Approximate dynamic programming for an inventory problem: Empirical comparison

Abstract

This study investigates the application of learning-based and simulation-based Approximate Dynamic Programming (ADP) approaches to an inventory problem under the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model. Specifically, we explore the robustness of a learning-based ADP method, Sarsa, with a GARCH(1,1) demand model, and provide empirical comparison between Sarsa and two simulation-based ADP methods: Rollout and Hindsight Optimization (HO). Our findings assuage a concern regarding the effect of GARCH(1,1) latent state variables on learning-based ADP and provide practical strategies to design an appropriate ADP method for inventory problems. In addition, we expose a relationship between ADP parameters and conservative behavior. Our empirical results are based on a variety of problem settings, including demand correlations, demand variances, and cost structures.