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Shuttle-based compact systems are new automated multideep unit-load storage systems with lifts that can potentially achieve both low operational cost and large volume flexibility. In this paper, we develop novel queuing network models to estimate the performance of both single-tier and multitier shuttle-based compact systems. Each tier is modeled as a multiclass semi-open queuing network, whereas the vertical transfer is modeled using an open queue. For a multitier system, the models corresponding to tiers and vertical transfer are linked together using the first and second moment information of the queue departure processes. The models can handle both specialized and generic shuttles and both continuous and discrete lifts. The accuracy of the models is validated through both simulation and a real case. Errors are acceptable for conceptualizing initial designs. Numerical studies provide new design insights. Results show that the best way to minimize expected throughput time in single-tier systems is to have a depth/width ratio around 1.25. Moreover, specialized shuttles are recommended for multitier systems because the higher cost of generic shuttles is not balanced by savings in reduced throughput time and equipment needs.

Robotic compact storage and retrieval systems (RCSRS) have seen many implementations over the last few years. In such a system, the inventory items are stored in bins, organized in a grid. In each cell of the grid, a certain number of bins are stored on top of each other. Robots with transport and lifting capabilities move on the grid roof to transport bins between manual workstations and storage stacks. We estimate performance and evaluate storage policies of RCSRS, considering both dedicated and shared storage policies coupled with random and zoned storage stacks. Semi-open queuing networks (SOQNs) are built to estimate the system performance, which can handle both immediate and delayed reshuffling processes. We approximate the models by reduced SOQNs with two load-dependent service nodes and use the matrix-geometric method to solve them. Both simulations and a real case are used to validate the analytical models. Assuming a given number of stored products, our models can be used to optimize not only the length-to-width ratio of the system but also the stack height, depending on the storage strategy used. For a given inventory and optimal system configuration, we demonstrate that the dedicated storage policy outperforms the shared storage policy when the objective is to minimize dual command throughput time. However, from a cost perspective, with a maximum dual command throughput time as a constraint, we show that shared storage substantially outperforms dedicated storage. The annualized costs of dedicated storage are up to twice as large as those of shared storage, as a result of the larger number of storage positions required by dedicated storage and the relatively lower filling degree of storage stacks. The online appendix is available at https://doi.org/10.1287/trsc.2017.0786 .

The requirements for modern storage systems are steadily increasing due to limited space, cost, time, and personnel. Robotic compact storage and retrieval systems (RCS/RS), where containers are stacked and arranged in a block layout with robots operating from above, offer a promising solution. Some systems benefit from a self-sorting effect, where robots relocate previously moved containers after accessing non-directly accessible ones, resulting in demand-based sorted stacks. Despite various analytical models for automated storage systems, RCS/RS remain under-researched. Apart from two distinct papers on performance evaluation, there are no general, fast, and easy-to-use tools to assess system throughput under demand-based access patterns. Additionally, the performance benefits of self-sorting have not yet been studied. This paper presents an analytical approach to predict RCS/RS performance using a class-based access structure. A discrete event simulation validates the model, and an optimization example demonstrates the model's broad applicability and ease of use.

Warehouses occupy much space and land, which has become increasingly scarce in many parts of Europe, Asia, and the United States, particularly close to areas where demand is generated, such as large cities. This paper studies live-cube compact storage systems that may solve this space shortage problem as they do not require travel aisles. Each stored unit load is accessible individually and can be moved in x and y directions by a shuttle as long as an empty location is available, comparable to the well-known 15-puzzle in which 15 numbered tiles slide within a 4 × 4 grid. When multiple empty locations are available on a level, the shuttles can cooperate to create a virtual aisle for fast retrieval of a desired unit load. A lift moves the unit loads across different levels in z direction. Such storage systems are increasingly used in different service sectors like car parking, warehousing, and container handling, but so far they have hardly been studied. For live-cube systems, many research questions still have to be answered, including cycle time calculations, cost comparisons, and energy requirements. In this paper, we first derive simple to use closed-form formulas for expected retrieval time of an arbitrary unit load and validate the quality of these formulas by comparing them with a real application. Second, we propose and solve a mixed-integer nonlinear model to optimize system dimensions by minimizing the retrieval time. We obtain closed-form expressions for minimum retrieval time that are simple to apply in practice. Third, we compare the investment, operational costs, and energy consumption of live-cube systems with traditional systems based on a real application.

