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.     

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.     

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.     

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.     

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.     

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.     

Analytical models for analysis of automated warehouse material handling systems

Automated storage and retrieval systems (AS/RSs) and autonomous vehicle storage and retrieval systems (AVS/RSs) are two competing technologies for the handling, storage and retrieval of unit-loads in the reserve section of an automated warehouse. In this paper, we model variants of the two systems as an open queuing network (OQN) and use an existing tool for the analysis of OQNs, called the manufacturing system performance analyser (MPA), for analysing the performance of the AS/RS and AVS/RS. Experimental results are provided to show that MPA is a better choice than simulation to quickly evaluate alternate configurations of the two systems. We use MPA to answer a series of design questions for AS/RS and AVS/RS design conceptualisation.     

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.     

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.     

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.     

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.     

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.     

Modelling an automated storage and retrieval system using Petri nets

We investigated the feasibility of using stochastic Petri nets (SPNs) to describe the behaviours of automated storage/retrieval systems as well as to evaluate the performance of different control policies of such systems. SPNs have been studied in the past 2 decades, and have become a powerful tool in modelling concurrent and distributed systems that exhibit synchronization and contention of shared resources. It appeared that some important characteristics of AS/RS could be well modelled with SPNs. The SPN is a graph-based tool suitable for modelling systems (manufacturing, computer, biological, etc.). It can be used to model a system at different levels of abstraction. In this study, the efficiency, control rules, bay assignment, and many other performance issues associated with AS/RS have been studied in detail using SPN models. SPNs are shown to be equivalent to the stochastic processes in which embedded Markov chains can be recognized. In addition, a stochastic Petri net package, SPNP, was adopted to solve the reachability trees from which an embedded Markov chain was generated. Finally, the performance of those systems of our interest was evaluated. The unique features and flexibility of SPNs are presented. Furthermore, the SPN models for different control algorithms of an AS/RS are discussed with examples.     

On Sequencing Retrievals In An Automated Storage/Retrieval System

This paper addresses throughput improvement by retrieval sequencing in conventional unit load automated storage/retrieval systems when several retrieval requests are available and dual command cycles are performed. Taking first-come-first-served as the reference sequencing rule, the potential for improvement is identified. A “nearest-neighbor” sequencing rule is proposed as an alternative, an analytic model for its expected performance is developed, and Monte Carlo simulation is used for evaluation. In addition, a lower bound on dual command cycle times is developed, and the dynamic behavior of two heuristic sequencing rules is discussed.     

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.     

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.     

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.     

Optimal partitioning of vertical zones in vehicle-based warehouse systems

New innovations in warehouse automation systems such as autonomous vehicle-based storage and retrieval (AVS/R) system offer greater flexibility and responsiveness in processing unit-load storage and retrieval transactions in high-density storage areas. To optimise system performance, new technologies should be implemented with optimal setting of design parameters. This research is a first attempt to model a ‘zone-captive’ AVS/R system and understand the effect of number and boundary of vertical zones on system performance measures. Further, we also analyse the effect of aisle orientation within a tier on cycle times. A detailed simulation model of a multi-tier zone-captive system is built to capture the dynamics of the system i.e. interaction among the vehicles, lift and incoming transaction requests, and estimate the performance measures of interest. The numerical experiments show that the transaction cycle times can be reduced by 1–12% with optimal partitioning of vertical zones and further reduced by 0.2–15.0% by a better aisle orientation.     

Maximization of the throughput of a computerized automated warehousing- system under system constraints

This paper attempts to determine the maximum number of storage and retrieval requests that can be handled by automated warehousing systems under physical and operational constraints. The system is formulated as a stochastic constrained optimization problem and an algorithm is developed for its solution. Due to the stochastic nature of the operation of the system, a simulation model is constructed to evaluate the system for various values of its parameters. The optimization routine interacts with the simulation model and systematically moves towards the optimum solution. The problem is studied under various levels of constraints. Also several levels of the risk of violation of constraints are examined.