Stacker Crane Research Articles

A heuristic algorithm based on an improvement strategy to exploit idle time periods for the Stacking Problem

In this paper, we address the Stacking Problem. Its objective is to determine the sequence of movements carried out by a stacking crane to store and retrieve a set of homogeneous blocks in a two-dimensional storage during a well-defined planning horizon in such a way that the number of relocation movements is minimized. We propose a heuristic algorithm that determines the target stack of each incoming block and those placed above the next to retrieve. Our heuristic algorithm also exploits the time periods in which the stacking crane is idle with the goal of improving its performance. The computational experiments reveal that our heuristic algorithm overcomes those approaches found in the related literature in terms of number of crane relocation movements. Its high performance and short computational times encourage its application in real-world environments.

A Double-Population Genetic Algorithm for ASC Loading Sequence Optimization in Automated Container Terminals

Shu, F.; Mi, W.; Li, X.; Zhao, N.; Mi, C., and Yang, X., 2015. A double-population genetic algorithm for ASC loading sequence optimization in automated container terminals.An automated container terminal (ACT) emphasizes the autonomy of equipment scheduling. The scheduling of the automated stacking crane (ASC) as major equipment has an important impact on the yard operating efficiency. In the export process, ASC cooperated with the quay crane in loading operations. Although traditionally the loading sequence of ASC is generated directly in terms of the stowage plan, with the trend towards automated intelligent terminals, the ASC is becoming increasingly the content of dynamic decision. This paper presents a method of dynamic planning ASC loading sequence after the stowage plan. The method took reshuffling number and ASC movement frequency into account, considered the target vessel slots defined by the stowage plan as constraints, and established a multi-objective mathematical model. Taking into account the problem with NP-hard characteristics, this paper proposed a double-population genetic algorithm based on a general genetic algorithm, establishing a solution mechanism by leveraging genetic exchanges between populations to change the convergence speed. With the completion of a certain bay in the block, it online adjusted the next block collection, and eventually formed a solution of real-time loading sequence. Experiments demonstrated that the algorithm could dynamically obtain the near optimal solution of the problem, adapt the timeliness demand of ASC dynamic decision, and improve the intelligence of the equipment control system (ECS).

Task scheduling for multi-tier shuttle warehousing systems

Multi-tier shuttle warehousing systems are increasingly popular because of their high flexibility and robustness. These systems consist of a multi-tier shuttle sub-system that controls horizontal movement and a lift sub-system that manages vertical movement. The combination of shuttles and lifts undertakes inbound/outbound tasks instead of the stacker crane in conventional automated storage and retrieval systems. Scheduling different devices to reduce expected cycle time is an important concern. Thus, we propose a time sequence mathematical model of task operation on the basis of the movement characteristics of shuttles and lifts. The task scheduling problem between shuttles and lifts is converted into an assembly line parallel job problem by analysing the mathematical model, which generates the scheduling task queue model in the specified time window. In addition, a Pareto optimal based on an elitist non-dominated sorting genetic algorithm is adopted to solve the multi-objective optimisation function in the task scheduling problem. Finally, we illustrate the findings of the study through a practical example. Results show that the optimisation scheduling solution can reduce the total lift idle time and the total shuttle waiting time. Furthermore, it can improve warehousing efficiency and lower operation costs.

Multi-objective Iterated Greedy Variable Neighborhood Search Algorithm For Solving a full-load automated guided vehicle routing problem with battery constraints

The Stacker Crane Problem consists in finding a set of minimum-cost roads starts and stops at the same location to satisfy a set of predefined transportation request assuming to have a server with a capacity one. This work deals with an extension of the stacker crane problem that impose distance and time constraints for the roads. We propose specifically an application to this extension on specific set of on-demand transportation system. We propose also an approach based on Variable Neighborhood Search and iterated greedy metaheuristics to deal with the multi-objective version of this problem. One important feature of our specific algorithm is the use of the distruction/contruction method as a shake function for the Variable Neighborhood Search algorithm. This feature combined with the multi-neighborhood Search led us to a preliminary promising results.

