On sequencing policies for unit-load automated storage and retrieval systems

Automated Storage and Retrieval System (AS/RS) performance highly depends on the characteristics of the mechanical equipment. However, once the system has been physically implemented, achieving its maximum efficiency depends on the way the system is operated. This paper shows that request sequencing (i.e. planning the order in which storage and retrieval requests are performed) is of paramount importance in AS/RS performance. This paper reviews and adapts the most popular storage and sequencing policies to dynamic contexts, and then it proposes a ‘sequencing mathematical model’ (SMM) to simultaneously solve the sequencing and storage location problems. Extensive computational results based on a thorough simulation experiment plan confirm that performing the requests in the right sequence can have a positive impact on AS/RS performance. Our results show that the proposed SMM regularly outperforms other methods. When used in a dynamic context, the proposed SMM may yield up to a 25% reduction in average travel-time compared to the situation where a no-sequencing method is applied.     

A bi-directional flow-rack automated storage and retrieval system for unit-load warehouses

Flow-rack is a multi-deep rack containing multi-row and multi-column slope bins. Traditionally, bins slope in the same direction in a flow-rack to make unit-loads slide from the storage face to the retrieval face driven by gravity, which cause unit-loads are stored to the storage face and retrieved from the retrieval face. In this paper, a bi-directional flow-rack (BFR) is designed, in which bins in adjacent columns slope to opposite directions. In each side of a BFR, unit-loads are stored in half of the bins and retrieved from the other half. Therefore, dual-command (DC) operations could be simultaneously performed on both faces and blocking unit-loads are re-stored to available bins on the same face directly. We develop a travel time model for BFR systems, which provides the throughput baseline for different configurations of BFR. A DC operation generation method is introduced for BFR systems. Simulation experiments are conducted to evaluate the effectiveness of the BFR travel time model, to compare the throughput performance between BFR and SFR systems and to evaluate the performance of the proposed DC operation generation method.     

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 shift-based sequencing method for twin-shuttle automated storage and retrieval systems

The continuing need for high-throughput Automated Storage and Retrieval Systems (AS/RS) has lead to the introduction of storage/retrieval machines that can carry more than one unit-load. However, this technology involves a large capital investment so careful operating methods are desired to make the most of its capabilities. In this paper, we study a shift-based sequencing problem for twin-shuttle AS/RS, where depletion (retrieval operations) and replenishment (storage operations) of items occur over different shifts. For example, certain warehouses or distribution depots deplete their items in stock during morning shifts and replenish during later shifts. We show that this problem can be transformed into the minimum-cost perfect matching problem and present an efficient polynomial-time optimum method that can achieve a large throughput gain over other methods. We also provide average-case and lower bound analyses for this problem.     

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.     

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.     

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.     

Sequencing approaches for multiple-aisle automated storage and retrieval systems

Automated storage and retrieval systems (AS/RS) are used in high velocity distribution centres to provide accurate and fast order processing. While almost every industrial system is comprised of many aisles, most of the academic research on the operational aspects of AS/RS is devoted to single-aisle systems, probably due to the broadly accepted hypothesis proposing that an m aisles system can be modelled as m 1-aisle independent systems. In this article, we present two multi-aisles sequencing approaches and evaluate their performance when all the aisles are managed independently first, and then in a global manner. Computational experiments conducted on a multi-aisle AS/RS simulation model clearly demonstrate that a multi-aisle system cannot be accurately represented by multiple single-aisle systems. The numerical results demonstrate that, when dealing with random storage, globally sequencing multi-aisle AS/RS leads to makespan reductions ranging from 14 to 29% for 2- and 3-aisle systems, respectively.     

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.     

Throughput bounds for miniload automated storage/retrieval systems

To compute miniload system throughput, the distribution of the pick times is needed. Unfortunately, during the design phase, only partial information may be available such as the mean pick time. In this paper, we determine tight upper and lower bounds on throughput for several different types of partial information. We also give numerical examples to show how to apply the bounds.     

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.     

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.     

Models for automated storage and retrieval systems: a literature review

Automated Storage and Retrieval Systems (AS/RS) are warehousing systems that use mechanised devices to accomplish the repetitive tasks of storing and retrieving parts in racks. Since these systems represent a significant investment and considerable operating costs, their use must be as efficient as possible. AS/RS performance is the result of the interaction of many complex and stochastic subsystems. This reality creates a need for robust and efficient evaluation models. This article complements previous surveys on AS/RS by focusing on the particular research question addressed by each work and the associated assumptions used for the various models designed for evaluating AS/RS. Dynamic models based on simulation dominate the most recent literature; however, static approaches based on travel-time modelling have strongly contributed to the study of AS/RS. This review includes dynamic – simulation-based – models, but considers also steady-state (travel-time-based) models. We believe that this review may be of great help to researchers and industrial users in their search for the best modelling approach for a specific problem.     

A cross-entropy method for optimising robotic automated storage and retrieval systems

In this paper, we consider a robotic automated storage and retrieval system (AS/RS) where a Cartesian robot picks and palletises items onto a mixed pallet for any order. This robotic AS/RS not only retrieves orders in an optimal sequence, but also creates an optimal store ready pallet of any order. Adapting the Travelling Salesman Problem to warehousing, the decision to be made includes finding the optimal sequence of orders, and optimal sequence of items inside each order, that jointly minimise total travel times. In the first phase, as a control problem, we develop an avoidance strategy for the robot (or automatic stacker crane) movement sequence. This approach detects the collision occurrence causing unsafe handling of hazardous items and prevents the occurrence of it by a collision-free robot movement sequence. Due to the complexity of the problem, the second phase is attacked by a Cross-Entropy (CE) method. To evaluate the performance of the CE method, a computational analysis is performed over various test problems. The results obtained from the CE method are compared to those of the optimal solutions obtained using CPLEX. The results indicate high performance of the solution procedure to solve the sequencing problem of robotic AS/RSs.     

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.     

Order batching algorithms and travel-time estimation for automated storage/retrieval systems

In this paper we present heuristics and analytical models for the order batching problem. Orders are batched into tours such that the total travel time is minimized. Four heuristics are developed for the order batching problem, for which no exact solution exists. All heuristics are based on the time-saving criterion of combining two or more orders in a single tour rather than processing them one order at a time. Among the heuristics that are presented, the SL algorithm has the best performance. An analytical model is developed to estimate the travel time of the S/R machine as a function of the number of locations to be visited and the physical specifications of the structure. Expressions for upper and lower bounds for travel time are presented.     

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.     

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.     

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.     

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.