🤖 AI Summary
This study addresses the computational challenges in analyzing non-Markovian (s, S) inventory systems under general inter-demand and lead-time distributions, where analytical solutions are intractable and conventional simulation methods incur high computational costs. To overcome this, the authors propose a supervised learning–based neural network framework that leverages only low-order moments of the demand and lead-time distributions as inputs to efficiently predict key steady-state performance metrics—such as the inventory level distribution, expected cycle time, and stockout probability. The approach achieves high-accuracy, near-instantaneous predictions across a broad range of parameter settings, substantially reducing computational overhead while demonstrating strong potential for extension to other complex inventory models.
📝 Abstract
The continuous-review (s,S) inventory model is a cornerstone of stochastic inventory theory, yet its analysis becomes analytically intractable when dealing with non-Markovian systems. In such systems, evaluating long-run performance measures typically relies on costly simulation. This paper proposes a supervised learning framework via a neural network model for approximating stationary performance measures of (s,S) inventory systems with general distributions for the interarrival time between demands and lead times under lost sales. Simulations are first used to generate training labels, after which the neural network is trained. After training, the neural network provides almost instantaneous predictions of various metrics of the system, such as the stationary distribution of inventory levels, the expected cycle time, and the probability of lost sales. We find that using a small number of low-order moments of the distributions as input is sufficient to train the neural networks and to accurately capture the steady-state distribution. Extensive numerical experiments demonstrate high accuracy over a wide range of system parameters. As such, it effectively replaces repeated and costly simulation runs. Our framework is easily extendable to other inventory models, offering an efficient and fast alternative for analyzing complex stochastic systems.