Based on the standard “FEM9.851 Stacker Operation Cycle”

Research on the Calculation and Application of Throughput and Inbound/Outbound Frequency for Specialized Automated Storage Systems

(Ma Xiao, Shanxi Yingcai Logistics Equipment Technology Co., Ltd., 030000)

October 26, 2021

[Abstract] According to FEM 9.851, the standard provides calculations only for six types of inbound and outbound operations. In practical applications, however, there are numerous different types of inbound and outbound processes, and the demand for increasingly precise calculations of throughput volumes is growing. This paper introduces current research on the calculation and application of inbound and outbound frequencies in automated storage systems featuring various types of inbound and outbound operations. To date, this area of study remains entirely unexplored.

[Keywords] FEM9.851, Stacker Crane, Inbound and Outbound Frequency

[References]

1. FEM9.851 Stacker Operation Cycle
2. JB/T9018-2011 Code for Design of Automated Stereoscopic Warehouses
3. Ma Xiao and Liu Changqi, "Practical Techniques for Classification of Logistics Distribution Centers and Picking Systems"
4. Ma Xiao and Liu Changqi, "Intelligent Logistics Distribution Centers—Design, Equipment, and Case Studies"

[About the Author] Ma Xiao, male, Senior Engineer, Shanxi Province’s “San Jin Ying Cai” Talent, and a High-end Innovation Talent in Taiyuan City, is the recipient of numerous scientific and technological achievements and the inventor of multiple patents. He has published two monographs and currently serves as the Chairman of Shanxi Yingcai Logistics Equipment Technology Co., Ltd.

The “FEM9.851 Stacker Operation Cycle” standard issued by the European Material Handling Association in 2003 and China’s “JB/T9018-2011 Design Code for Automated Stereoscopic Warehouses” provide detailed instructions on calculating and testing the inbound and outbound frequency of conventional stereoscopic warehouses. These standards serve as crucial references for data analysis when logistics companies develop planning schemes. Among these two standards, the FEM standard is more detailed than the JB standard. It specifies in great detail the methods for selecting spatial characteristic points within the warehouse area, provides a comprehensive process analysis, calculation steps, and formulas for determining inbound and outbound frequencies, thus offering an excellent basis for accurate calculations. Moreover, these standards have been extensively validated in practical applications.

However, with the emergence of various types of automated storage systems on the market, this standard can no longer fully cover the current market situation. In our interactions with customers today, a key issue under discussion—between users and solution planners—is whether a particular layout can meet the production takt time. Below, we’ll explore the inbound and outbound frequencies for fixed-turn automated storage systems, switch-turn automated storage systems, and intelligent-rack automated storage systems.

1. Fixed-turn stacker, one-entry/one-exit configuration:

(Figure 1: A project featuring a fixed turning configuration, two aisles, and one in-and-out storage system)

The diagram above shows a top-down view of an automated three-dimensional warehouse with fixed-turning and double-deep racking. Such a layout, when implemented in a limited space, clearly allows for the storage of more goods while using the fewest possible pieces of equipment. In the diagram, apart from the racking itself, only one stacker crane and one set of inbound and outbound conveyor systems are used. It’s evident that this configuration represents the lowest possible investment. So, how do we calculate the frequency of inbound and outbound operations under such a layout?

In the FEM9.851 standard, the calculation of the inbound and outbound frequency for double-deep automated storage systems is performed by selecting feature points according to the model shown in the figure below:

(Figure 2: Double-depth layout for straight-line segments in FEM9.851, with a single-sided inbound and outbound calculation model for the storage system)

Among them, point E is the inbound location, point A is the outbound location, and the two feature coordinate points P1 and P2 shall have their dimensions selected according to the following coordinate parameters.

According to this standard, with a warehouse length of 50 meters and a height of 12 meters, the calculated coordinate points are:

As shown in Figure 1, if the aisle has no turns and the stacker crane operates on a straight section, and assuming the stacker crane’s conventional operating speed is 120 m/min, its lifting speed is 24 m/min, its fork speed is 60 m/min when unloaded, and 30 m/min when loaded, according to FEM 9.851 standard, the design of this storage location’s straight section yields the results illustrated in the figure below. As can be seen, the combined operation rate is 27 cycles per hour.