The stacker crane problem and the directed general routing problem

In this article, we deal with the polyhedral description and the resolution of the directed general routing problem (DGRP) and the stacker crane problem (SCP). The DGRP, in which the service activity occurs both at some of the nodes and at some of the arcs of a directed graph, contains a large number of important arc and node routing problems as special cases, including the SCP. We describe large families of facet‐defining inequalities for the DGRP. Furthermore, a branch‐and‐cut algorithm for these problems is presented. Extensive computational experiments over different sets of DGRP and SCP instances are included. These results show that our algorithm is among the best solution procedures proposed for both problems. © 2015 Wiley Periodicals, Inc. NETWORKS, Vol. 65(1), 43–55. 2015

자동창고 시스템의 최적안 도출을 위한 모의실험적 연구

The functional role of warehouses in modern industry is changing from an established concept of storage to a concept of circulation. The target of this study is to improve the stacker crane's efficiency for the internal operations of the Automated Storage and Retrieval System (AS/RS). Eight operating schemes are proposed under the combination of three conditions, namely, the storing method, the layout type, and the sequence of command execution. The moving distance of the stacker crane is calculated using the same gateway data through a simulation based on a C# program. The optimal operating scheme is proposed based on the analyzed simulation results. In conclusion, the combination of conditions of random storage, two-way type warehouse, and dual command execution elicits optimum results in travel efficiency for the stacker crane.Received 6 April 2014Revised 18 July 2014Accepted 6 September 2014

Aviator System as an Alternative to Warehouse Handling Devices

The Aviator is a floor-free working warehouse vehicle, which gives a third alternative to the market of stacker cranes that consist also of the narrow aisle stacker and the rack feeder. Officially introduced as Transfaster in 2002, this full-automatic working system has been realized several times. This article will give an overview concerning the structure of the system and its functionality, and will compare it to conventional systems regarding advantages, disadvantages and performance. Therefore ways of calculating cycle times are introduced.

Approaches for solving the container stacking problem with route distance minimization and stack rearrangement considerations

We consider an optimization problem of sequencing the operations of cranes that are used for internal movement of containers in maritime ports. Some features of this problem have been studied in the literature as the stacker crane problem (SCP). However, the scope of most literature (including SCP) is restricted to minimizing the route or distance traveled by cranes and the resulting movement-related costs. In practice, cargo containers are generally stacked or piled up in multiple separate columns, heaps or stacks at ports. So, the cranes need to often rearrange or shuffle such container stacks, in order to pick up any required container. If substantial re-stacking is involved, cranes expend considerable effort in container stack rearrangement operations. The problem of minimizing the total efforts/time of the crane must therefore account for both – the stack rearrangement costs and also the movement-related (route distance) costs. The consolidated problem differs from standard route distance minimization situations if stack rearrangement activities are considered. We formally define the consolidated problem, identify its characteristic features and hence devise suitable models for it. We formulate several alternative MIP approaches to solve the problem. We compare the performance of our MIP formulations and analyze their suitability for various possible situations.

Distributed parameter modeling of single-mast stacker crane structures

This paper presents distributed parameter dynamical modeling capabilities of single-mast stacker crane structures. In the frame structure of stacker cranes due to external excitation or inertial forces undesirable structural vibrations may arise. These vibrations reduce the stability and positioning accuracy of stacker crane and causes increasing cycle time of storage/ retrieval operation. Thus it is necessary to investigate of these vibrations. In this paper the dynamical behavior of single-mast stacker cranes is approximated by means of distributed parameter models. The first model is a cantilever beam model with uniform material and cross-sectional properties. This model is used to demonstrate fundamental properties of Euler-Bernoulli beam models. The second model is cantilever beam model with variable cross-sectional properties and lumped masses. The eigenfrequencies and mode shapes of this mast-model are determined by means transfer matrix method. In the third model the whole structure of single-mast stacker crane is modeled. Beside the eigenfrequencies and mode shapes of this model the Bodediagrams of frequency response function is also calculated.

