Ordering policies for multi-item inventory systems with correlated demands

We investigate optimal ordering policies for a multi-item periodic-review inventory system, considering demand correlations and historical data for the products involved. We extend inventory models by transitioning from an autoregressive moving average (ARMA) demand process to a vector autoregressive moving average (VARMA) framework, explicitly characterizing optimal ordering policies when there is both autocorrelation and cross-correlation among multiple items. Through experimental studies, we evaluate inventory costs and cost improvements compared to multi-item ordering policies where demands are assumed to be independent under different degrees of correlation, noise levels, and training data window sizes. The results show that the framework effectively reduces inventory costs, particularly for products with moderate to high dependence. Cost reductions can reach up to 25% for moderate and up to 65% for strong dependence. We also apply our findings to real-world data to optimize inventory policies for immunoglobulin sub-products, intravenous (IVIg) and subcutaneous (SCIg), demonstrating cost improvements using the proposed policy. Furthermore, an empirical study analyzing a large sales dataset reinforces the applicability of our approach.