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.     

A decision model to determine the number of shuttles in a tier-to-tier SBS/RS

Shuttle-based storage and retrieval systems (SBS/RSs), which are designed to increase throughput capacity and flexibility, are a type of automated storage and retrieval system used for lightweight loads. SBS/RSs can increase throughput capacity by using multiple shuttles and elevators as storage and retrieval machines (SRMs). They can also facilitate improvements in flexibility since they are able to adjust the number of SRMs according to transaction demands. Thus, determining the number of shuttles is an important issue in tier-to-tier SBS/RSs. In this paper, a decision model to determine the number of shuttles is proposed. The model is based on the travel time model, and it considers parameters such as the physical configuration, velocity profile and the probability that the shuttle operates a dual command. Finally, the throughput capacity from the travel time model is compared with that from a simulation-based approach in order to verify the effects of the model. In addition, a critical discussion regarding the characteristics of the tier-to-tier system is provided.     

Travel-time models and fill-grade factor analysis for double-deep multi-aisle AS/RSs

Double-deep multi-aisle automated storage/retrieval systems are increasingly applied for storing and retrieving unit loads, with advantages of increased space utilisation, reduced number of aisles and improved efficiency of storage rack (S/R) machines. In such systems, the retrieval process may consist of the rearrangement of blocking loads, based on the assumptions of uniformly distributed storage locations and random storage policy. We formulate analytical travel-time models of both single- and dual-command cycles under three rearrangement rules. We validate the analytical travel-time models by simulation and conduct numerical experiments to analyse the effect of the number of aisles an S/R machine serves, the fill-grade factor and the command cycles on the expected travel time of the S/R machine. The results show that the expected travel time of the S/R machine is increasing with the increase in the number of aisles an S/R machine serves and the increase in the fill-grade factor, and dual command cycle outperforms single-command cycle in terms of cycle time. To deal with the trade-off between the storage space cost and the operational cost of the S/R machine, we develop a decision model for finding an optimal fill-grade factor to minimise the total cost. We find the condition when an optimal fill-grade factor exists and show how to calculate it. Based on the decision model, we compare the performance of double-deep multi-aisle automated storage/retrieval system (AS/RSs) and single-deep single-aisle AS/RSs. The results show that double-deep multi-aisle AS/RSs outperform single-deep single-aisle AS/RSs in terms of total cost, although double-deep multi-aisle AS/RSs need more storage locations.     

The impact of dwell point policy in an Automated Storage/Retrieval System

Automated storage and retrieval systems (AS/RS) are devices that allow intensive storage of materials. They can improve the supply chain performance, assuring more available volume for storage, lower labour costs and higher handling throughput of warehousing. Furthermore, the automated control allows the probability of errors in storage and retrieval to be minimised, along with the probability of product damage during movements. The purpose of the paper is to find the best solution in order to find the optimal dwell point policy, among different rules, able to minimise the travel time and distance travelled by stacker cranes, and consequently warehousing costs. An original and innovative model was developed in order to investigate the dwell point position for random allocation of unit loads. A software platform was developed to validate the proposed model by computer simulations. The performance of the system was analysed in a parametric/continuous way, varying at the same time the number of spans and levels, the height of the input/output point and the interval between requested missions. The results show that the developed model allowed convenience areas to be identified among the policies in which the travel time, distance travelled, and consequently warehousing costs are minimised, by varying different parameters.     

Modelling and design for a shuttle-based storage and retrieval system

The shuttle-based storage and retrieval system (SBS/RS) is a relatively new part-to-picker order picking system. We have developed a performance estimation and design algorithm for the SBS/RS. The performance estimation is based on a queuing model. The design algorithm aims to find the minimum cost configurations in terms of number of tiers, aisles, lifts and workstations with given throughput, tote capacity and order cycle time requirements. We used simulation driven by parameters abstracted from an actual SBS/RS to verify the performance estimation, and applied the design algorithm in the case study. The results indicate that: (1) compared to simulation results, the throughput of the performance estimation is nearly identical when the arrival rate is below the maximum capacity; (2) the design algorithm yields a configuration with 28.1% cost reduction in the current system. In addition, we also compared the shuttle system with the competing robotic order fulfilment system (robotic system in short) in terms of facility cost, building cost and order cycle time. We found that the shuttle system is a better choice if large storage capacity and high throughput are required whereas the robotic order fulfilment system performs better if small storage capacity and low throughput are required.     

