Optimasi Bobot Model Ensemble untuk Peramalan Penjualan Menggunakan Grey Wolf Optimizer

Abstract

Sales forecasting plays a crucial role in supporting strategic corporate decision-making, such as production planning, inventory management, and the formulation of marketing strategies. However, sales data that is complex, non-linear, and seasonal causes conventional methods such as Moving Average (MA), Exponential Smoothing (ES), and Linear Regression (LR) to often produce limited accuracy. This study aims to optimize the ensemble model weights of these three methods using the Grey Wolf Optimizer (GWO) algorithm to improve sales forecasting accuracy. The proposed method evaluates a large-scale retail sales dataset comprising 3,000,888 raw daily transactions from 54 stores and 33 product families (2013–2017), aggregated into 1,674 daily time-series records and split chronologically into 80% training data (1,339 records) and 20% testing data (335 records). Individual baseline models of Seasonal MA, Holt-Winters ES, and LR were developed alongside a weighted ensemble model with weights optimized by GWO. The performance was evaluated using MAE, MSE, RMSE, MAPE, and R² metrics. The results show that the GWO-optimized ensemble model achieved a MAPE of 11.60%, outperforming all individual baseline models. Compared to the best baseline model (Seasonal MA with MAPE 12.62%), the GWO ensemble achieved an accuracy improvement of 1.02%, which was proven statistically significant via Diebold–Mariano and Wilcoxon tests (p < 0.001). The GWO algorithm demonstrated high stability with a standard deviation of only 0.000026% across 30 independent runs.