(Figure 3: According to FEM 9.851, double-deep configuration with straight-line segments, a single-sided storage and retrieval system, based on storage and retrieval calculations for a 50-meter-long, 13-meter-high facility.)

However, in reality, since the stacker crane operates in two aisles, this calculation does not accurately reflect the actual situation. According to the layout shown in Figure 1, when the stacker crane reaches the turning point at the far-left end, its linear velocity will abruptly drop from 120 m/min on the straight section to 30 m/min. Given that the center-to-center distance between aisles is 6.5 m, the time t1 required for the crane to traverse this curved section with a given radius can be easily calculated as follows:

t1 = l1/v = 6.5 m × 3.14 / (2 × 30) = 0.34 min

Since the goods are normally distributed across two aisles and the stacker crane travels on average in both aisles, if the crane travels along a straight segment within 0.34 minutes, the distance it should travel is:

L2 = 0.34 × 120 = 40 m,

This travel process is a critical factor affecting the efficiency of the stacker crane. Therefore, when calculating for two aisles, we should take into account the cumulative effect, as shown in the figure below: The first segment actually covers 50 meters, but the turning section is equivalent to 40 meters; the second segment is 50 meters. In total, this amounts to 140 meters. Based on this segment length, the stacking crane’s inbound and outbound frequency calculations need to be recalibrated and re-evaluated.

(Figure 4: According to FEM9.851, with two tunnels plus a fixed turn, when converted to single-tunnel operation, the equivalent length would be 140 meters. The figure below shows the computational model for operation in a 140-meter-long tunnel.)

After superimposing the simulation with the turning section, the calculated feature coordinate points are:

The results calculated based on these feature points should be as shown in the figure below. The calculated results are also shown in the figure below, from which it can be seen that the combined operation rate is 19 times per hour.

(Figure 5: Double-depth design for curved segments, a set of inbound and outbound system models,) According to the calculation results for operation in a 140-meter-long alleyway. )

As for whether the above calculation represents the optimal speed combination, that still depends on the speed-versus-distance performance curve.

In this process, taking point E to point P1 as an example, the plots of horizontal motion and vertical ascent/descent velocity versus distance show that the velocity and acceleration are remarkably well-matched.

(Figure 6: Speed-distance curve from feature point E to point P1, plotted against the lifting speed)

1. Fixed-turn stacker, two entry/exit configurations:

If the layout is adjusted as shown in the following figure, the two alleyways will each have two entrances and exits:

(Figure 7: A project featuring a fixed-turn, double-deep racking system with two aisles and two separate storage/retrieval systems.)

Since the entrances and exits are located at both ends, the calculation of the inbound and outbound frequency should take into account the actual travel trajectories as follows. The calculation results are shown in the figure below; as you can see, the combined operation rate is 13 times per hour.

(Fig. 8: As shown in Fig. 4, the calculation results for two sets of inbound and outbound system models, based on the double-deep configuration where curved segments are folded into a single-lane layout, with operation parameters of 140 meters in length and 13 meters in height.)

The shift from 27 runs using a single lane to 19 runs with single-sided loading and unloading through a single lane, and then to 13 runs with double-sided loading and unloading, has had a significant impact on efficiency. Whether we can meet or exceed customer expectations requires careful consideration.

1. Under the fixed-turn stacker configuration with two entry/exit types, the results of software intervention will differ significantly:

In actual use, if the configuration is as shown in Figure 4 but under the intervention of WMS software, different results may occur. The underlying principle is that, during the inbound and outbound processes, we instruct customers—whether during inbound operations or MES production—to store and retrieve goods in an orderly manner according to the final customer’s requirements and by designated aisles. For example, the first aisle is reserved exclusively for goods destined for a particular customer in Beijing, while the second aisle is reserved exclusively for goods destined for a customer in Nanjing. Under such operational conditions, in real-world usage, when a customer in Beijing is loading goods while a customer in Nanjing remains idle—or in situations involving time-sharing control—we can minimize the time wasted by stacker cranes making unnecessary turns.

