency,reduce the picking time,this paper take artificial picking operation of a certain distribution center which has double-area warehouse as the studying object.Discuss the picking task allocation and routing problems.Establish the TSP model of order-picking system.Create a heuristic algorithm bases on the Genetic Algorithm(GA)which help to solve the task allocating problem and to get the associated order-picking routes.And achieve the simulation experiment with the Visual 6.0C++platform to prove the rationality of the model and the effectiveness of the arithmetic.

Perfect Pick系统订单拣选策略优化研究

作为电商仓库作业中耗时最长、成本最高的环节,订单拣选的作业效率一直是仓库管理中的关键问题。文章针对拣选策略选择问题,选择Perfect Pick系统的电商仓库作为背景,对单个拣选台进行研究,提出订单分批和订单排序两种拣选策略并进行对比分析;以货箱搬运次数最少为目标,分别构建订单分批与订单排序两种拣选策略的整数规划模型,并设计贪婪算法进行求解。通过数值实验验证,订单排序策略在所有订单规模中均优于订单分批策略,根据仓库的订单规模,合理设置拣选台最大容量并选择合理的拣选策略,能够更好地提高拣选效率、优化仓库作业环节。

Intelligent Control Mechanism of Part Picking Operations of Automated Warehouse

This paper studies the part picking operations of a ut omated warehouse. It assumed the demand of picking orders of automated warehouse are dynamic generated. Once the picking orders of certain period of time are kn own, it is necessary to decide an efficient order picking sequence and routing t o minimize the total travel distance to complete those orders. Assumed there are n i items to be picked in order O i. Each item in the picking ord er is located in different locations in the warehouse. Since it is possible the same items appear in the different picking orders, it will reduce the picking di stance if these orders can be batched and picked in one path. However, there are several constraints for the order batching and order picking operations. These constraint are (1) the crane of the automated warehouse has the carrying capacit y of C, and (2) for the management convenience, it is assumed that one picki ng order must be completed in one path. Because of the complexity of problem, it is inefficient to solve the problem by analytical approach. Although the heuristic method can significantly reduce of the computation time, the quality of the solution is always unacceptable. It is the intention of this paper to integrate the advantages of neural network and simulated annealing technique to develop the control mechanism for the planning of order picking operations of automated warehouse. A systematic computational simulation is conducted to evaluate the proposed method. The results show the pr oposed method can generate superior solution in most cased.

Analytical and Traveling Wave Solutions to the Fifth Order Standard Sawada-Kotera Equation via the Generalized exp(-Φ(ξ))-Expansion Method

In this article, we propose a generalized exp(-Φ(ξ))-expansion method and successfully implement it to find exact traveling wave solutions to the fifth order standard Sawada-Kotera (SK) equation. The exact traveling wave solutions are established in the form of trigonometric, hyperbolic, exponential and rational functions with some free parameters. It is shown that this method is standard, effective and easily applicable mathematical tool for solving nonlinear partial differential equations arises in the field of mathematical physics and engineering.

Decomposition Theorems for Semi-order Fuzzy Supermartingales and Submartingales

Based on semi - order fuzzy supermaringales andsubmartingales, the semi- order fuzzy supermartingaleand submartingale theory is developed. The main resultis to generalize the Doob decomposition and the Riesz de-composition theorems of standard martingale theory tosemi - order fuzzy supermaringales and submartingales.The structure of semi - order fuzzy supermaringales andsubmartingales and the conditions of that they has Doobdecomposition (resp. Riesz decomposition) are discussedin detail.

O(t^(-β))-SYNCHRONIZATION AND ASYMPTOTIC SYNCHRONIZATION OF DELAYED FRACTIONAL ORDER NEURAL NETWORKS

This article explores the O(t^(-β))synchronization and asymptotic synchronization for fractional order BAM neural networks(FBAMNNs)with discrete delays,distributed delays and non-identical perturbations.By designing a state feedback control law and a new kind of fractional order Lyapunov functional,a new set of algebraic sufficient conditions are derived to guarantee the O(t^(-β))Synchronization and asymptotic synchronization of the considered FBAMNNs model;this can easily be evaluated without using a MATLAB LMI control toolbox.Finally,two numerical examples,along with the simulation results,illustrate the correctness and viability of the exhibited synchronization results.

