Integration of ARIMA and Grey Wolf Optimizer Models for Multi-Criteria Optimization of Stunting-Oriented Nutritional Menus Based on Food Price Forecasting

Fajar Andaru; Fresy Nugroho; Yunifa Miftachul Arif; Muhammad Faisal; M. Imamudin

doi:10.63922/ijevss.v5i04.6481

Fajar Andaru Master of Informatics Study Program, Faculty of Science and Technology, State Islamic University of Maulana Malik Ibrahim Malang, Malang, Indonesia
Fresy Nugroho Master of Informatics Study Program, Faculty of Science and Technology, State Islamic University of Maulana Malik Ibrahim Malang, Malang, Indonesia
Yunifa Miftachul Arif Master of Informatics Study Program, Faculty of Science and Technology, State Islamic University of Maulana Malik Ibrahim Malang, Malang, Indonesia
Muhammad Faisal Master of Informatics Study Program, Faculty of Science and Technology, State Islamic University of Maulana Malik Ibrahim Malang, Malang, Indonesia
M. Imamudin Master of Informatics Study Program, Faculty of Science and Technology, State Islamic University of Maulana Malik Ibrahim Malang, Malang, Indonesia

DOI: https://doi.org/10.63922/ijevss.v5i04.6481

Keywords: Menu optimization, Grey Wolf Optimizer, forecasting, ARIMA, food prices

Abstract

Stunting among children under five is closely associated with the fulfillment of adequate nutritional requirements, while the affordability of nutritional menus is influenced by changes in food prices. This study aims to develop an adaptive nutritional menu optimization model for children under five that responds to food price changes by integrating price forecasting and the Grey Wolf Optimizer (GWO). The study uses data from eight food commodities, namely premium rice, broiler chicken, chicken eggs, mackerel, carrots, potatoes, green beans, and beef, with 821 daily observations for each commodity over the period from April 1, 2024, to June 30, 2026. The research stages include preprocessing, stationarity testing, ARIMA modeling, forecasting evaluation, 30-day price forecasting, price pattern and volatility analysis, formulation of the GWO fitness function, and menu composition optimization based on the nutritional requirements of children under five. The results show that the lowest testing MAPE of 0.26% was obtained for premium rice and beef, while the rolling forecast for premium rice achieved an average MAPE of 0.1131%. The 30-day forecasts indicate that green beans experienced the highest projected price increase of 13.1344%, whereas carrots showed a projected price decrease of 1.8907%. In the GWO optimization, the price and volatility weights were 0.676063 and 0.323937, respectively, while return received no weight. The optimization produced a total menu portion of approximately 445.34 grams, with an estimated cost of IDR 9,557.65, while satisfying all minimum targets for energy, protein, fat, and carbohydrates. These findings indicate that integrating food price forecasting with metaheuristic optimization can support the development of nutritional menus that account for future price conditions, thereby potentially improving cost efficiency and the adaptability of nutritional menu planning for children under five.

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