There is no doubt that such control measures are effective; the time spent making turns can even be negligible. When the stacker crane operates on straight sections, the calculated results—as shown in Figure 3—demonstrate a significant improvement in efficiency.

1. The turning stacker of the switching device, with multiple entry and exit configurations, requires weighted calculation under this configuration:

For some automated storage systems, if more aisles are required while fewer stacker cranes are needed, a switching device becomes necessary. The switching mechanism for overhead rail systems makes it possible to accommodate more aisles using fewer stacker cranes. In 2003, the author participated in the construction of the Southern Airlines Maintenance Hangar at Guangzhou Baiyun Airport, where 15 aisles were served by just three stacker cranes.

(Figure 9: Automated stereoscopic warehouse with switching device)

The use of switching devices affects system timing, so when calculating frequencies, you need to take this into account by incorporating the turning method shown in Figure 1 into the operational analysis. For example, whether traffic flows from Lane 1 into Lane 3 or from Lane 1 into Lane 2, these scenarios should be weighted and integrated into the overall system calculation.

The example calculation is shown in the figure below:

(Figure 9: From the First Tunnel to the Second Tunnel—Single-Tunnel Operation Model)

(Figure 10: From the first tunnel to the second tunnel, a dual-tunnel system, with each tunnel having one entrance and one exit—running calculation results)

(Figure 11: From the First Lane to the Third Lane—Single-Lane Operation Model)

(Figure 12: From the First Lane to the Third Lane, a dual-lane system, with one entrance and one exit per lane; calculation results shown)

In a certain case, if the route is from the first lane to the second lane—as shown in Figure 10—this results in 12 trips per hour. However, if the route is from the first lane to the third lane, due to the longer sliding-turning distance, the calculated result is 11 trips per hour. Furthermore, considering the actual operational requirements or software scheduling constraints—that is, 60% of the time the route is from the first lane to the second lane and 40% of the time it’s from the first lane to the third lane—the weighted calculation of the composite efficiency should be:

12 ´ 60% + 11 ´ 40% = 11.6 times per hour.

1. Calculation of Intelligent Vehicle Entry and Exit Frequency

(Figure 13, a smart automated storage and retrieval system for vehicles)

As shown in the figure above, when using a traveling-type stacker crane to switch between different aisles, the calculation method for inbound and outbound operations is essentially the same. In each aisle, the calculation is performed based on straight-line segments; the switching process is treated as the stacker crane’s turning maneuver, and then the result can be obtained using FEM9.851’s calculation tool.

There are many different types of intelligent driving systems, and if these systems are converted into a computational model for stacker cranes, the results can be easily calculated.

1. Combining computation with simulation allows the results to mutually validate each other.

In practice, a large number of simulation software programs are available for use in decision-making. In a three-dimensional warehouse with multiple input and output points, before putting the equipment into operation, it’s crucial to verify the accuracy of the above-mentioned detailed calculations by leveraging simulation results. This approach ensures that the actual application is closer to reality and that the data obtained are more accurate.

(Figure 14: Simulation results output for a certain intelligent automated warehouse)

1. Closing remarks

There’s no such thing as the “best” logistics solution—only the solution that best suits the customer is truly the best. To devise a plan that not only meets the customer’s needs but also requires minimal investment, we need to engage in repeated comparisons and thorough discussions. Currently, simple automated storage systems are increasingly being integrated with peripheral equipment, and their functionalities are becoming ever more sophisticated. In many cases, inbound and outbound operations involve multiple levels, rows, and columns, and poor analysis of inbound and outbound frequency can directly impact the success or failure of the entire factory.

Accurate and effective calculations can provide a solid basis for decision-making; however, these calculations must be broken down step by step with meticulous precision. Only by accounting for every single step can we ensure accuracy—and only then can the results truly assist in decision-making. We hope our research will contribute to more efficient computational methods.