Travel time models for double-deep automated storage and retrieval systems

In this paper new analytical travel time models for the computation of cycle times for unit-load double-deep automated storage and retrieval systems (in continuation double-deep AS/RS) are presented. The proposed models consider the real operating characteristics of the storage and retrieval machine and the condition of rearranging blocking loads to the nearest free storage location during the retrieval process. With the assumption of the uniform distributed storage rack positions and the probability theory, the expressions of the single and modified dual command cycle have been determined. The proposed models enable the calculation of the mean cycle time for single and dual command cycles, from which the performance of the double-deep AS/RS can be evaluated. A simulation model of the selected double-deep AS/RS has been developed to compare the performances of the proposed analytical travel time models. The numerical analyses show that with regard to the examined type of double-deep AS/RS with a different fill-grade factor, the results of the proposed analytical travel time models correlate with the results of simulation models of double-deep AS/RS.     

Travel-time model of dual-command cycles in a 3D compact AS/RS with lower mid-point I/O dwell point policy

Three-dimensional compact automated storage/retrieval systems (AS/RS) have been extensively applied in warehouses, with advantages of full automation, time efficiency and high space utilisation. While previous studies that use lower mid-point input/output (I/O) dwell point policy consider single-command cycles (SC), this paper builds travel-time models of dual-command cycles (DC). The S/R crane also dwells in the lower mid-point of the rack when it is idle. We validate analytical models using simulation and use analytical models to optimise system dimensions. Numerical experiments are used to compare DC with SC. The results show that DC outperform SC in terms of cycle time of one command.     

Power-load management reduces energy-dependent costs of multi-aisle mini-load automated storage and retrieval systems

For economic and ecological reasons, the interest in the energy demand of material-handling systems is rising. As a result, the operators of these systems increasingly pay attention to the energy demand and the costs resulting from it. The energy demand of automated warehouses, with multi-aisle automated storage and retrieval systems, is volatile with uncontrolled power-peaks. These power-peaks result in high energy and hardware costs. In this paper, the effect of a power-load management on the throughput of the material-handling systems is investigated. We assume that the peaks of energy consumption can be significantly reduced by delaying tasks, without having an impact on the throughput. The goal is to find out the interdependence between the electrical power-limits of the power-load management (mean power demand in a period and maximum power demand) and the throughput of the warehouse. The results show that, with a maximum power-limit and a mean power-limit, the peaks in energy consumption can be avoided with only a slight loss of throughput. Load management is an effective method to reduce the energy peaks of an automated warehouse, thereby lowering the costs of automated warehouses.     

自动化立体仓库出入库调度优化

针对自动化立体仓库的出入库调度优化问题,提出一种基于遗传算法/层次分析法(GA/AHP)的调度规则优化方法.遗传算法中的每个染色体都代表一组可用于描述具体调度方案的规则组合,并对染色体采用分段整数编码;为获得适应度函数值,利用一种集成层次分析法的决策优化方法求取相应的适应度值.优化调度仿真结果表明,该方法能有效地应用在自动化立体仓库的出入库调度规则的优化问题上.     

基于FlexSim 的军队自动化立体仓库货位优化研究

为提高军队自动化立体仓库出货速度和运行稳定性,提出了在堆垛机闲时对货位进行以分类存储L 形分区为导向的再分配优化设计。根据用户需求,程序自动生成分类存储的L 形分类存储货位分区信息,并调用堆垛机对在存货品逐一判断、搬运,让所有货品按照L 形区域排列,完成货位优化。利用FlexSim 软件对具体实例进行了仿真,结果表明,优化后的货位能较大程度地提高仓库的输出效率。     

Simplified mechanistic models of gene regulation for analysis and design

Simplified mechanistic models of gene regulation are fundamental to systems biology and essential for synthetic biology. However, conventional simplified models typically have outputs that are not directly measurable and are based on assumptions that do not often hold under experimental conditions. To resolve these issues, we propose a ‘model reduction’ methodology and simplified kinetic models of total mRNA and total protein concentration, which link measurements, models and biochemical mechanisms. The proposed approach is based on assumptions that hold generally and include typical cases in systems and synthetic biology where conventional models do not hold. We use novel assumptions regarding the ‘speed of reactions’, which are required for the methodology to be consistent with experimental data. We also apply the methodology to propose simplified models of gene regulation in the presence of multiple protein binding sites, providing both biological insights and an illustration of the generality of the methodology. Lastly, we show that modelling total protein concentration allows us to address key questions on gene regulation, such as efficiency, burden, competition and modularity.     