Given the low space usage rate of the traditional automated storage/retrieval system and the long aisle, it is easy for a stacker to take a long time to enter/leave the warehouse. Thus, a new type of double-ended compact storage system is proposed. This paper addresses the scheduling problem for the stacker to execute the single and dual commands mixed tasks in the system where the I/O ports are located at both ends of the aisle, and the power conveyor devices on the rack can meet the requirement of multi-depth storage and generate displacement. An improved shuffled frog leaping algorithm (ISFLA) is developed for the scheduling problem. In order to eliminate the disadvantages of local optimum and slow convergence in the standard shuffled frog leaping algorithm, a set of hybrid perturbation update methods are designed based on a role model learning strategy, and the feasibility of the improved algorithm is verified by a numerical simulation. The experimental results show that the solution quality and the convergence ability of the ISFLA are significantly improved, and it can effectively solve the stacker-scheduling problem in the double-ended compact storage system.

This study performs a Life Cycle Assessment on the production of a commercial PCM building application developed by RUBITHERM to quantify its environmental impacts and identify environmental hotspots across manufacturing, unlocking climate change mitigation potential. This research adds to the consideration of embodied energy demands and emissions when developing building efficiency solutions, especially for innovative material applications where knowledge is limited. The building application under examination is a compact storage module, consisting of an aluminium case filled with salt hydrate PCM, with a targeted performance of 94 Wh heat storage capacity. The LCA of the manufacturing stage resulted in a climate change impact of 5.81 kg CO2 eq. The research showed that the aluminium of the case to be filled in with PCM is the main contributor to almost all impact categories addressed, including climate change, while the sensitivity analysis revealed that the total climate change of the final product is highly dependent on the recycled aluminium content, which could be decreased by 46% by increasing the new scrap and post-consumer scrap aluminium streams. Finally, the study provides detailed Life Cycle Inventory data, based on real data shared by RUBITHERM, and methodology transparency to facilitate built-up research in the field.

Reduction in storage and number of operations are considered through avoiding the representation of zeros in storage as well as in the calculations. The importance of this approach has its effect in large problems that appear in numerical treatments of boundary value problems in general and becomes more effective when fuzzy concepts are considered. We introduce an extended embedding solution model named fuzzy compact storage Gauss–Seidel (FCGS) for solving linear systems of equations with a fuzzy-based right-hand side. The model starts by applying the embedding approach to the n × n fuzzy linear system, a compact storage technique is then applied to the resultant 2 n × 2 n de-fuzzification matrix, and finally, a Gauss–Seidel method is applied to the system. The FCGS experimental results and algorithm are clarified on some numerical examples including a fuzzy boundary value problem (FBVP). The error improvements through Gauss–Seidel iterations of fuzzy solution computations are reported. The fuzzy solutions at α -cuts are shown and compared to the exact solutions. FCGS achieved a reduction of at least 50% of storage by using the compact storage concepts and consequently obtain a reduction in the mathematical operations and accordingly the running time especially in FBVP applications.

The autonomous shuttle and stacker crane (AC/SC) warehousing system, as a new automated deep-lane unit load storage/retrieval system, has been becoming more popular, especially for batch order fulfilment because of its high flexibility, low operational cost and improved storage capacity. This system consists of a shuttle sub-system that controls motion along the x-axis and a stacker crane sub-system that controls motion along the y-axis and z-axis. The combination of shuttles and a stacker crane performs storage and retrieval tasks. Modelling the parallel motion is an important design tool that can be used to calculate the optimal number of shuttles for a given configuration of the warehousing system. In this study, shuttle movements from one lane to another are inserted into the stock-keeping unit (SKU) task queue, and convert such that they are consistent with the retrieval tasks. The tasks are then grouped according to their starting lane, and converted to an assembly-line parallel job problem by analysing the operating mode with the objectives of minimising the total working time of the stacker crane and the wasted shuttle time. A time sequence mathematical model based on the motion of the shuttles and stacker crane is proposed, and an improved Pareto-optimal elitist non-dominated sorting genetic algorithm is used to solve this multi-objective optimization problem. The model is validated via a simulation study, and via a real-world warehousing case study. We go on to describe guidelines for the layout and configuration of AS/SC warehousing systems, including the optimal number of shuttles and number of x-axis storage cells of lanes, which can improve efficiency and minimise both capital investment and operating costs.

In this paper we discuss a memory allocation problem first introduced by Wolman in [1] (see also [2]). A general solution formula is presented, from which closed form expressions for a few special cases may be easily derived.