GPU-Accelerated Fokker–Planck Modeling of Inventory Dynamics Under Intermittent Sales Using Stochastic Safety-Stock Optimization: Evidence from the M5 Retail Dataset

Background: Intermittent retail sales create substantial uncertainty for inventory control, particularly across large portfolios of heterogeneous item–location systems. This study develops a scalable GPU-accelerated Fokker–Planck framework for probabilistic inventory modeling and safety-stock optimization. Methods: The framework is evaluated using 30,490 item–store sales series from the M5 dataset. Empirical sales characteristics are mapped to mean-reverting stochastic inventory dynamics, while a conservative finite-volume scheme and normalized formulation enable canonical policy densities to be solved on the GPU and mapped across the portfolio. Results: Numerical verification confirms analytical agreement, probability-mass preservation, grid convergence, and CPU–GPU consistency. More than 70% of the series exhibit intermittent sales characteristics. Across 35 economic scenarios, global and demand-class policies select no incremental safety-stock buffer beyond the baseline target. Item-specific optimization yields a 21.23% mean in-sample model-implied cost reduction under the original objective, whereas the mean locked-test personalization benefit is 2.46%. Conclusions: GPU-accelerated Fokker–Planck modeling provides a numerically stable and scalable framework for portfolio-level probabilistic inventory analysis, although the benefits of item-level personalization depend on the sales process, economic objective, and out-of-sample environment.