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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Dynamic relative positioning of AGVs in a loop layout to minimize mean system response time

One of the control decisions in the operation of an automated guided vehicle (AGV) system is to determine the home locations of idle vehicles. In this paper, the problems of selecting home location of a vehicle when idle in a single loop AGV network is presented. As the number of unit loads to be picked up at each workstation dynamically changes over time, the optimum home location of vehicles may also change. Based on the objective of minimizing the expected response time of a vehicle, models are constructed. Example problems are given to illustrate the use of the solution algorithms. The results of the system response times obtained using the dynamic dwell point models are compared with those of other dwell point rules.     

EMS频率对应电能表计量误差值精确测量的方法

针对目前电能表EMS试验中人工干预过多、驻留时间无法确定等问题，提出一种与EMS频率相对应的电能表计量误差值精确测量的方法。利用该方法可使EMS频率点与电能表计量误差值——匹配，同时可动态设置驻留时间，提高测量数据的精确性和测量速度，并以实例说明该方法的有效性。     

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.     

Integrated optimization of location assignment and sequencing in multi-shuttle automated storage and retrieval systems under modified 2n-command cycle pattern

This article explores the integrated optimization problem of location assignment and sequencing in multi-shuttle automated storage/retrieval systems under the modified 2n-command cycle pattern. The decision of storage and retrieval (S/R) location assignment and S/R request sequencing are jointly considered. An integer quadratic programming model is formulated to describe this integrated optimization problem. The optimal travel cycles for multi-shuttle S/R machines can be obtained to process S/R requests in the storage and retrieval request order lists by solving the model. The small-sized instances are optimally solved using CPLEX. For large-sized problems, two tabu search algorithms are proposed, in which the first come, first served and nearest neighbour are used to generate initial solutions. Various numerical experiments are conducted to examine the heuristics’ performance and the sensitivity of algorithm parameters. Furthermore, the experimental results are analysed from the viewpoint of practical application, and a parameter list for applying the proposed heuristics is recommended under different real-life scenarios.     

Response to Al-Hakim's note

Storage location assignment and interleaving policy are two closely related problems in warehousing management. This paper addresses the location assignment and interleaving problem at the same time in an automated storage/retrieval system with duration-of-stay based shared storage policy. Based on the heuristics for single command operation, a two-step procedure is developed to solve the problem. A tabu search algorithm is proposed to improve the solution for medium and large sized problems. The computational results indicate that the tabu search algorithm is effective in finding high quality solutions, and efficient in solving large sized problems.     

离子束加工中驻留时间的求解模型及方法

驻留时间求解问题是离子束加工中的关键问题．通常,离子束加工过程可以描述为一个包含驻留时间的二维卷积方程,理论上通过反卷积即可以求解出驻留时间．然而,反卷积问题是一个病态问题,所以驻留时间一般较难很好地求解出．为了解决这个问题,介绍了一个离散的线性模型——CEH模型,分析了该模型的优点．提出应用截断奇异值分解法（TSVD）来求解CEH模型;深入分析了该方法的优点,并利用“L-曲线”分析了驻留误差和加工量之间的关系以及用“L-曲线”对CEH模型中去除点和驻留点的不同取法进行了评价．仿真结果表明,CEH模型和TSVD方法对于求解光学镜面离子束加工中的驻留时间很有效．     

Optimally Locating Multiple Dwell Points in a Single Loop Guide Path System

Dwell points for idle vehicles affect the performance of automated guided vehicle systems. An exact polynomial-time algorithm to solve idle vehicle positioning problems in both unidirectional and bidirectional single loop systems is developed to minimize the maximum response time. The proposed algorithm considers several potential locations for the first dwell point and applies a dynamic programming procedure to obtain the remaining dwell points for each initial location. The algorithm is streamlined by applying certain optimality properties. Computational results show that the algorithm can solve large-scale problems in reasonable time.     

Flexible space-sharing strategy for storage yard management in a transshipment hub port

In this paper, a storage yard planning problem is studied for a transshipment port with limited space and high-throughput level. Generally, the consignment strategy is used in the yard for a transshipment port, where containers to the same destination vessel are stored together. This is to facilitate faster loading process as it reduces reshuffles as well as long distance movements of yard cranes. However, the consignment strategy is known to be inefficient in space utilization since each storage location must be dedicated to a particular vessel. To improve the space utilization while retaining the advantage of consignment, a new approach named the “flexible space-sharing strategy” is proposed. The idea is that the container space can be shared by two different vessels as long as their containers do not occupy the space at the same time. This strategy allows the same storage location to be reserved for two vessels. The amount of space will only be allocated to a specific vessel on the arrival of corresponding containers. By controlling where to stack the containers in the storage locations, the containers to each vessel are not mixed and the consignment feature can be preserved. This strategy is first formulated as a mixed integer program (MIP). As the MIP model has a block diagonal structure, we develop a search algorithm which combines MIP and heuristics to find the solution. The numerical experiments show that the “flexible space-sharing strategy” can handle much more containers within the same storage space compared with the “non-sharing strategy”.     

A mixed integer programming model for optimal ATC tower height and location: a case study for Singapore Changi Airport's third runway extension

ABSTRACT

With continued growth in air traffic, airports worldwide are expanding their runway infrastructure. This leads to the problem of determining an appropriate location and height for an Air Traffic Control (ATC) tower that can provide the right vantage point for coordinating runway and taxiway movements. The challenge involves finding the right location and optimal height that can satisfy the visibility and obstruction constraints for a complex airport-airside environment with multiple runways and civil infrastructure under different weather conditions. This article formulates the ATC tower location and height problem as a Mixed-Integer-Programming (MIP) model while considering the visibility and obstruction constraints. Singapore Changi Airport's proposed third runway extension is used as a case study to determine the set of location and height of ATC Tower using the proposed approach. A visual analytic test is conducted in an ATC tower simulator for different tower locations and heights under varying visibility conditions.     

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.