Belief-Aware Inventory Control with Deep Mixture Models

Moritz Beck, Anh-Duy Pham

Keywords: Inventory Management, Mixture Models, Operations Research, POMDP

TL;DR: This paper introduces a framework that combines deep mixture models with inven- tory optimization under uncertain demand, tackling key challenges at the intersec- tion of machine learning and operations research.

Abstract:

This paper introduces a framework that combines deep mixture models with inven-
tory optimization under uncertain demand, tackling key challenges at the intersec-
tion of machine learning and operations research. We propose deep neural mixture
models for demand forecasting that capture multimodal, bounded, and correlated
patterns while maintaining computational tractability for downstream optimization.
Our approach formulates inventory control as a partially observable Markov deci-
sion process (POMDP) where belief states over mixture components evolve via
Bayesian updates. In order to enable practical implementation, we develop a belief
space clustering approach using medoid clustering that reduces the belief space to
a finite set of representative points. We provide theoretical guarantees including
contraction properties of belief updates, Lipschitz continuity bounds, and explicit
performance bounds under belief discretization. The framework supports diverse
neural architectures, including state-of-the-art deep learning time series forecasting
models. Experiments on real-world pharmaceutical demand data demonstrate that
the method is computationally efficient and can lead to promising performance
when the forecasts are well calibrated.

Submission Number: 103