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 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.     

An efficient cycle time model for autonomous vehicle storage and retrieval systems

A computationally efficient cycle time model for conceptualizing autonomous vehicle storage and retrieval systems and comparing their performance with crane-based automated storage and retrieval systems is presented. The model is based on an iterative computational scheme exploiting random storage assumptions and queuing model approximations. Relative to earlier models, the procedure scales up efficiently for large problems thereby enabling more extensive search of a design solution space. Simulation based validation studies suggest that model accuracy is adequate for system conceptualization. The procedure is demonstrated using realistically sized sample problems.     

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.     

Conceptualizing tools for autonomous vehicle storage and retrieval systems

Autonomous vehicle storage and retrieval systems utilize rail-guided vehicles moving in rectilinear paths within and between the aisles of unit load storage racks. Vertical vehicle movement is provided by lifts installed at fixed locations along the rack periphery. As an alternative to traditional automated storage and retrieval systems, autonomous vehicle systems enable users to match vehicle fleet size and the number of lifts to the level of transactions demand in a storage system. Analytical conceptualizing tools based on the features of autonomous vehicle systems are proposed for modelling expected performance as a function of key system attributes including storage capacity, rack configuration and fleet size. The models are demonstrated for a sample problem and compared with analytical conceptualizing tools used for automated storage and retrieval systems.     

Multi-shuttle automated storage/retrieval systems

Multi-shuttle automated storage/retrieval systems have been developed for use in factories and distribution centers because they are more efficient than single-shuttle systems (owing to less empty travel). This improved efficiency results in more agile support (flexible response, less waiting time, etc.) for the production system the storage/retrieval system serves. In this paper we develop analytical models to estimate the throughput in multi-shuttle systems. Throughput improvements greater than 100% are illustrated when triple-shuttle systems are compared with single-shuttle systems.     

Modelling load retrievals in puzzle-based storage systems

Puzzle-based storage systems are a new type of automated storage systems that allow storage of unit loads (e.g. cars, pallets, boxes) in a rack on a very small footprint with individual accessibility of all loads. They resemble the famous 15-sliding tile puzzle. Current models for such systems study retrieving loads one at a time. However, much time can be saved by considering multiple retrieval loads simultaneously. We develop an optimal method to do this for two loads and heuristics for three or more loads. Optimal retrieval paths are constructed for multiple load retrieval, which consists of moving multiple loads first to an intermediary ‘joining location’. We find that, compared to individual retrieval, optimal dual load retrieval saves on average 17% move time, and savings from the heuristic is almost the same. For three loads, savings are 23% on average. A limitation of our method is that it is valid only for systems with a very high space utilisation, i.e. only one empty location is available. Future research should investigate retrieving multiple loads for systems with multiple empty slots.     

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.     

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.     

Design and storage cycle time analysis for the automated storage system with a conveyor and a rotary rack

In this paper, we analyse the performance of an automated Work-In-Process (WIP) storage system consisting of a conveyor and a rotary rack. The stability condition and the expected storage cycle time are derived to analyse the performance of the WIP storage system. As part of the storage cycle time analysis, the derived expected waiting times at the conveyor and the rotary rack are important performance measures that can be used for buffer-sizing purpose in such systems. Given the fixed storage space of the rotary rack, we also develop a heuristic approach to determine the near optimum ‘shape’ of the rotary rack so that the expected storage cycle time is minimized. Numerical results are presented to examine the storage cycle time model and the proposed shape design. The analytical model introduces a simple approach over simulation with acceptable accuracy; it is useful when designing such WIP storage systems. Moreover, it can be expanded to model more complex systems. The derived model also provides insightful information on the design parameters that a typical simulation tool can hardly provide.     

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.     

Analysis of storage assignment policies in less than unit load warehousing systems

Analytical models for the analysis of item location policies in unit load storage and retrieval systems are extended to less than unit load warehousing systems. The models are used to compare dedicated storage using cube per order index item dispatching and randomized storage using closest open location item dispatching with respect to total item space requirements, orderpicking cycle times and system responsiveness. Despite a number of computational limitations, it is argued that the models provide practical tools for analysis of less than unit load systems prior to development of simulation-based models or for validation of simulation-generated model results. The application of the models are demonstrated for a sample problem.     

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.     

Rule of thumb heuristics for configuring storage racks in automated storage and retrieval systems design

A well-known rule of thumb for evaluating storage rack configurations in automated storage and retrieval (ASR) systems is modified to avoid the need for two key assumptions. These are the proportion of single and dual command order picking cycles used in operating a system and the total storage capacity requirements when randomized versus dedicated storage is used. Procedures for generating ASR system cost estimates are also directly coupled with models for estimating the utilization of storage and retrieval machines. Additional performance criteria for evaluation of alternative rack configurations are proposed. The modified rules of thumb are also designed for implementation on PC-level hardware, but with adequate computational efficiency for analysing a broad range of rack design alternatives in large-scale applications. They are demonstrated using a realistic sample problem.     

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.     

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.     

A generalized design and performance analysis model for end-of-aisle order-picking systems

In this paper we present an analytical design algorithm to determine the near-minimum number of pickers required in an end-of-aisle order-picking operation based on a miniload automated storage/retrieval system. The algorithm is based on an approximate analytical model we developed to estimate the expected picker utilization (and the storage/retrieval machine utilization) for general system configurations with two or more pick positions per aisle and/or two or more aisles per picker. For systems with two pick positions, we also investigate the possibility of improving the picker utilization by sequencing container retrievals within each order.     

TRIP-BASED MATERIAL HANDLING SYSTEMS: THROUGHPUT CAPACITY ANALYSIS

In this paper we present a general-purpose analytical model to compute die approximate throughput capacity of a trip-based material handling system used in a manufacturing setting. A wide variety of handling systems, including freight elevators, cranes, microload automated storage/retrieval (AS/R) systems, industrial lift trucks, and automated guided vehicle (AGV) systems can be modeled as trip-based handling systems. To our knowledge, this model is one of the few analytical models that explicitly considers an empty device dispatching rule. The model is first developed for a single-device system (such as a crane) and subsequently, with a simple modification, it is extended to multiple-device systems (such as lift trucks and AGVs). Using this model one can rapidly evaluate a wide range of handling and layout alternatives for given flow data. Hence, die model would be most effective when used early in the design phase to narrow down die set of alternative handling systems and configurations prior to simulation.     

Heavy traffic analysis of a single vehicle loop in an automated storage and retrieval system

We consider an automated storage/retrieval system in which cargo moves between the storage/retrieval machines and the system entrance/exit stations through a single automated vehicle loop. Past studies indicated that the cargo waiting time in the loop is affected by the dispatching rules, which govern the sequence of the cargo to be handled. In this paper, we show that the loop configuration, which has received little research attention, also has a big impact on the cargo waiting time. When the first-come-first-served dispatching rule is used, we derive the relationship between the number of stations and the ratio of the average cargo retrieval time to the average cargo storage time. When the first-encountered-first-served dispatching rule is used, we show that even the arrangement of the input channel and the output channel of a station can have significant impact on the cargo waiting time. Furthermore, we derive a formula for the vehicle visit rate for each station under heavy traffic conditions. This formula helps to explain the phenomenon that the waiting times at different stations can be very different even when the loop is symmetrically designed and the cargo arrival rates to the stations are similar. In addition to analytical models, we use simulations to evaluate the performance of different loop configurations. Our research suggests that a substantial improvement can be achieved by making proper adjustments to the loop configuration.