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- Creator:
- Zaerpour, Nima, Yu, Yugang, and de Koster, René B. M.
- Description:
- We study a next generation of storage systems: live-cube compact storage systems. These systems are becoming increasingly popular, due to their small physical and environmental footprint paired with a large storage space. At each level of a live-cube system, multiple shuttles take care of the movement of unit loads in the x and y directions. When multiple empty locations are available, the shuttles can cooperate to create a virtual aisle for the retrieval of a desired unit load. A lift takes care of the movement across different levels in the z-direction. Two-class-based storage, in which high turnover unit loads are stored at storage locations closer to the Input/Output point, can result in a short response time. We study two-class-based storage for a live-cube system and derive closed-form formulas for the expected retrieval time. Although the system needs to be decomposed into several cases and sub-cases, we eventually obtain simple-to-use closed-form formulas to evaluate the performance of systems with any configuration and first zone boundary. Continuous-space closed-form formulas are shown to be very close to the results obtained for discrete-space live-cube systems. The numerical results show that two-class-based storage can reduce the average response time of a live-cube system by up to 55% compared with random storage for the instances tested. This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives. Copyright © 2017 Nima Zaerpour, Yugang Yu, and René B. M. de Koster. Published with license by Taylor & Francis.
- Resource Type:
- Article
- Identifier:
- 2472-5579
- Campus Tesim:
- San Marcos
- Department:
- Operations and Supply Chain Management
- Creator:
- de Koster, René, Yu, Yugang, and Zaerpour, Nima
- Description:
- Live-cube compact storage systems realize high storage space utilization and high throughput, due to full automation and independent movements of unit loads in three-dimensional space. Applying an optimal two-class-based storage policy where high-turnover products are stored at locations closer to the Input/Output point significantly reduces the response time. Live-cube systems are used in various sectors, such as warehouses and distribution centers, parking systems, and container yards. The system stores unit loads, such as pallets, cars, or containers, multi-deep at multiple levels of storage grids. Each unit load is located on its own shuttle. Shuttles move unit loads at each level in the x and y directions, with a lift taking care of the movement in the z-direction. Movement of a requested unit load to the lift location is comparable to solving a Sam Loyd's puzzle game where 15 numbered tiles move in a 4 × 4 grid. However, with multiple empty locations, a virtual aisle can be created to shorten the retrieval time for a requested unit load. In this article, we optimize the dimensions and zone boundary of a two-class live-cube compact storage system leading to a minimum response time. We propose a mixed-integer nonlinear model that consists of 36 sub-cases, each representing a specific configuration and first zone boundary. Properties of the optimal system are used to simplify the model without losing any optimality. The overall optimal solutions are then obtained by solving the remaining sub-cases. Although the solution procedure is tedious, we eventually obtain two sets of closed-form expressions for the optimal system dimensions and first zone boundary for any desired system size. In addition, we propose an algorithm to obtain the optimal first zone boundary for situations where the optimal system dimensions cannot be achieved. To test the effectiveness of optimal system dimensions and first zone boundary on the performance of a two-class-based live-cube system, we perform a sensitivity analysis by varying the ABC curve, system size, first zone size, and shape factor. The results show that for most cases an optimal two-class-based storage outperforms random storage, with up to 45% shorter expected retrieval time. This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License ( http://creativecommons.org/licenses/by/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited and is not altered, transformed, or built upon in any way.
- Resource Type:
- Article
- Identifier:
- 2472-5579
- Campus Tesim:
- San Marcos