From Modeling to Robust Control Design of Single-Mast Stacker Cranes

The paper presents the reduction of mast-vibration of single-mast stacker cranes by using a robust controller. During non-stationary movement undesirable mast vibrations may occur. These vibrations can reduce the positioning accuracy of the machine. The aim of this paper is to present the design procedure from the dynamic modeling to robust control design, in which accurate signal tracking and mast-vibration attenuation are guaranteed. The dynamic modeling of single-mast stacker cranes by means of multi-body modeling approach is summarized. The handling of varying dynamic behavior due to varying lifted load position is presented. For control design purposes the order of the model is reduced. Based on the modeling technique an appropriate robust H∞ controller design method is applied. The trade-off between accurate reference signal tracking and mast-vibration attenuation is presented through demonstration example.

Order scheduling of multiple stacker cranes on common rails in an automated storage/retrieval system

An order scheduling method for improving the work efficiency of multiple cranes on a common rail in an automated storage/retrieval system (AS/RS) is proposed in this paper. Most AS/RSs are equipped with one stacker crane. However, this is logistically challenging, and higher work efficiency in warehouses, such as those using more than one stacker crane, is required. In this paper, a warehouse with multiple stacker cranes working simultaneously is proposed. Unlike warehouses with only one crane, order scheduling is very difficult because there are multiple cranes working simultaneously and collisions are possible. Warehouse order must be maintained while avoiding collisions. Sometimes, detours are necessary to avoid collisions. As a result, work efficiency will decrease if a sequence of orders is not properly planned. Nevertheless, as transport works in AS/RSs are occurring randomly, scheduling cannot be conducted in advance, which makes the order scheduling of multiple cranes difficult. A fast order scheduling method is proposed here. Several orders are combined into an order cluster, and dynamic programming is used to obtain the best combination of order clustering. By utilising this method, cranes can work cooperatively, improving work efficiency to 0.95 with a two-crane AS/RS and to 0.78 with a three-crane AS/RS.

Design Methodology for Human Symbiotic Machines Based on the Description of User’s Mental Model

This research establishes a methodology for designing human symbiotic machines. In our proposal, the mental model of a user is described by a user model diagram as an extended version of the well-known System Modeling Language (SysML). The user model diagram originated in the state machine diagram and the activity diagram of SysML. Concretely, the behavior of a machine observed by a user (user model), is drawn as a parallel to the actual behavior of a machine (system model). The user model diagram can visualize the physical processes required to use the machine and can reveal any inconsistencies between user and system models. We have selected a non-industrial stacker crane, which stores and retrieves containers through human manual operation, as an application target of the proposed design methodology. To make the stacker crane interface more user-friendly, several design plans are proposed and discussed together with descriptions of user model diagrams. To evaluate the relationship between diagrams and actual performance, prototypes of interfaces are developed, and usability tests are conducted. Results of usability tests indicate that the user model diagram is a good design tool for estimating the basic usability of a human symbiotic machine.

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.

Comparison of the operating performance of automated and traditional container terminals

This paper explores key factors affecting the operating performance of container terminals, and compares the performance of various container yard (CY) facilities at the port of Kaohsiung using grey relational analysis (GRA) and the concept of entropy. The paper's findings can be summarised as follows: (1) The most important attributes affecting the operating performance of CY equipment include number of CY facilities, transport distance of CY tractors, speed of movement of CY facilities, handling efficiency of CY facilities, and number of working tractors. (2) Based on entropy weighting value and GRA, CY handling facilities can be ranked in terms of operating performance in the order of automatic rail transtainer, automatic stacking crane, rail transtainer, straddle carrier, and rubber tyred transtainer. (3) From both operating performance and green terminal perspectives, automatic rail transtainers represent the optimal CY model compared with other container handling facilities.

