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.     

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.     

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.     

Routing problem under the shared storage policy for unit-load automated storage and retrieval systems with separate input and output points

In this study the routing problem for unit-load automated storage and retrieval systems (AS/RSs) with separate input and output points is considered under the shared storage policy. The problem is to find an optimal travel route of a S/R (storage and retrieval) machine to process given storage and retrieval requests so that the total travel time is minimised, where the input and output points are possibly separate and the shared storage policy is assumed. We first give two types of formulations as 0–1 integer linear programming problems corresponding to two types of dwell point settings: the dwell point is the input point and the output point. Next, we propose a simple but efficient exact solution algorithm based on the formulations that utilises a general MILP (Mixed Integer Linear Programming) solver. Its efficiency is then demonstrated by numerical experiments. Instances with 400 items (200 for each storage and retrieval) are solved within 100 s.     

Sequencing the storages and retrievals for flow-rack automated storage and retrieval systems with duration-of-stay storage policy

Sequencing of storages and retrievals is an important topic in the automated storage and retrieval system (AS/RS), which largely influences the throughput performance and the operational cost of an AS/RS. In this paper, the problem of sequencing the storages and retrievals in a flow-rack AS/RS with duration-of-stay storage policy is analysed and a two-step heuristic called the grouping-matching method is proposed for minimising the total travel time of operations. The proposed grouping-matching method assigns unit-loads into groups in the grouping step and matches groups and bins of flow rack in the matching step. Two grouping heuristics are designed for the grouping step. The matching subproblem is formulated as an assignment to be solved. Simulation experiments are conducted to evaluate the effectiveness and efficiency of the grouping-matching method and the two grouping heuristics used for the grouping subproblem.     

A discrete-time queueing network approach to performance evaluation of autonomous vehicle storage and retrieval systems

In this paper, we present a method for performance evaluation of autonomous vehicle storage and retrieval systems (AVS/RSs) with tier-captive single-aisle vehicles. A discrete-time open queueing network approach is applied. The data obtained from the evaluation of the lift and vehicle movements can be used directly as input for the general discrete service time distributions of the queueing network. Furthermore, the approach allows for the computation of the retrieval transaction time distribution as well as of the distribution of the number of transactions waiting to be stored. Consequently, not only expected values and variances but also quantiles of the performance measures can be obtained. Comparison to discrete-event simulation quantifies approximation errors resulting from the decomposition approach in the discrete-time domain. Moreover, the errors obtained by the discrete-time approach are compared to the errors obtained using a continuous-time open queueing network approach. Finally, it will be outlined how the model can be used for designing AVS/RSs according to given system requirements, such as storage capacity, throughput, height and length of the system as well as the 95% quantile of the retrieval transaction time.     

Enhancing performance in order picking processes by dynamic storage systems

Increasing productivity and reducing labour cost in order picking processes are two major concerns for most warehouse managers. Particularly picker-to-parts order picking methods lead to low productivity as order pickers spend much of their time travelling along the aisles. To enhance order picking process performance, an increasing number of warehouses adopt the concept of dynamic storage where only those products needed for the current order batch are dynamically stored in the pick area, thereby reducing travel time. Other products are stored in a reserve area. We analyse the stability condition for a dynamic storage system with online order arrivals and develop a mathematical model to derive the maximum throughput a DSS can achieve and the minimum number of worker hours needed to obtain this throughput, for order picking systems with a single pick station. We discuss two applications of dynamic storage in order picking systems with multiple pick stations in series. In combination with simulation modelling, we are able to demonstrate that dynamic storage can increase throughput and reduce labour cost significantly.     

Graph-based solution for performance evaluation of shuttle-based storage and retrieval system

The aim of this study is to provide a graph-based solution for performance evaluation of a new autonomous vehicle-based storage and retrieval system, shuttle-based storage and retrieval system (SBS/RS), under various design concepts. By the graph-based solution, it is aimed the decision-maker (i.e. warehouse manager) evaluates a pre-defined system’s performance promptly and decides on the correct design concept based on his/her requirements from thousands of alternative design scenarios of SBS/RS. The design concepts include number of bays (NoB), aisles (NoA) and tiers (NoT) for the rack design and arrival rate of storage/retrieval (S/R) transactions to an aisle of the warehouse (AR). The performance of the system is evaluated in terms of average utilisation of lifts and average cycle time of S/R transactions. Simulation is utilised for the modelling purpose. Seven NoT, seven NoB and six AR scenarios are considered in the experiments. Hence, 294 experiments are completed to obtain the graphs. By this study, to the best of our knowledge it is the first time a graph-based solution including comprehensive design concepts of SBS/RS is presented.     

Designing an optimal turnover-based storage rack for a 3D compact automated storage and retrieval system

Compact, multi-deep (3D) automated storage and retrieval systems (AS/RS) are becoming increasingly popular for storing products. We study such a system where a storage and retrieval (S/R) machine takes care of movements in the horizontal and vertical directions of the rack, and an orthogonal conveying mechanism takes care of the depth movement. An important question is how to layout such systems under different storage policies to minimize the expected cycle time. We derive the expected single-command cycle time under the full-turnover-based storage policy and propose a model to determine the optimal rack dimensions by minimizing this cycle time. We simplify the model, and analytically determine optimal rack dimensions for any given rack capacity and ABC curve skewness. A significant cycle time reduction can be obtained compared with the random storage policy. We illustrate the findings of the study by applying them in a practical example.     

