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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Allocating Items to an Automated Storage and Retrieval System

To reduce material handling costs, distribution centers purchase automated storage and retrieval systems (AS/RS). It is often the case that the capacity of the AS/RS is insufficient to store all items. The distribution center must then decide which items to assign to the AS/RS and in what quantities they will be stored. In this paper, we develop a heuristic procedure to solve this problem. A priori and a posteriori tests of the data for the optimality of this heuristic procedure are provided. The proposed procedure is testedwith data gathered fr oma naval supply center.     

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.     

Optimising space utilisation in block stacking warehouses

Block stacking storage is an inexpensive storage system widely used in manufacturing systems where pallets of stock keeping units (SKUs) are stored in a warehouse at the finite production rates. However, determining the optimal lane depth that maximises space utilisation under a finite production rate constraint has not been adequately addressed in the literature and is an open problem. In this research, we propose mathematical models to obtain the optimal lane depth for single and multiple SKUs where the pallet production rates are finite. A simulation model is used to evaluate performance of the proposed models under stochastic uncertainty in the major production parameters and the demand.     

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.     

Applying the corridor method to a blocks relocation problem

In this paper, we present a corridor method inspired algorithm for a blocks relocation problem in block stacking systems. Typical applications of such problem are found in the stacking of container terminals in a yard, of pallets and boxes in a warehouse, etc. The proposed algorithm applies a recently proposed metaheuristic. In a method-based neighborhood we define a two-dimensional “corridor” around the incumbent blocks configuration by imposing exogenous constraints on the solution space of the problem and apply a dynamic programming algorithm capturing the state of the system after each block movement for exploring the neighborhoods. Computational results on medium- and large-size problem instances allow to draw conclusions about the effectiveness of the proposed scheme.     

An integrated storage assignment method for manual order picking warehouses considering cost,workload and posture

This paper presents an integrated storage assignment method for low-level picker-to-parts order picking warehouses taking into account economic and ergonomic objectives. Three different pallet rack layouts are studied in this paper, namely (a) picking from full pallets on the floor, (b) picking from half-pallets on the floor, and (c) picking from half-pallets on the upper rank of the shelf. First, cost functions are developed to assess the total order picking performance impact of these different pallet rack layouts. Second, with regard to workload, the metabolic cost and energy expenditure rates for picking from the different rack layouts under study are derived. Third, for assessing the working posture during order picking, the Ovako Working Posture Analysing System index is used where the required data is collected using a motion capturing system. The developed models are combined to propose a heuristic storage assignment procedure that supports the decision of which item to store on which pallet. The developed storage assignment method is then applied to an industrial case study. The results of the paper support warehouse managers in assessing the order picking storage assignment from an ergonomics viewpoint and in estimating its impact on financial order picking performance.     

The impact of acceleration/deceleration on travel-time models for automated storage/retrieval systems

In this note we propose a travel-time model of automated storage/retrieval (S/R) machines by considering the speed profiles that exist in real-world applications. Compact forms of expected travel-times under randomized storage conditions have been determined for both single and dual command cycles.     

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.