Motion Planning Method for Two Stacker Cranes in an Automated Storage and Retrieval System

In this paper, a motion planning method for two stacker cranes in an Automated Storage and Retrieval System (AS/RS) is proposed. For the cranes to operate cooperatively, they must perform tasks while avoiding collisions. In addition, the requirements, which include fast operation and short calculation time, must be satisfied, along with a specific mechanical constraint on the motion of the stacker cranes. For these problems, an approach is proposed in which a motion is generated on two levels. On the first, collision is avoided by using constraint on trajectories. A trajectory generated on this level ensures the shortest travel time. If a collision cannot be avoided on the first level, the system shifts to the second, in which heuristics are used for collision avoidance. The proposal is for highspeed heuristics based on a binary search. The effectiveness of the proposed algorithm is shown through simulations. The simulation results indicate that, in a layout of 60 racks in the horizontal direction and 10 in the vertical direction under standard task conditions, the method has an efficiency of 1.91 with respect to a single crane system and 1.66 seconds for the motion planning of one task when a computer with a 3.0 GHz CPU is used.

The machine layout within a TFT-LCD bay with a multiple-stacker crane in-line stocker

In this paper, we study the machine layout problem in a TFT-LCD (thin-film transistor liquid-crystal display) bay with a multiple-stacker crane in-line stocker. Unlike other material-handling systems, such as automated guided vehicles and conveyors that only have a transportation function, in-line stockers have both transportation and storage functions. They rely on stacker cranes to perform their transportation function. The in-line stocker in a TFT-LCD bay is often divided into zones. Each zone is served by a stacker crane. Due to its multiple-zone in-line stocker, solving a TFT-LCD bay's machine layout requires us to determine not only the positions of the machines, but also the zone division design. The objectives include the minimisation of total flow distance and the workload balance between stacker cranes. We propose a layout procedure that adopts heuristic and mathematical approaches to assist us in accomplishing the aforementioned tasks. An example problem mimicking a real-case problem was solved to illustrate the proposed layout procedure. The layout design found by the proposed layout procedure was validated with computer simulations. It was also compared with layouts obtained by approaches proposed by other researchers. The simulation and comparison results demonstrate the capability of the proposed layout method in producing a feasible and good machine layout in a TFT-LCD bay with a multiple-stacker crane in-line stocker.

자동차 생산을 위한 통합창고 연구

자동차 생산라인은 차체라인, 도장라인, 의장라인으로 구성된다. 이러한 생산라인들은 직렬로 배치되어 흐름생산을 거치기 때문에 전후 공정의 상태에 따라 라인에서는 starvation(물량 부족으로 인한 생산 불가능) 또는 blocking(용량 초과로 인한 생산 불가능)으로 인한 정지가 발생한다. 이에 starvation이나 blocking으로 오는 생산 손실을 막기 위해 WBS, PBS와 같은 창고를 개별적으로 보유하여 운영된다. 본 논문은 라인의 버퍼역할을 하는 각 창고들을 통합하여 운영할 수 있는 통합창고 시뮬레이션 모형을 제안한다. 적정 Stacker Crane 대수와 AGV 대수를 구하고, 이를 운영할 수 있는 운영방법론을 제안한다. 또한 개별창고와 통합창고 모형을 시뮬레이션을 이용하여 효율성 비교를 한다. Automobile manufacturing consists of body-line, painting-line, and assembly-line. These production lines are disposed in series and go through a flow process, so according to the status of pre & post processing, a suspension happens in a line by a starvation(impossibility of production by insufficient supply) or blocking(impossibility of production by exceed capacity). Therefore, to prevent a loss of production coming from a starvation or blocking, a storage such as WBS or PBS is independently owned and operated. The paper suggests the simulation model of integrated storage which can operate it by integrating each storage performing a role as a buffer of line. Specifically, the paper found the answers about reasonable number of Stacker Crane and AGV(Automatic Guided Vehicle) and suggested a methodology of operation which is available to operate them. Also, it compared an efficiency between a model of current storage and integrated storage through simulation. As a result, it turned out that the model suggested in the paper was more efficient on suspension of painting-line stop than a current storage.