Throughput performance of automated storage/retrieval systems under stochastic demand

In this paper we are concerned with the throughput performance of an Automated Storage/Retrieval (AS/R) system under stochastic demand, i.e., the case where storage and retrieval requests arrive randomly. Although AS/R systems have been the subject of extensive research, their performance under stochastic demand remains relatively unexplored. In fact, with random storage and retrieval requests, the primary tool for AS/R system analysis has been simulation. Assuming a particular dwell point strategy for the storage/retrieval machine, in this paper we derive closed-form analytical results to evaluate the performance of an AS/R system under stochastic demand and determine whether or not it meets throughput. Although the results are derived for a given system, they can also be used in the design or evaluation of new/proposed systems.     

A two-sided picking model of M-AS/RS with an aisle-assignment algorithm

The mobile automated storage/retrieval system (M-AS/RS) has overcome the manual operational problems of mobile storage systems (MSSs). However, it remains a single-sided picking model with an integrated multi-level conveying device (IMCD) running in a right-angled path. To enhance the picking performance, the present paper proposes that the IMCD path be modified to run in a straight-line path. A picking-aisle-assignment algorithm is developed to reduce the number of picking aisles in which the IMCD is required to run. This proposed picking-aisle-assignment algorithm, together with the modified IMCD movement action and a ‘no-skip’ approach to arranging a picking sequence, are used to construct a two-sided M-AS/RS. Simulations of the proposed model are undertaken, and the results demonstrate that the two-sided operational model proposed in this paper addresses the weaknesses of the existing single-sided M-AS/RS model, especially in environments characterized by poor ventilation or the movement of heavy products.     

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.     

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.     

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.     

Travel time models for deep-lane unit-load autonomous vehicle storage and retrieval system (AVS/RS)

Autonomous vehicle storage and retrieval systems use vehicles that move horizontally along rails within the storage racks, while vertical movements are provided by lifts. The solution proposed in this paper addresses a particular system configuration that works with multiple deep storage lanes that are widely used in the food and beverage industry, characterised by large volumes of products of limited variety. The generic deep lane is single item, i.e. one stock keeping unit, and single batch, i.e. one production lot, thereby affecting the performance of the system in terms of storage capacity utilisation and throughput. Determining the number and depth of the lanes is crucial to aid the design and control of such a storage system. The aim of this paper was to support the design of AVS/RSs though a set of original analytic models for the determination of the travelled distance and time for single-command and dual-command cycles given alternative layout configurations. The models are validated by simulation and exemplified with a real-warehousing case study. The paper presents useful guidelines for the configuration of the system layout including the determination of the optimal shape ratio and the length of the lanes.     

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.     

Quantification of uncertainty modelling in stochastic analysis of FRP composites

The extensive use of FRP composite materials in a wide range of industries, and their inherent variability, has prompted many researchers to assess their performance from a probabilistic perspective. This paper attempts to quantify the uncertainty in FRP composites and to summarise the different stochastic modelling approaches suggested in the literature. Researchers have considered uncertainties starting at a constituent (fibre/matrix) level, at the ply level or at a coupon or component level. The constituent based approach could be further classified as a random variable based stochastic computational mechanics approach (whose usage is comparatively limited due to complex test data requirements and possible uncertainty propagation errors) and the more widely used morphology based random composite modelling which has been recommended for exploring local damage and failure characteristics. The ply level analysis using either stiffness/strength or fracture mechanics based models is suggested when the ply characteristics influence the composite properties significantly, or as a way to check the propagation of uncertainties across length scales. On the other hand, a coupon or component level based uncertainty modelling is suggested when global response characteristics govern the design objectives. Though relatively unexplored, appropriate cross-fertilisation between these approaches in a multi-scale modelling framework seems to be a promising avenue for stochastic analysis of composite structures. It is hoped that this review paper could facilitate and strengthen this process.     

Performance of carousel systems with ‘organ-pipe’ storage

It is well known that, for carousel systems, a dedicated storage, referred to as the ‘organ-pipe’ storage in the literature, is optimal with respect to the expected travel distance for processing successive requests. What remains unanswered is how to determine its performance, which is the motivation of this study. We consider bi-directional carousels under a ‘floating’ dwell point strategy. Two important performance measures considered are system capacity (maximum throughput) and job sojourn time. We also investigate the effect of activity skew on system performance.     

Tradeoff analysis of non-linear dynamical systems under stochastic excitation

An efficient methodology to carry out multi-objective optimization of non-linear structural systems under stochastic excitation is presented. Specifically, an efficient determination of particular Pareto or non-inferior solutions is implemented. Pareto solutions are obtained by compromise programming which is based on the minimization of the distance between the point that contains the individual optima of each of the objective functions and the Pareto set. The response of the structural system is characterized in terms of the first two statistical moments of the response process, i.e. the mean and variance. An efficient sensitivity analysis of non-inferior solutions with respect to the design variables becomes possible with the proposed formulation. Such information is used for decision making and tradeoff analysis. The compromise programming problem is solved by an efficient procedure that combines a local statistical linearization approach, modal analysis, global approximation concepts, and a sequential optimization scheme. Numerical results show that the total number of stochastic analyses required during the multi-objective optimization process is in general very small. Hence, different compromise solutions including the design that best represents the outcome that the designer considers potentially satisfactory are obtained in an efficient manner. In this way, the analyst can conduct a decision-making analysis through an efficient interactive procedure.