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.     

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.     

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.     

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.     

A comparison of alternative conceptualizing tools for automated storage and retrieval systems

The throughput performance model and the state equation model are alternative analytical approaches for determining the proportion of dual versus single command crane cycles in automated storage and retrieval systems that utilize opportunistic interleaving. The different assumptions underlying these models result in biases in the estimation of expected crane cycle times. The magnitude of the biases is investigated to assess whether the use of the older, less computationally efficient state equation model is still warranted in practical conceptualizing situations. The results suggest that the TP model is a dominating alternative for AS/RS conceptualizing applications.     

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.     

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.     

自动存取系统及其仿真分析

自动存取系统是一种新的存取系统,其效率取决于库位地址的分配方式、存取方式以及堆垛机的运行方式等特性。自动存取系统相对于传统存取方式有优点也有缺点。其效率主要采用通过率来评价。对此,提出了用数学模型的方法来仿真分析,给出了模型的一些相应参数、重要假设和理论结果。最后,对一个实例运用Ａｗｅｓｉｍ软件仿真,给出仿真结果。     

Travel-Time Models for Automated Storage/Retrieval Systems

Travel-time models are developed for automated storage/retrieval (AS/R) machines. The S/R machine travels simultaneously horizontally and vertically as it moves along a storage aisle. For randomized storage conditions expected travel times are determined for both single and dual command cycles. Alternative input/output (I/O) locations are considered. Additionally, various dwell-point strategies for the storage/retrieval machine are examined.     

Performance analysis for automated storage and retrieval systems

Automated storage and retrieval (AS/R) systems have had a dramatic impact on material handling and inventory control in warehouses and production systems. A unit-load AS/R system is generic and other AS/R systems represent its variations. Common techniques that are used to predict performance of a unit-load AS/RS are a static analysis or computer simulation. A static analysis requires guessing a ratio of single cycles to dual cycles, which can lead to poor prediction. Computer simulation can be time-consuming and expensive. In order to resolve these weaknesses of both techniques, we present a stochastic analysis of a unit-load AS/RS by using a single-server queueing model with unique features. To our knowledge, this is the first study of a stochastic analysis of unit-load AS/R systems by an analytical method. Experimental results show that the proposed method is robust against violation of the underlying assumptions and is effective for both short-term and long-term planning of AS/R systems.     

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.     

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.     

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.     

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.     

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.     

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.     

Dual command travel times and miniload system throughput with turnover-based storage

We analyze travel times for automated storage/retrieval systems. In particular, we apply our travel time model to turnover-based storage systems and determine the mean and variance of dual command travel times. We present detailed numerical results for selected rack shape factors and ABC inventory profiles. We then investigate the effect of alternative rack configurations on travel time performance measures. We also show how to determine the throughput of miniload systems with turnover-based storage and exponentially distributed pick times.     

On Sequencing Retrievals In An Automated Storage/Retrieval System

This paper addresses throughput improvement by retrieval sequencing in conventional unit load automated storage/retrieval systems when several retrieval requests are available and dual command cycles are performed. Taking first-come-first-served as the reference sequencing rule, the potential for improvement is identified. A “nearest-neighbor” sequencing rule is proposed as an alternative, an analytic model for its expected performance is developed, and Monte Carlo simulation is used for evaluation. In addition, a lower bound on dual command cycle times is developed, and the dynamic behavior of two heuristic sequencing rules is discussed.     

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.     

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.