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.     

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.     

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.     

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.     

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.     

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 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.     

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.     

Experimental investigation of shared storage assignment policies in automated storage/retrieval systems

In this study, two shared storage assignment policies are compared in an Automated Storage/Retrieval System (AS/RS) by using computer simulation. The AS/RS is assumed to operate under a continuous review, order quantity, reorder point inventory policy. The average travel time of the AS/R machine for storing and retrieving products is used as the main performance measure. Sensitivity of the system to product variety, inventory replenishment lead time, and demand rate is investigated, as well as the effects of the inventory policy and the product classification technique used. Our main conclusion is that the turnover-based policy, in general, outperforms the duration of stay-based policy. However, the' difference between the performance of the two policies becomes insignificant under certain conditions.     

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 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.     

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.     

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.     

An optimal dwell point policy for automated storage/retrieval systems with uniformly distributed,rectangular racks

This study is to develop an optimal dwell point policy for automated storage/retrieval systems with uniformly distributed racks. For non-square-in-time racks, we present the closed form solution for the optimal dwell point in terms of the probability of the next transaction demand type: storage or retrieval. We also introduce various return paths to the dwell point for the efficient operation of the storage/retrieval machine.     

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.     

Optimal dwell point policies for automated storage/retrieval systems with dedicated storage

This study is to develop an optimal dwell point policy for automated storage/retrieval systems. For square-in-time racks with dedicated storage, we determine the optimal dwell points in closed form. We also confirm the intuitive remit that the input point is a good alternative dwell point for dedicated storage.     

Intelligent control schemes for automated storage and retrieval systems

A new information system approach to the operational controls of automated storage and retrieval systems (AS/RS) is developed and examined. This approach is based on artificial intelligence, state-operator framework for problem solving. Gradually increasing the information level, several operational goal functions are identified for an industrial unit-load food produce AS/RS. These functions use real-time statistical interpolations to select the desired storage and retrieval bins. As a result the AS/RS response adapts itself to stochastic perturbations in the system conditions. Experimental evaluations using multiple variance analysis technique and detailed simulations have shown that the proposed dynamic approach is superior to the common industrial control method currently used in those industrial systems characterized by batch arrivals (and retrievals) of the UL's and non-stationary demand patterns, These evaluations further suggest that improved performance is realized with the increase in the information level. The operational control scheme developed in this paper appears to be an excellent control alternative for unit-load AS/RSs. This is due to its limited computational requirements and the augmented productivity as demonstrated here for a real case study.     

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.     

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.