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.     

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.     

Throughput performance of automated storage/retrieval systems under stochastic demand

In this paper we are concerned with the throughput performance of an Automated Storage/Retrieval (AS/R) system under stochastic demand, i.e., the case where storage and retrieval requests arrive randomly. Although AS/R systems have been the subject of extensive research, their performance under stochastic demand remains relatively unexplored. In fact, with random storage and retrieval requests, the primary tool for AS/R system analysis has been simulation. Assuming a particular dwell point strategy for the storage/retrieval machine, in this paper we derive closed-form analytical results to evaluate the performance of an AS/R system under stochastic demand and determine whether or not it meets throughput. Although the results are derived for a given system, they can also be used in the design or evaluation of new/proposed systems.     

Closed form models for determining the optimal dwell point location in automated storage and retrieval systems

This paper examines the problem of where a storage/retrieval machine should reside, or dwell, when an automated storage and retrieval system (AS/RS) becomes idle to minimize the expected value of the next transaction time. After a review of the relevant literature on AS/RS dwell point strategies, this paper proposes several analytical models of these expected response times of the AS/RS based on the relative locations of the input and output ports of the AS/RS. It uses a continuous rack approximation to provide analytical models of the dwell point location problem. These models provide closed form solutions for the dwell point location in an AS/RS. Extensions are made to consider AS/RS with a variety of configurations including multiple input and output ports. These models not only provide solutions to the dwell point location problem, but they provide considerable insight into the nature of this problem, which is particularly valuable when the requirements facing the AS/RS are uncertain.     

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.     

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.     

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.     

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.     

A study on multi-aisle system served by a single storage/retrieval machine

Multi-aisle S/R machine system (MASS) can substantially reduce high initial investment cost which is a major reason for the low popularity of AS/RS in manufacturing companies. The objective of this study is mainly related to the design aspects of MASS. With a travel time model developed, average travel time of S/R machine is determined. We propose rack-class-based storage assignment procedure and class selection procedure to find the minimum number of S/R machines required and identify the number of aisles each S/R machine serves. Example problems are solved to illustrate the procedures. The results show that MASS is effective in reducing initial installation cost, provided that the pallet demands are relatively low.     

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.     

Travel-time models considering the operating characteristics of the storage and retrieval machine

Existing travel-time models of automated storage/retrieval systems (AS/RS) assume the average uniform velocity, ignoring the operating characteristics of storage/retrieval (S/R) machine such as the acceleration/deceleration rate and the maximum velocity. Consequently, the optimal design and schedule based on the existing models is far from optimal from the practical point of view. This paper presents continuous analytical models of travel time which integrate the operating characteristics of S/R machine. Using a randomized assignment policy, travel times are determined for both single and dual command cycles. The models developed are examined through discrete evaluation procedures.     

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.     

Travel-time model of dual-command cycles in a 3D compact AS/RS with lower mid-point I/O dwell point policy

Three-dimensional compact automated storage/retrieval systems (AS/RS) have been extensively applied in warehouses, with advantages of full automation, time efficiency and high space utilisation. While previous studies that use lower mid-point input/output (I/O) dwell point policy consider single-command cycles (SC), this paper builds travel-time models of dual-command cycles (DC). The S/R crane also dwells in the lower mid-point of the rack when it is idle. We validate analytical models using simulation and use analytical models to optimise system dimensions. Numerical experiments are used to compare DC with SC. The results show that DC outperform SC in terms of cycle time of one command.     

Performance analysis of automatic storage/retrieval systems by stochastic modelling

This study considers an automated storage/retrieval system that performs either single or dual commands and analyses it as a queuing system with two waiting spaces and one server. It is assumed that the storage and retrieval commands arrive at the system according to Poisson processes with different rates and that the service times of single and dual commands are distributed differently. The steady-state probability distribution of the number of commands in the system at the service completion epochs is derived; subsequently, the semi-Markov process is employed to obtain the distribution at an arbitrary time. Several performance measures are derived and include the expected number of commands in the system, the expected waiting time, the probability that an arbitrary command cannot enter the system (the ‘blocking probability’) and the utilization of the storage/retrieval machine.     

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.     

Closed form models for dwell point locations in automated storage carousel systems

This research focuses on determining the optimal dwell point location in an automated storage carousel system (ASCS) to minimise the expected response time for incoming service requests (storages and retrievals). This can be achieved by modelling the problem as a minisum location problem on a line segment with two-dimensional existing facilities (demands) using a continuous approximation of the individual storage locations of the ASCS. Closed form solutions of the associated dwell point location problem have been provided for the two different cases used to model this problem. These two cases arise from the two possible different configurations of the ASCS parameters; the travel times in circumference and height.     

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.     

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.     

Relative positioning of a load extractor for a storage carousel

The use of carousels in manufacturing for the storage of work-in-process items is very common. A major reason for the popular use of carousels is to store work-in-process items closer to the workstations and therefore minimize handling and the time taken to satisfy an item retrieval request from storage. Although carousel load retrieval times are considerably less than those of normal warehouses, the average response time can be further improved through proper prepositioning of the load extractor machine in anticipation of storage/retrieval requests. Two models are presented in this paper to strategically preposition the extractor machine when idle to minimize the system response time. In the first model the emphasis is on preposition of the extractor machine to minimize the maximum system response time when the extractor machine becomes idle. In contrast, the emphasis on the second model is to preposition the machine to minimize the expected system response time when the machine becomes idle. Two modes of carousel operation, (a) unidirectional rotation capability and (b) bidirectional rotation capability, are considered. Solution procedures based on mathematical models are developed to obtain optimal solutions. The developed procedures can be embedded in a carousel controller and used for on-line control and prepositioning of the extractor machine to improve the carousel system's operational efficiency. Computer simulation is performed under various traffic rates and storage methods to analyze the system performance under these two prepositioning strategies and one other traditional carousel prepositioning strategy commonly in use today. An on-line control architecture to implement the proposed prepositioning strategies is also presented.     

Optimal storage rack design for a multi-deep compact AS/RS considering the acceleration/deceleration of the storage and retrieval machine

This paper explores the optimal storage rack design for a multi-deep compact Automated Storage and Retrieval System (AS/RS) considering the acceleration and deceleration of storage and retrieval (S/R) machine. The expected travel time under the single-command cycle and dual-command cycle for a random storage strategy is derived. Based on the travel time, the general models we propose calculate the optimal ratio between three dimensions that minimises the travel time under different speed profile scenarios. From the result, it is proven that the optimal storage rack design model in the constant speed situation can be treated as a special case of the model considering the acceleration and deceleration of S/R machine. Finally, this study investigates the effect of speed profile of S/R machine and fixing dimensions by various numerical experiments.