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.     

Performance of carousel systems with ‘organ-pipe’ storage

It is well known that, for carousel systems, a dedicated storage, referred to as the ‘organ-pipe’ storage in the literature, is optimal with respect to the expected travel distance for processing successive requests. What remains unanswered is how to determine its performance, which is the motivation of this study. We consider bi-directional carousels under a ‘floating’ dwell point strategy. Two important performance measures considered are system capacity (maximum throughput) and job sojourn time. We also investigate the effect of activity skew on system performance.     

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.     

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.     

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.     

An optimal storage assignment for automated rotating carousels

Automated rotating carousels (ARCs) are increasingly used as building blocks for material storage and control systems in factories to provide easy and quick access to materials. This technical note introduces a simple and robust storage assignment policy that minimizes the expected turnaround time for accessing an item in an automated rotating carousel. The policy is shown to be optimal for a class of dwell point strategies.     

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.     

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.     

Optimising two dwell point policies for AS/RSs with input and output point at opposite ends of the aisle

Automated storage and retrieval systems (AS/RSs) are widely used for storing and retrieving products in all types of warehouses. Dwell point policy is a vital control policy that can greatly affect the performance of AS/RSs. In this paper, we study dwell point policies in AS/RSs with input and output stations at opposite ends of the aisle. We first propose two dwell point policies. We find that five existing dwell point policies in the literature are special cases of exactly one of our policies. We then develop expected travel time models for the proposed policies, solve these models with the objective of minimising expected travel time, and obtain closed-form solutions for the optimal dwell location(s). We prove that one proposed policy dominates the other in terms of expected travel time. Numerical experiments are performed to quantify the percentage gap of expected travel time between the proposed policies and policies in the literature. We find that, in some situations, the better proposed policy can achieve up to 8%–10% reduction in expected travel time in comparison with the best literature policy. A real-data case study validates that these situations arise with high probability in typical daily warehouse operations.     

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.     

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.     

A framework for the selection of idle vehicle home locations in an automated guided vehicle system

In the study of automated guided vehicles systems (AGVS), one assumption often made in the management of vehicles is the existence of either home locations or a circulatory loop to buffer or hold idle vehicles. A review of AGVS literature reveals that different researchers pursue one idle vehicle management policy or the other. In some studies, idle vehicles are assumed to circulate in some loops in the system while others assume they are routed to some dwell point locations where they are held until they are reassigned. When the dwell point option is implemented, different strategies for implementation are also available. However, what is generally lacking in references to dwell point strategies are the techniques for selecting the optimal or best dwell points for a given facility. In this study, the problem of dwell point or home location specification is addressed. The problem was modelled mathematically to determine the optimal home locations. The emphasis in the paper is on a unidirectional AGVS guide path. The criterion of optimization employed is the minimization of the system response time to vehicle demand points when dispatched from home locations. Solution methodologies are presented and example problems solved to illustrate the applications of the models presented.     

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.     

The impact of dwell point policy in an Automated Storage/Retrieval System

Automated storage and retrieval systems (AS/RS) are devices that allow intensive storage of materials. They can improve the supply chain performance, assuring more available volume for storage, lower labour costs and higher handling throughput of warehousing. Furthermore, the automated control allows the probability of errors in storage and retrieval to be minimised, along with the probability of product damage during movements. The purpose of the paper is to find the best solution in order to find the optimal dwell point policy, among different rules, able to minimise the travel time and distance travelled by stacker cranes, and consequently warehousing costs. An original and innovative model was developed in order to investigate the dwell point position for random allocation of unit loads. A software platform was developed to validate the proposed model by computer simulations. The performance of the system was analysed in a parametric/continuous way, varying at the same time the number of spans and levels, the height of the input/output point and the interval between requested missions. The results show that the developed model allowed convenience areas to be identified among the policies in which the travel time, distance travelled, and consequently warehousing costs are minimised, by varying different parameters.     

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.     

Analysis of storage assignment policies in less than unit load warehousing systems

Analytical models for the analysis of item location policies in unit load storage and retrieval systems are extended to less than unit load warehousing systems. The models are used to compare dedicated storage using cube per order index item dispatching and randomized storage using closest open location item dispatching with respect to total item space requirements, orderpicking cycle times and system responsiveness. Despite a number of computational limitations, it is argued that the models provide practical tools for analysis of less than unit load systems prior to development of simulation-based models or for validation of simulation-generated model results. The application of the models are demonstrated for a sample problem.     

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.     

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.     

Superconducting magnetic energy storage

After a brief review of the reasons for and forms of secondary energy storage and of the elements and history of inductive or magnetic storage, we discuss the four distinct areas in which superconducting magnetic energy storage can be applied. Differences in energy transfer times place different requirements on the storage coil, on the switch or transfer element, and on the energy losses in the superconductor. We report on designs and experiments in one of these areas with 2 to 300 kJ units, and on the analysis and plans for an installation that is to provide 250 MJ of plasma compression energy for the theta-pinch controlled thermonuclear fusion test reactor. We point out those elements of inductive storage that need further development before a theta-pinch fusion reactor can become economically competitive. Finally, we compare the size and costs of the energy storage components of these systems with similar and with larger inductive storage systems that are to interact reversibly with electric utility networks.