Expected travel time and optimal boundary formulas for a two-class-based automated storage/retrieval system

Our paper studies a two-class-based rectangular-in-time automated storage/ retrieval system (AS/RS). We present explicit formulas for the optima! boundary of the two storage areas as well as for the expected single command cycle time for an optimally designed rack. In the basic model each crane handles a single aisle. These formulas provide the designer with a full picture of the quantitative effects of the various factors (i.e., access frequencies of the two storage areas, and dimensions of the rack) on the optimal boundary of the two storage areas and the achievable cycle lime in the warehouse. We also develop expected travel time formulas for the dual command AS/RS with two-class-based storage policies and obtain the optimal boundary with a one-dimensional search procedure. Similar developments (i.e., expected travel time formulas and optimal boundary search procedures) are discussed for AS/RS with a single command policy but with each crane handling multiple aisles.     

Optimal storage rack design for a multi-deep compact AS/RS considering the acceleration/deceleration of the storage and retrieval machine

This paper explores the optimal storage rack design for a multi-deep compact Automated Storage and Retrieval System (AS/RS) considering the acceleration and deceleration of storage and retrieval (S/R) machine. The expected travel time under the single-command cycle and dual-command cycle for a random storage strategy is derived. Based on the travel time, the general models we propose calculate the optimal ratio between three dimensions that minimises the travel time under different speed profile scenarios. From the result, it is proven that the optimal storage rack design model in the constant speed situation can be treated as a special case of the model considering the acceleration and deceleration of S/R machine. Finally, this study investigates the effect of speed profile of S/R machine and fixing dimensions by various numerical experiments.     

Analytical model to estimate performances of autonomous vehicle storage and retrieval systems for product totes

In today's competitive scenario of increasingly faster deliveries and smaller order sizes, material-handling providers are progressively developing new solutions. A recent, automated material-handling technology for unit load storage and retrieval consists of an autonomous vehicle storage and retrieval system (AVS/RS). The present paper presents an analytical model to estimate the performances (the transaction cycle time and waiting times) of AVS/RS for product tote movement. The model is based on an open queuing network approach. The model effectiveness in performance estimation is validated through simulation.     

Aisle changing shuttle carriers in autonomous vehicle storage and retrieval systems

The objective of this study is to propose analytical travel time models for aisle changing shuttle carriers, which are capable of travelling in the horizontal and in the cross-aisle directions. The expressions for the single and dual command travel times have been determined assuming uniform distributed storage locations and the probability theory. A simulation model has been applied for the performance analysis of the proposed analytical models. The proposed models enable the calculation of the expected travel times for single and dual command cycles of the aisle changing shuttle carriers, from which the performance can be evaluated.     

Travel-time models considering the operating characteristics of the storage and retrieval machine

Existing travel-time models of automated storage/retrieval systems (AS/RS) assume the average uniform velocity, ignoring the operating characteristics of storage/retrieval (S/R) machine such as the acceleration/deceleration rate and the maximum velocity. Consequently, the optimal design and schedule based on the existing models is far from optimal from the practical point of view. This paper presents continuous analytical models of travel time which integrate the operating characteristics of S/R machine. Using a randomized assignment policy, travel times are determined for both single and dual command cycles. The models developed are examined through discrete evaluation procedures.     

Interleaving models for the analysis of twin shuttle automated storage and retrieval systems

A system of state equations is formulated for describing the dynamic behaviour of the queue of storage and retrieval transactions in a storage aisle served by twin shuttle storage and retrieval (S/R) machines. Using estimates of order picking cycle times in conjunction with storage and retrieval transaction demand levels, an estimate of the probability distribution of storage queue states is derived for a given storage aisle. System performance measures under an opportunistic interleaving discipline including S/R machine utilization, transaction queue lengths, average cycle times and expected transaction waiting times are approximated using the state probability distribution. The modelling tools are demonstrated using sample problems where the performance of twin versus single shuttle systems is contrasted for alternative combinations of storage and retrieval machine travel speeds, storage rack configurations, and transactions demand scenarios.     

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.     

