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.     

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.     

Conceptualizing tools for autonomous vehicle storage and retrieval systems

Autonomous vehicle storage and retrieval systems utilize rail-guided vehicles moving in rectilinear paths within and between the aisles of unit load storage racks. Vertical vehicle movement is provided by lifts installed at fixed locations along the rack periphery. As an alternative to traditional automated storage and retrieval systems, autonomous vehicle systems enable users to match vehicle fleet size and the number of lifts to the level of transactions demand in a storage system. Analytical conceptualizing tools based on the features of autonomous vehicle systems are proposed for modelling expected performance as a function of key system attributes including storage capacity, rack configuration and fleet size. The models are demonstrated for a sample problem and compared with analytical conceptualizing tools used for automated storage and retrieval systems.     

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.     

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.     

Rack shape and energy efficient operations in automated storage and retrieval systems

Energy efficiency has become a primary goal to be pursued for sustainable logistics. In automated storage and retrieval systems this leads to revise the traditional control policies aimed at picking time minimisation and to pay more attention to rack configuration, which has been not a research concern from the time-based perspective. Proper models for energy calculation should be developed by introducing new factors neglected in time analysis, such as the weight of unit loads and the differentiation of shifts along the horizontal and vertical axis as regard energy requirements, due to different contribution of gravity, inertia and friction. In this study, a classification of racks based on system height is proposed in order to select the proper crane specifications needed to compute the torque to be overcome by motors to serve a given location within a rack. An overall optimisation model based on Constraint Programming hybridised with Large Neighborhood Search is developed, allowing the joint application of the best control policies for storage assignment and sequencing both for time and energy-based optimisation, as well as the introduction of multiple weight unit loads and energy recovery. Simulations analysis is performed in order to assess the impact of the rack shape on energy saving. Results show how, regardless the demand curve and the optimisation objective, the best performances in terms of energy efficiency are reached by the intermediate height rack shapes, while the lower ones outperform when considering travel time performance.     

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 for the rack-moving mobile robot system

The rack-moving mobile robot (RMMR) system is a special parts-to-picker automated warehousing system that uses hundreds of rack-moving machines to accomplish the repetitive tasks of storing and retrieving parts by lifting and transporting unit racks autonomously. This paper investigates the operation cycle of the rack-moving machine for storage and retrieval from the perspective of the lane depth, especially exploring the particularity of the RMMR system in multi-deep lanes, and proposes expected travel time models of the rack-moving machine for single- and multi-deep layouts of the RMMR system. To validate the effectiveness of the proposed models, an experimental simulation was conducted with a 1–4-deep layout under six scenarios of different numbers of aisles and layers, and results were compared with results obtained using proposed models. The paper presents useful guidelines for the configuration of the RMMR system layout including the determination of the optimal lane depth.     

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.     

Determination of unit load sizes of AGV in multi-product multi-line assembly production systems

This study deals with the problem of determining unit load sizes of automated guided vehicles (AGVs) in multi-product and multi-line assembly production systems. It is assumed that an AGV delivers assembly parts to each workstation of assembly lines from a miniload automated storage/retrieval system (AS/RS), and conveyor lines transport subassemblies between workstations. In this system, determination of the unit load sizes of parts carried by the AGV becomes an important decision factor due to its effects on the work-in-process inventory level and the operating cost of the system. Under a proposed AGV dispatching policy, a nonlinear mathematical model which allows unequal unit load sizes among assembly lines is formulated. Based on the characteristics of the objective function and feasible regions, a heuristic solution algorithm is developed. To illustrate the model, problems are chosen and solved.     

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.     

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.     

Travel time models for deep-lane unit-load autonomous vehicle storage and retrieval system (AVS/RS)

Autonomous vehicle storage and retrieval systems use vehicles that move horizontally along rails within the storage racks, while vertical movements are provided by lifts. The solution proposed in this paper addresses a particular system configuration that works with multiple deep storage lanes that are widely used in the food and beverage industry, characterised by large volumes of products of limited variety. The generic deep lane is single item, i.e. one stock keeping unit, and single batch, i.e. one production lot, thereby affecting the performance of the system in terms of storage capacity utilisation and throughput. Determining the number and depth of the lanes is crucial to aid the design and control of such a storage system. The aim of this paper was to support the design of AVS/RSs though a set of original analytic models for the determination of the travelled distance and time for single-command and dual-command cycles given alternative layout configurations. The models are validated by simulation and exemplified with a real-warehousing case study. The paper presents useful guidelines for the configuration of the system layout including the determination of the optimal shape ratio and the length of the lanes.     

Dynamic Operational Policies in an Automated Warehouse

In this paper we consider the optimal relocation of pallets with a high expectancy of retrieval within each storage rack of an automated warehouse to meet the fluctuating, short-term throughput requirements imposed on the automated storage-retrieval machines. The prepositioning of these pallets closer to the input/output point of each rack during off-peak periods will reduce the expected travel time for the storage/retrieval machines during future peak periods of the planning horizon.

As the model has been abstracted from an actual operating environment, we first describe the environment in which the problem has been posed. We then exploit the special structure of the problem to develop conditions that an optimal relocation policy should satisfy. Based on these optimality conditions, we develop a very efficient optimal relocation algorithm. Finally, we present the performance of several relocation policies in the warehouse studied.     

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.     

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.     

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.     

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.     

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.     

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.