Analytical Model vs. Discrete Event Simulation: A Comparison of Cycle Times for Robotic Picking in Warehousing
A study benchmarks an analytical model with discrete event simulation, finding mean cycle time error below 1% but a systematic overestimation.
The study benchmarks Lerher et al.'s analytical model for in-aisle robotic picking using discrete event simulation (DES). The simulation strictly reproduces the rack geometry, shuttle motion profile, and picking conditions, and finds that reproducing published tables requires specific distances dES=1.5m and dTB=0m. Across 180 scenarios, the 174 main scenarios show a mean absolute relative cycle time difference of 0.8655%, median 0.6758%, maximum 7.0370%, and RMSE 2.744s. Simulation values are consistently lower, indicating slight systematic overestimation by the analytical model. The model is deemed suitable for preliminary estimation, while extreme scenarios need simulation support; results lack real-warehouse validation.
Introduction
In automated warehousing systems, the cycle time of robotic picking operations directly affects overall throughput. Analytical models are widely used for rapid evaluation due to their computational efficiency, but their accuracy needs verification. A recent study benchmarked the analytical model proposed by Lerher et al. using discrete event simulation (DES), focusing on in-aisle robotic picking scenarios. The study not only reproduced the original analytical results but also built a large-scale simulation benchmark, revealing subtle differences between the two approaches.
Discrete Event Simulation (DES) is an event-driven modeling method that advances the system state at discrete points in time. In warehousing and logistics research, DES can explicitly capture stochastic or deterministic time consumption such as shuttle start/stop, tote handover, and picking actions, thereby generating cycle time distributions rather than a single mean. Compared with analytical models (typically based on average speed and fixed path assumptions), DES is more computationally intensive but can capture details such as queuing, conflicts, and nonlinear motion profiles, and is therefore often used as a "ground truth" or validation tool for analytical models. This article leverages this characteristic of DES to conduct a systematic numerical comparison with the analytical model of Lerher et al.
Analytical Model and Simulation Setup
The picking cycle considered in the study includes three core elements: horizontal shuttle movement, tote handling, and item picking at the storage location. For a fair comparison, the simulation strictly follows the rack geometry, shuttle motion profile, handling and picking conditions, and the definitions of cycle time and derived item throughput in the analytical model of Lerher et al.
A key finding is that reproducing the published analytical tables requires a specific interpretation of distances: dES = 1.5 m (distance from shuttle to picking point) and dTB = 0 m (tote handling distance). This suggests that the analytical model is sensitive to the interpretation of input parameters, and the physical meaning of these distances must be clearly defined in practical applications.
Shuttle motion profile refers to the timing arrangement of the horizontal shuttle during acceleration, constant speed, and deceleration phases. The common paired motion profile assumes that the shuttle accelerates to rated speed and then decelerates to a stop between two points; its actual travel time is not simply "distance divided by speed" but a piecewise function determined jointly by acceleration, deceleration, maximum speed, and distance. Analytical models typically approximate this time with closed-form formulas, while DES integrates the kinematic equations segment by segment. The difference between the two approaches is more pronounced in short-distance or high-acceleration scenarios, which is one reason why the definition of the motion profile must be strictly controlled in the comparison presented in this article.
Benchmark Design
The analytical-DES benchmark comprises 180 scenarios, formed by combining three rack lengths, two paired motion profiles, and n = 1 to 30 visited picking locations. Each scenario was simulated with ten replications to ensure statistical stability. Six cases with n = 1 are reported separately because there is no movement component between picking locations, resulting in a different cycle time composition.
The remaining 174 main scenarios cover more complex picking routes and can comprehensively test the performance of the analytical model at different scales. This systematic scenario design makes the comparison results more convincing.
Paired motion profiles in the benchmark design of this article refer to two preset speed-time patterns for the shuttle's back-and-forth movement between adjacent picking locations. Different profiles affect the proportion of acceleration and deceleration phases, thereby changing the cycle time. Including two profiles in the 180 scenarios is intended to test the sensitivity of the analytical model to kinematic assumptions: if the analytical model is accurate only under a certain profile, its applicable scope should be clearly defined. This factorial experimental design (rack length × motion profile × number of picking locations) allows the sources of differences to be attributed rather than reporting overall errors in aggregate.
Numerical Comparison Results
In the 174 main scenarios, the simulation and analytical model showed high numerical agreement, though not perfect agreement. The mean absolute relative cycle time difference was 0.8655%, the median was 0.6758%, and the maximum was 7.0370%. The mean absolute error was 2.411 seconds, and the root mean square error (RMSE) was 2.744 seconds.
You may not have noticed that in all 174 scenarios, the scenario-average cycle time obtained from simulation was lower than the analytical value. This systematic bias suggests that the analytical model may slightly overestimate cycle time, although the difference is small. The researchers explicitly state that the results only indicate numerical closeness under the tested conditions and do not constitute exact agreement, formal statistical equivalence, or validation for actual operating warehouses.
Root mean square error (RMSE) is a common metric for measuring the deviation between predicted values and simulation values, calculated as the square root of the mean squared error across scenarios, in seconds. Compared with mean absolute error, RMSE is more sensitive to large deviations; therefore, an RMSE of 2.744 seconds is higher than the mean absolute error of 2.411 seconds, suggesting the presence of a few scenarios with larger errors (such as the case with a maximum relative difference of 7.04%). In the evaluation of analytical models, reporting mean absolute relative difference, median, maximum, and RMSE together helps distinguish "typical accuracy" from "worst-case risk" and avoids underestimating deviations in extreme scenarios based on the mean alone.
Significance and Limitations
The value of this work lies in providing a reproducible benchmark that helps practitioners understand the applicable boundaries of the analytical model. A mean relative difference of less than 1% means that the analytical model is reliable in the preliminary design stage, but a maximum difference exceeding 7% suggests caution is needed in extreme scenarios (such as long racks or complex motion profiles).
In terms of limitations, the study did not conduct validation in an actual warehouse and only addressed specific rack configurations and motion profiles. Future work can extend to more robot types, dynamic order profiles, and multi-robot collaborative scenarios.
Conclusion
The analytical model and discrete event simulation show good agreement in predicting in-aisle robotic picking cycle times, with a mean relative difference below 1%. However, the systematic underestimation and the larger deviations in individual scenarios remind us that the analytical model is suitable for rapid estimation, while precise decision-making still requires simulation support. This benchmark provides a transparent and reproducible comparison framework for future research.
One-line Summary
A study benchmarked an analytical model using discrete event simulation, finding a mean cycle time error below 1% but a systematic overestimation.
Paragraph Summary
This study benchmarked the in-aisle robotic picking analytical model of Lerher et al. using discrete event simulation (DES). The simulation strictly reproduced the rack geometry, shuttle motion profile, and picking conditions of the analytical model, and found that reproducing the published tables required a specific distance interpretation of dES=1.5m and dTB=0m. The benchmark comprised 180 scenarios; for the 174 main scenarios, the mean absolute relative cycle time difference was 0.8655%, the median 0.6758%, the maximum 7.0370%, and the RMSE 2.744 seconds. In all scenarios, the simulation values were lower than the analytical values, indicating a slight systematic overestimation by the analytical model. The study concludes that the analytical model is suitable for preliminary rapid estimation, but extreme scenarios require simulation support, and the results have not been validated in an actual warehouse.
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