On the Caginalp for a Conserve Phase-Field with a Polynomial Potentiel of Order 2<i>p</i>- 1

Our aim in this paper is to study on the Caginalp for a conserved phase-field with a polynomial potentiel of order 2p - 1. In this part, one treats the conservative version of the problem of generalized phase field. We consider a regular potential, more precisely a polynomial term of the order 2p - 1 with edge conditions of Dirichlet type. Existence and uniqueness are analyzed. More precisely, we precisely, we prove the existence and uniqueness of solutions.

High-Order BAM, Its Modifications and Performance Analyses

Based on Tai’ s high - order bidirectional associative memory ( HOBAM) and Stmposon’ s intraconnected BAM (IBAM) , two Improved models are first presented and discussed in this paper. The improved models not only retain the advantages of both HOBAM and ISAM but overcome the shortcomings of Kosko’ s BAM also. Secondly their recall stabilities in synchronous and asyn-chronous update modes have been proven by defining corresponding energy functions which decrease as the re-call process proceeds such that the systems can ensure all the training pattern pairs to become local minima of the energy surfaces. Finally with signal - to - noise ratio (SNR) approach, we show that their storage capacities and error correction capabilities are better than that of the HOBAM.

基于eM-Plant的物流配送中心拣货作业优化研究

为了减少仓库拣货行走时间和提高拣货效率,以某配送仓库为背景,运用e M-Plant仿真工具,建立拣选作业仿真模型,分别对存储策略、拣货单分批方式、路径选择及拣货分区策略进行研究。在存储策略上,考虑货品之间的关联性,运用weka关联分析挖掘出货物之间的关联性。在拣货单分批方式上,依次研究基于拣货单数合并和拣货行数合并两种分批方式。仿真结果表明：5~8张拣货单合并和50订单行合并均为最佳订单分批方式。在路径选择上,分别研究了Z字形、“8”字形和新中点路径策略。计算结果表明：新中点拣货路径选取策略最佳。在拣货分区策略上,用按工作量动态分区的方案有效降低了拣货员的等待时间,增加协同性。提出的方法已应用于某配送仓库的实际运作中。

Integrated schedule of order picking and delivery for instant delivery

In this study,we introduce an integrated schedule of order picking and delivery for instant delivery.Order picking,including order batching and picking sequencing,is scheduled online under real-time order arrival,which integrates order delivery by depicting order location dispersion in an online order picking strategy.Order delivery,including delivery person assignment and route planning,is modeled to minimize the total duration of order fulfillment by considering the influence of the order picking completion time.A rule-based online order picking strategy is established,and a customized ant colony optimization(ACO)algorithm is proposed to optimize order delivery.Experiments on 16 simulated instances of different scales demonstrate that our online order picking schedule considering order delivery outperforms existing approaches and that the customized ACO algorithm for order delivery is effective.

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。

基于0-1分块矩阵求解的B2C配送中心订单分批优化模型构建

在同一时间窗下研究多品种、多批次、少批量的订单分批处理具有较高的理论和实际意义。本文在考虑按单拣货和并单拣货的最优拣货策略的基础上,构建针对B2C配送中心拣货时间数学模型,运用分块矩阵以及MATLAB对模型进行求解。将模型应用到配送中心实际订单拣选中,得到最优订单分批处理方案,证明该模型具有可行性和实际应用价值,可为B2C配送中心订单分批处理问题提供定量决策方法。

