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.     

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.     

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.     

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.     

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.     

A study on multi-aisle system served by a single storage/retrieval machine

Multi-aisle S/R machine system (MASS) can substantially reduce high initial investment cost which is a major reason for the low popularity of AS/RS in manufacturing companies. The objective of this study is mainly related to the design aspects of MASS. With a travel time model developed, average travel time of S/R machine is determined. We propose rack-class-based storage assignment procedure and class selection procedure to find the minimum number of S/R machines required and identify the number of aisles each S/R machine serves. Example problems are solved to illustrate the procedures. The results show that MASS is effective in reducing initial installation cost, provided that the pallet demands are relatively low.     

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.     

The impact on rack configuration on the speed profile of the storage and retrieval machine

The travel-time models of automated storage/retrieval machines, proposed by Chang, Wen and Lin (IIE Transactions, 27 (1), 108-111(1995)), which consider the speed profiles in real world applications, have been extended in this paper to investigate the impact on the rack configuration. The results demonstrate that the optimal rack configuration of the single-command cycle is square-in-time whereas the dual-command cycle may not be. Furthermore, the travel times for both single- and dual-command cycles are quite insensitive to the deviation in the length of the rack configuration.     

Relative pre-positioning of storage/retrieval machines in automated storage/retrieval systems to minimize maximum system response time

In this paper, the problem of pre-positioning a storage/retrieval (S/R) machine in an automated storage/retrieval system (AS/RS) when the machine is idle is addressed. The objective of the pre-positioning strategy is to minimize the maximum response time to service incoming requests into the AS/RS. A model is developed under the operating condition that each machine can serve one or multiple dedicated aisle(s) of the system. The aisles are assumed to exist in the same region of the AS/RS and thus form a valid order storage/retrieval zone. A solution algorithm for determining the optimal dwell point or location is developed. The paper assumes a dynamic environment where orders arrive over time and are to be serviced by the S/R machine. A dwell point or strategic point to pre-position the machine is to be determined whenever the S/R machine becomes idle in anticipation of an incoming service request. A numerical example is provided to demonstrate how the technique can be used in an actual production setting to improve the overall order turnaround time.     

Relative pre-positioning of storage/retrieval machines in automated storage/retrieval system to minimize expected system response time

This paper is focused on the control problem of determining the dwell point of an idle storage/retrieval (S/R) machine in an automated S/R system to improve the overall system service level as measured by the turnaround time of requests to the system. The emphasis of the paper is on the minimization of the expected response time over all retrieval and storage requests executed by the system. The model presented is developed under the operating condition that each machine serves several dedicated aisles of the system. The aisles are assumed to exist in the same region of the automated storage/retrieval system (AS/RS) and thus form a valid order S/R zone. A solution algorithm for determining the optimal dwell point location is developed. The paper assumes a dynamic environment where orders arrive over time and are to be serviced by the S/R machine. A dwell point or strategic point to pre-position the machine is to be determined whenever the machine becomes idle in anticipation of an incoming service request. A numerical example is provided to demonstrate how the technique can be used in an actual production setting to improve the overall order turnaround time.     

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.     

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.     

The impact of acceleration/deceleration on travel-time models for automated storage/retrieval systems

In this note we propose a travel-time model of automated storage/retrieval (S/R) machines by considering the speed profiles that exist in real-world applications. Compact forms of expected travel-times under randomized storage conditions have been determined for both single and dual command cycles.     

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.     

A storage assignment policy in a man-on-board automated storage/retrieval system

This paper deals with a man-on-board automated storage/retrieval system where each customer order consists of a number of different items and is picked one at a time. For the system the problem examined is to allocate storage locations dedicatedly to items so that the total travel time required to pick all the given orders per period is minimized. The problem is shown to be formulated as a variant of the generalized assignment model. A heuristic for the storage layout problem is developed based on the group technology concept considering both order structure and frequency. Through the heuristic, close relationships between items are identified from the order structure, and then based on the relationships the items are compelled to be stored closely in the storage rack following a space-filling curve. Experimental results are provided to describe the performance of the heuristic     

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.     

Integrated optimization of location assignment and sequencing in multi-shuttle automated storage and retrieval systems under modified 2n-command cycle pattern

This article explores the integrated optimization problem of location assignment and sequencing in multi-shuttle automated storage/retrieval systems under the modified 2n-command cycle pattern. The decision of storage and retrieval (S/R) location assignment and S/R request sequencing are jointly considered. An integer quadratic programming model is formulated to describe this integrated optimization problem. The optimal travel cycles for multi-shuttle S/R machines can be obtained to process S/R requests in the storage and retrieval request order lists by solving the model. The small-sized instances are optimally solved using CPLEX. For large-sized problems, two tabu search algorithms are proposed, in which the first come, first served and nearest neighbour are used to generate initial solutions. Various numerical experiments are conducted to examine the heuristics’ performance and the sensitivity of algorithm parameters. Furthermore, the experimental results are analysed from the viewpoint of practical application, and a parameter list for applying the proposed heuristics is recommended under different real-life scenarios.     

Optimal routing in an automated storage/retrieval system with dedicated storage

We address the sequencing of requests in an automated storage/retrieval system with dedicated storage. We consider the block sequencing approach, where a set of storage and retrieval requests is given beforehand and no new requests come in during operation. The objective for this static problem is to find a route of minimal total travel time in which all storage and retrieval requests may be performed. The problem of sequencing a list of retrievals is equivalent to the Traveling Salesman Problem (TSP), and thus NP-hard in general. We show that the special case of sequencing under the dedicated storage policy can be solved in polynomial time. The results apply to systems with arbitrary positions of the input and output stations. Tlus generalizes the models in the literature, where only combined input/output stations are considered. Furthermore we identify a single command area in the rack. At the end we evaluate the model against heuristic procedures.     

Simulation study of an automated storage/retrieval system

In this paper we present a simulation study of an automated storage/retrieval system and examine a wide variety of control policies. We compare several storage location assignment policies. For the class-based storage policy, we apply a recent algorithm that enables us to evaluate the trade-off between storage space requirements and travel times. We also study a new storage location policy which combines low storage space requirements with short mean travel times. Furthermore, we study the sequencing of storage and retrieval requests whereby we focus on the trade-off between efficient travel of the S/R machines and response time performance.