自动化立体仓库出入库决策系统的开发与仿真

在对作业方式、出入库作业方式分析的基础上,开发出了自动化立体仓库的出入库决策系统.系统管理层用Visual Basic 6.0编程语言开发,可实现对系统参数的初始设置,记录和查询出入库信息,货位优化管理和堆垛机的优化调度.监控仿真层的开发选用了组态软件组态王6.5,可实现对立体仓库的输入输出作业过程的动态模拟,并对系统运行结果进行曲线分析.系统数据库平台的构建选用的是Access 2000数据库软件,该数据库平台为管理层和监控层搭建了数据桥梁.进行货位优化管理时要综合考虑分布描述指标、库存量指标、出库分发效率指标这三个指标;按照堆垛机作业路线的优先级来安排堆垛机作业指令;综合考虑货位管理、堆垛机调度和输送机的运送管理这三个问题.通过仿真试验证明了可以得到系统进行优化决策方案.     

Performance evaluation of In-Deep Class Storage for Flow-Rack AS/RS

This article presents a new storage-retrieval method called In-Deep Class Storage, designed for Flow-Rack AS/RS. Class-based storage is a well-known method that has an extensive literature; our method is based on the fact that it is more efficient to dedicate the front layers of each bin to the class of the most popular items rather than dedicating whole bins close to the drop-off station. Clearly, this idea is not trivial to implement due to the dynamic behaviour of such racks. Thus, two separate algorithms have been defined, one for storage and one for retrieval, enabling dynamic use of our approach, with the only hypothesis of a Pareto distribution of item demand. This article presents a simulation study designed to compare the performance of random storage and retrieval with the use of the algorithms. This study shows a significant improvement of the expected retrieval delay, the main performance indicator selected for the study.     

Travel time model for double-deep shuttle-based storage and retrieval systems

Technological developments in the global supply chain have changed processes in warehousing. This reflects in short response time in handling the orders, which has a consequence on high automation degree in warehousing. An important part of automated warehouses is presented by shuttle-based storage and retrieval systems (SBS/RS), which are used in practice when demand for the throughput capacity is high. In this paper, analytical travel time model for the computation of cycle times for double-deep SBS/RS is presented. The advantage of the double-deep SBS/RS is that fewer aisles are needed, which results in a more efficient use of floor space. The proposed model considers the real operating characteristics of the elevators lifting table and the shuttle carrier with the condition of rearranging blocking totes to the nearest free storage location during the retrieval process of the shuttle carrier. Assuming uniform distributed storage locations and the probability theory, the expressions for the single and dual-command cycle of the elevators lifting table and the shuttle carrier have been determined. The proposed model enables the calculation of the expected cycle time for single- and dual-command cycles, from which the performance of the double-deep SBS/RS can be evaluated. The analysis show that regarding examined type of the double-deep SBS/RS, the results of the proposed analytical travel time model demonstrate good performances for evaluating double-deep SBS/RS.     

Markovian models for deadlock analysis in automated manufacturing systems

Deadlocks constitute a major issue in the desing and operation of discrete event systems. In automated manufacturing systems, deadlocks assume even greater importance in view of the automated operation. In this paper, we show that Markov chains with absorbing states provide a natural model of manufacturing systems with deadlocks. With illustrative examples, we show that performance indices such as mean time to deadlock and mean number of finished parts before deadlock can be efficiently computed in the modelling framework of Markov chains with absorbing states. We also show that the distribution of time to deadlock can be computed by conducting a transient analysis of the Markov chain model.     

Improvement of AS/RS performance using design and application of common zone

Minimization of overall queue length in AS/RS is studied in this research. In general, class-based storage policy is recommended for overall AS/RS operation, but it has a rack shortage problem under demand variation. To resolve this problem, an area along the board of two classes in AS/RS racks is allocated and is named the common zone. This zone is designed to handle the rack shortage problem associated with the items in a particular class under class-based storage policy. Thirty percent common zone size is determined as the most favorable allocation among various sizes through simulation experiments. This particular size common zone policy is compared with other well-known policies such as class-based, relocation, and random storage policy. These four operation policies under three different levels of workloads with demand variations are simulated. Crane moving time, rack shortages, delay times as well as throughputs are checked for the policy evaluation.     

Optimal storage rack design for a 3-dimensional compact AS/RS

In this paper, we consider a newly designed compact three-dimensional automated storage and retrieval system (AS/RS). The system consists of an automated crane taking care of the pallets' movements in the horizontal and vertical direction. A gravity or powered conveying mechanism takes care of the pallets’ depth movement in the rack. Our research objective is to analyze the system performance and optimally dimension the system. For single-command cycles, the crane's expected retrieval travel time is the same for gravity and powered conveyors; we give a closed-form expression. From the expected travel time, we calculate the optimal ratio between three dimensions that minimizes the travel time for a random storage strategy. In addition, we derive an approximate travel time expression for dual command cycles for the system with powered and gravity conveyors, respectively, and use it to optimize the system dimensions. Finally, we illustrate the findings of the study by a practical example.     

