Culinary MSMEs struggle with inventory management because raw materials perish quickly and daily demand fluctuates unpredictably. Most forecasting tools require extensive historical data, often unavailable in kitchens with sparse, intermittent sales records. To address this gap, this study develops and validates a Demand Response Auto-Regressive Moving Average (DR-ARMA) model that performs reliably under severe data constraints. DR-ARMA extends classical ARMA through three stages: baseline ARIMA modeling, moving-average trend detection, and adaptive calibration that incorporates forecast errors directly into safety stock computation via an RMSE-buffered adjustment. This mechanism treats safety stock as endogenous to the forecasting workflow rather than a post hoc decision, representing the core methodological innovation. The model simultaneously enhances forecast accuracy and safety stock reliability. We validated DR-ARMA using a three-month daily sales dataset from an Indonesian culinary business, comprising 90 observations, with over 30% of days with zero sales. Results demonstrate that DR-ARMA achieves a Mean Absolute Percentage Error of 24.64%, substantially outperforming Simple Moving Average (42.70%) and marginally improving upon the Naïve benchmark (24.99%). In this zero-inflated context, even modest gains in forecast stability directly reduce spoilage and stockouts. The integrated safety stock buffer provides an empirical service level of 80%, with tighter inventory bounds that prioritize waste reduction. Finally, we embedded the model into a desktop system, converting predictions into daily procurement lists. This study confirms DR-ARMA as a practical, theoretically grounded solution for inventory optimization in data-scarce culinary settings.