Single-Response Optimization of Holt–Winters Smoothing Parameters for Seasonal Demand Forecasting

Abstract

Accurate demand forecasting is vital for effective supply chain and inventory management. The Holt–Winters Exponential Smoothing method is widely used for time series forecasting involving level, trend, and seasonality. However, its accuracy largely depends on the appropriate selection of three smoothing parameters: alpha (α), beta (β), and gamma (γ). Manual tuning often yields suboptimal results, leading to higher forecasting errors. This study introduces a systematic framework for optimizing Holt–Winters parameters using Taguchi design of experiments (DOEs), stepwise regression modelling, and response surface-based optimization. The approach is validated using a real-world quarterly demand dataset spanning 12 quarters (2014–2017), which exhibits all key time series components. Taguchi DOE efficiently explores 25 parameter combinations and their forecast outcomes. Stepwise regression is applied to develop a statistical model relating forecasting error to α, β, and γ, capturing significant parameter effects and interactions. Response surface optimization is then used to minimize error, constrained by parameter bounds and non-negativity. The optimized parameters significantly reduce forecasting error – over 30% in most quarters – compared to traditional trial-and-error tuning. The framework is repeatable, scalable, and enhances the reliability of exponential smoothing models, making it a practical tool for data-driven forecasting.