Response time analysis of a live-cube compact storage system with two storage classes

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 themovement 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 discretespace 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

Optimal two-class-based storage in a live-cube compact storage system

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

Modelling load retrievals in Puzzle-Based Storage systems

Puzzle-based storage systems are a new type of automated storage systems that allow storage of unit loads (e.g. cars, pallets, boxes) in a rack on a very small footprint with individual accessibility of all loads. They resemble the famous 15-sliding tile puzzle. Current models for such systems study retrieving loads one at a time. However, much time can be saved by considering multiple retrieval loads simultaneously. We develop an optimal method to do this for two loads and heuristics for three or more loads. Optimal retrieval paths are constructed for multiple load retrieval, which consists of moving multiple loads first to an intermediary ‘joining location’. We find that, compared to individual retrieval, optimal dual load retrieval saves on average 17% move time, and savings from the heuristic is almost the same. For three loads, savings are 23% on average. A limitation of our method is that it is valid only for systems with a very high space utilisation, i.e. only one empty locatio

The impact of integrated cluster-based storage allocation on parts-to-picker warehouse performance

Order picking is one of the most demanding activities in many warehouses in terms of capital and labor. In parts-to-picker systems, automated vehicles or cranes bring the parts to a human picker. The storage assignment policy, the assignment of products to the storage locations, influences order picking efficiency. Commonly used storage assignment policies, such as full turnover-based and class-based storage, only consider the frequency at which each product has been requested but ignore information on the frequency at which products are ordered jointly, known as product affinity. Warehouses can use product affinity to make informed decisions and assign multiple correlated products to the same inventory “pod” to reduce retrieval time. Existing affinity-based assignments sequentially cluster products with high affinity and assign the clusters to storage locations. We propose an integrated cluster allocation (ICA) policy to minimize the retrieval time of parts-to-picker systems based on both product turnover and affinity obtained from historical customer orders. We formulate a mathematical model that can solve small instances and develop a greedy construction heuristic for solving large instances. The ICA storage policy can reduce total retrieval time by up to 40% c