Interleaving dynamics in autonomous vehicle storage and retrieval systems

A state equation model is proposed for predicting the proportion of dual command cycles in autonomous vehicle storage and retrieval systems that use interleaving. This proportion is used to estimate storage and retrieval cycle times, system utilization and throughput capacity for alternative system design profiles defined by the number of storage aisles, storage rack height and depth, the vehicle fleet size and the number of lifts used for vertical movement. The state equation model enables the user to explicitly trade off model accuracy and computational complexity in the pre-engineering or 'concepting' stage of system development. A sample problem is used to demonstrate the model.     

Simulation-based regression analysis for the rack configuration of an autonomous vehicle storage and retrieval system

In this paper, a simulation-based regression analysis for the rack configuration of an autonomous vehicle storage and retrieval system (AVS/RS) is presented. The aim of this study is to develop mathematical functions for the rack configuration of an AVS/RS that reflects the relationship between the outputs (responses) and the input variables (factors) of the system under various scenarios. In the regression model, we consider five outputs: the average cycle time of storage and retrieval transactions, the average waiting time for vehicle transactions, the average waiting time of vehicles (transactions) for the lift, the average utilisation of vehicles and the average utilisation of the lifts. The input variables are the number of tiers, aisles and bays that determine the size of the warehouse. Thirty regression models are developed for six warehouse scenarios. The simulation model of the system is developed using ARENA 12.0 commercial software and the statistical analyses are completed using MINITAB statistical software. Two different approaches are used to fit the regression functions–stepwise regression and the best subsets. After obtaining the regression functions, we optimise them using the LINGO software. We apply the approach to a company that uses AVS/RS in France.     

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.     

A model for the design of zone control automated guided vehicle systems

An analytical modelling strategy is proposed as a screening device for use prior to the simulation phase in the design of zone control automated guided vehicle systems (AGVS). The proposed model predicts the effects of the major AGVS design variables on system-performance measures including maximum throughput capacity and risk factors associated with shop locking. This is done through a process which specifically evaluates the system operating dynamics associated with vehicle fleet size, guidepath layout, workstation storage capacity, routeing, and, to a less precise extent, vehicle dispatching. Operating dynamics are defined to include vehicle blocking resulting from guidepath contention and variation of in-process storage levels. The objective of the analytical model is to reduce the extent of simulation modelling necessary to design a zone-control AGVS for a given materials-handling workload. The model is illustrated for a sample AGVS with variation in the fleet size, workstation storage capacity and dispatching rule demonstrated.     

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.     

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.     

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.     

Belt-conveyor based efficient parallel storage system design and travel time model analysis

This paper presents a belt-conveyor based parallel storage system (PSS). Compared with the conventional AS/RS, it has advantages including more efficient utilisation of storage space, and faster storage and retrieval of products. The PSS consists of three components: the automated retrieval system (ARS), the automated storage system (ASS) and the compact storage rack (CSR). In the ARS, a vertical screw conveyor is used to facilitate the vertical movement of the unit loads, while a powered belt-conveyor is used for the horizontal dimension. Additionally, a powered conveyor system enables motion along the depth dimension, meaning each lane in the CSR is connected to several storage cells. Horizontal belt-conveyor and powered conveyor in the lane constitute cross-belt which causes the parallel process. On the other side of the rack, a unit load lift, a RGV lift, several rail-guided vehicles and a buffer rack constitute the ASS. Based on the system, we formulate separate travel-time models for ARS and ASS, under the assumption of randomised, uniformly distributed storage rack positions. Computer simulation with Matlab is used to validate the models, and optimise the automated storage system.     

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.     

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.     

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.     

Development of a framework for the design of autonomous vehicle storage and retrieval systems

In today’s competitive environment with increasingly faster deliveries and smaller order sizes, material handling providers are progressively developing new solutions. A more recent development in automated material-handling technology for unit load storage and retrieval is the autonomous vehicle storage and retrieval system (AVS/RS). The paper investigates the main design trade-offs for this new solution using simulation, and proposes a comprehensive design framework. Using data from a recently implemented AVS/RS, the application of the proposed framework is presented and the key design differences between the two types of AVS/RS configuration (i.e. tier-captive versus tier-to-tier) are identified.     

ECONOMIC DESIGN OF REFRIGERATED AUTOMATED STORAGE AND RETRIEVAL SYSTEMS

The objective of this paper is the development of a design model for refrigerated automated storage and retrieval systems (R-AS/RS). Compared with ordinary unit-load AS/RS, the R-AS/RS under this study has several different design and operating characteristics: (I) greater emphasis is placed on the storage function and so it has a double-depth lane in the storage rack; (2) cooling units are required to maintain a cold temperature environment in the system; (3) the maximum number of storage orders handled per unit time is limited by the system capacity. Considering the above characteristics, the design problem is formulated as a non-linear mixed integer programming problem in which the cost of the system is minimized. The decision variables are the storage volume, the number of storage and retrieval (S/R) machines, the type and number of cooling units, and the physical configuration of the building. A case problem is solved to illustrate the model.     

Graph-based solution for performance evaluation of shuttle-based storage and retrieval system

The aim of this study is to provide a graph-based solution for performance evaluation of a new autonomous vehicle-based storage and retrieval system, shuttle-based storage and retrieval system (SBS/RS), under various design concepts. By the graph-based solution, it is aimed the decision-maker (i.e. warehouse manager) evaluates a pre-defined system’s performance promptly and decides on the correct design concept based on his/her requirements from thousands of alternative design scenarios of SBS/RS. The design concepts include number of bays (NoB), aisles (NoA) and tiers (NoT) for the rack design and arrival rate of storage/retrieval (S/R) transactions to an aisle of the warehouse (AR). The performance of the system is evaluated in terms of average utilisation of lifts and average cycle time of S/R transactions. Simulation is utilised for the modelling purpose. Seven NoT, seven NoB and six AR scenarios are considered in the experiments. Hence, 294 experiments are completed to obtain the graphs. By this study, to the best of our knowledge it is the first time a graph-based solution including comprehensive design concepts of SBS/RS is presented.     

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.     

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.     

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.     

Determination of optimum unit load size of the AGV in an electronics assembly production system

This paper deals with the problem of determining an optimum unit load size of automated guided vehicle (AGV) in an electronics assembly production line. It is assumed that an AGV delivers assembly parts to each workstation from a miniload automated storage/retrieval system and a conveyor line transports subassemblies between workstations. Two types of operating policies for the AGV system are proposed. For each policy, a nonlinear mathematical model is formulated. Based on the characteristics of the objective function and feasible region, a solution algorithm is developed, which finds an optimum unit load size. To illustrate the models, problems are chosen and solved.     

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.     

New cycle time and space estimation models for automated storage and retrieval system conceptualization

New analytical models supporting the design conceptualization of automated storage and retrieval systems are proposed. They include an analytical cycle time model for automated storage and retrieval systems using dedicated storage and computationally efficient procedures for estimating space requirements with systems using randomized or class-based storage. These models fill two gaps in the existing literature focused on analysing space and cycle time tradeoffs for alternative system configurations defined by the number of storage aisles, rows and bays. They are illustrated through a sample problem.