Models for automated storage and retrieval systems: a literature review

Automated Storage and Retrieval Systems (AS/RS) are warehousing systems that use mechanised devices to accomplish the repetitive tasks of storing and retrieving parts in racks. Since these systems represent a significant investment and considerable operating costs, their use must be as efficient as possible. AS/RS performance is the result of the interaction of many complex and stochastic subsystems. This reality creates a need for robust and efficient evaluation models. This article complements previous surveys on AS/RS by focusing on the particular research question addressed by each work and the associated assumptions used for the various models designed for evaluating AS/RS. Dynamic models based on simulation dominate the most recent literature; however, static approaches based on travel-time modelling have strongly contributed to the study of AS/RS. This review includes dynamic – simulation-based – models, but considers also steady-state (travel-time-based) models. We believe that this review may be of great help to researchers and industrial users in their search for the best modelling approach for a specific problem.     

High-order finite elements reduced models for modal analysis of stiffened panels

A method is presented to build reduced (equivalent) models of stiffened panels made of thin-walled composite materials. The technique is developed to be used in the modal analysis of panels and wing boxes, allowing finite element modelling and analysis using a single-type, three-dimensional orthotropic p-element. The use of a single element guarantees speed and flexibility in the (re)modelling of the structure and reduces the modelling and analysis errors connected to finite element analysis in preliminary-design/multidisciplinary-optimization environments. The method is tested on two types of representative wing boxes. Different approaches for the equivalencing are tested and compared to each other. The results show that the equivalent models give results within few percent from those obtained running a full model, saving as much as one order of magnitude in the number of degrees of freedom employed.     

Performance analysis of automatic storage/retrieval systems by stochastic modelling

This study considers an automated storage/retrieval system that performs either single or dual commands and analyses it as a queuing system with two waiting spaces and one server. It is assumed that the storage and retrieval commands arrive at the system according to Poisson processes with different rates and that the service times of single and dual commands are distributed differently. The steady-state probability distribution of the number of commands in the system at the service completion epochs is derived; subsequently, the semi-Markov process is employed to obtain the distribution at an arbitrary time. Several performance measures are derived and include the expected number of commands in the system, the expected waiting time, the probability that an arbitrary command cannot enter the system (the ‘blocking probability’) and the utilization of the storage/retrieval machine.     

Understanding and controlling rotations in factor analytic models

Positive Matrix Factorization (PMF) is a least-squares approach for solving the factor analysis problem. It has been implemented in several forms. Initially, a program called PMF2 was used. Subsequently, a new, more flexible modeling tool, the Multilinear Engine, was developed. These programs can utilize different approaches to handle the problem of rotational indeterminacy. Although both utilize non-negativity constraints to reduce rotational freedom, such constraints are generally insufficient to wholly eliminate the rotational problem. Additional approaches to control rotations are discussed in this paper: (1) global imposition of additions among “scores” and subtractions among the corresponding “loadings” (or vice versa), (2) constraining individual factor elements, either scores and/or loadings, toward zero values, (3) prescribing values for ratios of certain key factor elements, or (4) specifying certain columns of the loadings matrix as known fixed values. It is emphasized that application of these techniques must be based on some external information about acceptable or desirable shapes of factors. If no such a priori information exists, then the full range of possible rotations can be explored, but there is no basis for choosing one of these rotations as the “best” result. Methods for estimating the rotational ambiguity in any specific result are discussed.     

On intrinsic priors for nonnested models

Model selection problems involving nonnested models are considered. Bayes factor based solution to these problems needs prior distributions for the parameters in the alternative models. When the prior information on these parameters is vague default priors are available but, unfortunately, these priors are usually imporper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. Intrinsic priors have been introduced for solving this difficulty. While these priors are well established for nested models, their construction for nonnested models is still an open problem. In this latter setting this paper studies the system of functional equations that defines the intrinsic priors. It is shown that the solutions to these equations are obtained from the solutions to a single homogeneous linear functional equation. The Bayes factors associated with these solutions are analyzed. Some illustrative examples are provided and, in particular, location, scale, and location-scale models are considered.     

Dynamic survival analysis for non-Markovian epidemic models

We present a new method for analysing stochastic epidemic models under minimal assumptions. The method, dubbed dynamic survival analysis (DSA), is based on a simple yet powerful observation, namely that population-level mean-field trajectories described by a system of partial differential equations may also approximate individual-level times of infection and recovery. This idea gives rise to a certain non-Markovian agent-based model and provides an agent-level likelihood function for a random sample of infection and/or recovery times. Extensive numerical analyses on both synthetic and real epidemic data from foot-and-mouth disease in the UK (2001) and COVID-19 in India (2020) show good accuracy and confirm the method’s versatility in likelihood-based parameter estimation. The accompanying software package gives prospective users a practical tool for modelling, analysing and interpreting epidemic data with the help of the DSA approach.