Asymptotically Optimal Algorithms for One-to-One Pickup and Delivery Problems With Applications to Transportation Systems

The Stacker Crane Problem is NP-Hard and the best known approximation algorithm only provides a 9/5 approximation ratio. The objective of this paper is threefold. First, by embedding the problem within a stochastic framework, we present a novel algorithm for the SCP that: (i) is asymptotically optimal, i.e., it produces, almost surely, a solution approaching the optimal one as the number of pickups/deliveries goes to infinity; and (ii) has computational complexity $O(n^{2+\eps})$, where $n$ is the number of pickup/delivery pairs and $\eps$ is an arbitrarily small positive constant. Second, we asymptotically characterize the length of the optimal SCP tour. Finally, we study a dynamic version of the SCP, whereby pickup and delivery requests arrive according to a Poisson process, and which serves as a model for large-scale demand-responsive transport (DRT) systems. For such a dynamic counterpart of the SCP, we derive a necessary and sufficient condition for the existence of stable vehicle routing policies, which depends only on the workspace geometry, the stochastic distributions of pickup and delivery points, the arrival rate of requests, and the number of vehicles. Our results leverage a novel connection between the Euclidean Bipartite Matching Problem and the theory of random permutations, and, for the dynamic setting, exhibit novel features that are absent in traditional spatially-distributed queueing systems.

Motion Planning of Two Stacker Cranes in a Large-Scale Automated Storage/Retrieval System

The authors propose a method for reducing the computational time of motion planning for stacker cranes. Most automated storage/retrieval systems (AS/RSs) are only equipped with one stacker crane. However, this is logistically challenging, and greater work efficiency in warehouses, such as those using two stacker cranes, is required. In this paper, a warehouse with two stacker cranes working simultaneously is proposed. Unlike warehouses with only one crane, trajectory planning in those with two cranes is very difficult. Since there are two cranes working together, a proper trajectory must be considered to avoid collision. However, verifying collisions is complicated and requires a considerable amount of computational time. As transport work in AS/RSs occurs randomly, motion planning cannot be conducted in advance. Planning an appropriate trajectory within a restricted duration would be a difficult task. The authors thereby address the current problem of motion planning requiring extensive calculation time. As a solution, they propose a “free-step” to simplify the procedure of collision verification and reduce the computational time. On the other hand, the authors proposed a method to reschedule the order of collision verification in order to find an appropriate trajectory in less time. By the proposed method, they reduce the calculation time to less than 1/300 of that achieved in former research.

Are Stacker Crane Problems easy? A statistical study

Many full truckload pick-up and delivery problems in the intermodal freight container transport industry can be modeled as Asymmetric Traveling Salesman Problems (ATSPs). Several authors have noted that while ATSPs are NP-hard, some instances are readily solved to optimality in only a short amount of time. Furthermore, the literature contains several references to the Stacker Crane Problem (SCP) as an “easy” problem amidst the ATSPs. We put this hypothesis to test by using statistical methods to build a model relating measurable distance matrix structures to the amount of time required by two existing exact solvers in finding solutions to over 500 ATSP instances. From this analysis we conclude that SCPs are not necessarily easier than other ATSPs, but a special subset of SCPs, termed drayage problems, are more readily solved. We speculate that drayage problems are “easy” because of a comparatively high number of zeros in symmetric locations within the distance matrix. In real-world drayage problems (i.e. the movement of containers a short distance to/from a port or rail terminal), these zeros correspond to the prevalence of jobs originating at or destined to a fixed number of freight terminals.