The Analysis of Zero Inventory Drift Variants Based on Simple and General Order-Up-To Policies

In this paper, simple and general Order-Up-To (OUT) models with Minimum Mean Square Error (MMSE) forecast for the AR(1) demand pattern are introduced in the control engineering perspective. Important insights about lead-time misidentification are derived from the analysis of variance discrepancy. By applying the Final Value Theorem (FVI), a final value offset (i.e., inventory drift) is proved to exist and can be measured even though the actual lead-time is known. In this regard, to eliminate the inherent offset and keep the system variances acceptable, two kinds of zero inventory drift variants based on the general OUT model are presented. The analysis of variance amplification suggests lead-times should always be estimated conservatively in variant models. The stability conditions for zero inventory drift variants are evaluated in succession and some valuable attributes of the new variants are illustrated via spreadsheet simulation under the assumption that lead-time misidentification is inevitable.