SOLVING STOCHASTIC INVENTORY MODEL EQUATION WITH DEEP NEURAL NETWORKS
Shijing Si, Yijin Gao, Haixia Sun, 凌爱凡 · Journal of Applied Analysis & Computation · 2026
The joint optimization of dynamic pricing and inventory control in stochastic inventory systems has been extensively investigated in the previous literature before. A general common approach is to transform the dynamic system into a time-independent ordinary differential equation that represents the stable state. In this study, we extend the model to incorporate the general case with time-dependent dynamics. Consequently, the problem can be reformulated as solving a corresponding partial differential equation (PDE) that lacks an analytical solution. However, assuming an analytical solution encounters certain limitations: (1) Ensuring the accurate existence and uniqueness of the solution is challenging, and (2) completely solving the reduced ordinary differential equation system becomes difficult from theoretical sense. To address these challenges, efficient numerical methods are commonly employed. Nevertheless, for high-dimensional problems, numerical methods like finite element or finite difference methods tend to be computationally slow and suffer from accuracy loss. To overcome these issues, we propose the use of a deep learning technique named Physics-informed Neural Networks (PINN) to solve this complex system, which is the first application of PINN application in this research topic. Simulated examples are presented to validate the usefulness of PINN methods.