Travel time models for the rack-moving mobile robot system

The rack-moving mobile robot (RMMR) system is a special parts-to-picker automated warehousing system that uses hundreds of rack-moving machines to accomplish the repetitive tasks of storing and retrieving parts by lifting and transporting unit racks autonomously. This paper investigates the operation cycle of the rack-moving machine for storage and retrieval from the perspective of the lane depth, especially exploring the particularity of the RMMR system in multi-deep lanes, and proposes expected travel time models of the rack-moving machine for single- and multi-deep layouts of the RMMR system. To validate the effectiveness of the proposed models, an experimental simulation was conducted with a 1–4-deep layout under six scenarios of different numbers of aisles and layers, and results were compared with results obtained using proposed models. The paper presents useful guidelines for the configuration of the RMMR system layout including the determination of the optimal lane depth.     

The impact of acceleration/deceleration on travel-time models in class-based automated S/R systems

The travel time models of Automated Storage and Retrieval systems (AS/RS) machines under randomized storage proposed by Chang et al. (IIE Transactions, 27(1), 108–111, 1995), which consider the speed profiles in real-world applications, are extended in this paper. In the present study, travel time models are proposed that consider various travel speeds with known acceleration and deceleration rates. Compact forms of expected travel times under the class-based storage assignment and full-turnover-based storage assignment have been determined. The results show that both the proposed exponential travel time model and the adjusted exponential model perform satisfactorily and could be useful tools for designing an AS/RS in real-world applications.     

New cycle time and space estimation models for automated storage and retrieval system conceptualization

New analytical models supporting the design conceptualization of automated storage and retrieval systems are proposed. They include an analytical cycle time model for automated storage and retrieval systems using dedicated storage and computationally efficient procedures for estimating space requirements with systems using randomized or class-based storage. These models fill two gaps in the existing literature focused on analysing space and cycle time tradeoffs for alternative system configurations defined by the number of storage aisles, rows and bays. They are illustrated through a sample problem.     

双载具式多层穿梭车立体仓库货位优化研究

目的为提高双载具式多层穿梭车立体仓库的运作效率,对其货位优化进行研究。方法针对双载具式多层穿梭车立体仓库货位优化作业系统的特点,考虑其运动过程中的加(减)速度特性,建立以入库时间最短为目标的货位分配优化模型。通过设计结合交叉变异算子的混合植物繁殖算法对该模型进行优化求解,从而确定最佳货位分配方案,缩短货位分配时间。结果实例分析表明,混合植物繁殖算法与遗传算法和物繁殖算法相比,收敛速度更快、优化效率更高。结论混合植物繁殖算法能够有效地缩短双载具式多层穿梭车立体仓库的货位分配时间,提高了仓库运作效率。     

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.     

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.     

Closed form models for determining the optimal dwell point location in automated storage and retrieval systems

This paper examines the problem of where a storage/retrieval machine should reside, or dwell, when an automated storage and retrieval system (AS/RS) becomes idle to minimize the expected value of the next transaction time. After a review of the relevant literature on AS/RS dwell point strategies, this paper proposes several analytical models of these expected response times of the AS/RS based on the relative locations of the input and output ports of the AS/RS. It uses a continuous rack approximation to provide analytical models of the dwell point location problem. These models provide closed form solutions for the dwell point location in an AS/RS. Extensions are made to consider AS/RS with a variety of configurations including multiple input and output ports. These models not only provide solutions to the dwell point location problem, but they provide considerable insight into the nature of this problem, which is particularly valuable when the requirements facing the AS/RS are uncertain.     

Retrieval sequencing for unit-load automated storage and retrieval systems with multiple openings

Automated storage and retrieval systems (AS/RS) have made a dramatic impact on material handling and inventory control in warehouses and product systems. A unit-load AS/RS is generic and other AS/RS represent its variations. In this paper, we study a problem of sequencing retrieval requests in a unit-load AS/RS. In a unit-load AS/RS, there are usually multiple openings and a unit-load can be stored in any opening. Given a list of retrieval requests and the locations of openings, this problem seeks a sequence of dual cycles that minimizes total travel time taken by a storage/retrieval machine. Previous researchers believed that this problem is computationally intractable and provided greedy-style heuristic algorithms. In this paper, we present an algorithm that combines the Hungarian method and the ranking algorithm for the assignment problem with tour-checking and tour-breaking algorithms. We show that this algorithm finds either a verified optimal or near-optimal solution quickly for moderate size problems. Using this algorithm, we also evaluate the effectiveness of the existing simple heuristics. Computational results are reported.