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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Optimising two dwell point policies for AS/RSs with input and output point at opposite ends of the aisle

Automated storage and retrieval systems (AS/RSs) are widely used for storing and retrieving products in all types of warehouses. Dwell point policy is a vital control policy that can greatly affect the performance of AS/RSs. In this paper, we study dwell point policies in AS/RSs with input and output stations at opposite ends of the aisle. We first propose two dwell point policies. We find that five existing dwell point policies in the literature are special cases of exactly one of our policies. We then develop expected travel time models for the proposed policies, solve these models with the objective of minimising expected travel time, and obtain closed-form solutions for the optimal dwell location(s). We prove that one proposed policy dominates the other in terms of expected travel time. Numerical experiments are performed to quantify the percentage gap of expected travel time between the proposed policies and policies in the literature. We find that, in some situations, the better proposed policy can achieve up to 8%–10% reduction in expected travel time in comparison with the best literature policy. A real-data case study validates that these situations arise with high probability in typical daily warehouse operations.     

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.     

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。     

Dynamic Operational Policies in an Automated Warehouse

In this paper we consider the optimal relocation of pallets with a high expectancy of retrieval within each storage rack of an automated warehouse to meet the fluctuating, short-term throughput requirements imposed on the automated storage-retrieval machines. The prepositioning of these pallets closer to the input/output point of each rack during off-peak periods will reduce the expected travel time for the storage/retrieval machines during future peak periods of the planning horizon.

As the model has been abstracted from an actual operating environment, we first describe the environment in which the problem has been posed. We then exploit the special structure of the problem to develop conditions that an optimal relocation policy should satisfy. Based on these optimality conditions, we develop a very efficient optimal relocation algorithm. Finally, we present the performance of several relocation policies in the warehouse studied.