基于改进遗传K-均值算法的多品种小批量订单分批方法

针对货品种类多且库位分散的多品种小批量订单问题,构建了以订单相似度最高为目标的分批拣选优化模型,并采用改进遗传K-均值算法对模型进行求解。针对传统K-均值算法中K值人为确定造成聚类结果误差大的缺点,采用密度和最小距离综合最优指标确定多个初始聚类中心,并运用改进遗传K-均值算法确定最优分批数量,进行订单分批优化;得到分批结果后,用穿越式路径方法计算拣选距离,并与简单分批得到的距离进行对比。以某机械设备生产公司售后服务备件仓的订单分批拣选问题为对象进行仿真实验,结果表明该方法有效。

SOME EULER SPACES OF DIFFERENCE SEQUENCES OF ORDER m

Kizmaz [13] studied the difference sequence spaces ∞（A）, c（A）, and co（A）. Several article dealt with the sets of sequences of m-th order difference of which are bounded, convergent, or convergent to zero. Altay and Basar [5] and Altay, Basar, and Mursaleen [7] introduced the Euler sequence spaces e0^r, ec^r, and e∞^r, respectively. The main purpose of this article is to introduce the spaces e0^r△^（m））, ec^r△^（m））, and e∞^r△^（m））consisting of all sequences whose mth order differences are in the Euler spaces e0^r, ec^r, and e∞^r, respectively. Moreover, the authors give some topological properties and inclusion relations, and determine the α-, β-, and γ-duals of the spaces e0^r△^（m））, ec^r△^（m））, and e∞^r△^（m））, and the Schauder basis of the spaces e0^r△^（m））, ec^r△^（m））. The last section of the article is devoted to the characterization of some matrix mappings on the sequence space ec^r△^（m））.

基于遗传算法的仓库拣选作业优化与eM-Plant实现

在建立了仓库拣选作业优化模型的基础之上,提出了用遗传算法(GA)求解堆垛机拣选作业最优路径的具体方法,并在一个实例中用eM-Plant软件中的遗传算法模块实现了仓库拣选作业的仿真优化。

Insights into the enhanced structure stability and electrochemical performance of Ti^(4+)/F^(-) co-doped P2-Na_(0.67)Ni_(0.33)Mn_(0.67)O_(2) cathodes for sodium ion batteries at high voltage

P2-Na_(0.67)N_(i0.33)Mn_(0.67)O_(2)is considered as a promising cathode material for sodium-ion battery (SIBs)because of its high capacity and discharge potential.However,its practical use is limited by Na^(+)/vacancy ordering and P2-O2 phase transition.Herein,a Ti^(4+)/F^(-) co-doping strategy is developed to address these issues.The optimal P2-Na_(0.67)Ni_(0.33)Mn_(0.37)Ti_(0.3)O_(1.9)F_(0.1) exhibits much enhanced sodium storage performance in the high voltage range of 2.0–4.4 V,including a cycling stability of 77.2%over 300cycles at a rate of 2 C and a high-rate capability of 87.7 m Ah g^(-1) at 6 C.Moreover,the P2-Na_(0.67)Ni_(0.33)Mn_(0.37)Ti_(0.3)O_(1.9)F_(0.1) delivers reversible capacities of 82.7 and 128.1 m Ah g^(-1) at-10 and 50℃ at a rate of 2 C,respectively.The capacity retentions over 200 cycles at-10℃ is 94.2%,implying more opportunity for practical application.In-situ X-ray diffraction analysis reveals that both P2-O2 phase transitions and Na^(+)/vacancy ordering is suppressed by Ti^(4+)/F^(-) co-doping,which resulting in fast Na^(+) diffusion and stable phase structure.The hard carbon//P2-Na_(0.67)Ni_(0.33)Mn_(0.37)Ti_(0.3)O_(1.9)F_(0.1) full cell exhibits a high energy density of 310.2 Wh kg^(-1) and remarkable cyclability with 82.1%retention after 300 cycles at 1 C in the voltage range of 1.5–4.2 V.These results demonstrate that the co-doping Ti^(4+)/F^(-) is a promising strategy to improve the electrochemical properties of P2-Na_(0.67)Ni_(0.33)Mn_(0.67)O_(2),providing a facile tactic to develop high performance cathode materials for SIBs.