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Este relatório descreve o projeto desenvolvido no âmbito do estágio curricular do Mestrado em Matemática Aplicada para a Indústria, centrado na melhoria do planeamento da procura através de metodologias quantitativas. O trabalho enquadra-se na necessidade de reforçar a fundamentação estatística associada à seleção de variáveis explicativas e à construção de modelos preditivos aplicados a séries temporais. A investigação desenvolvida incidiu sobre a análise de dados históricos de vendas de vários produtos pertencentes a quatro famílias distintas, tendo como objetivo principal identificar variáveis preditoras relevantes e avaliar o impacto da sua inclusão em modelos de previsão. Para tal, foi implementada uma abordagem metodológica estruturada que integrou análise descritiva, três métodos complementares de seleção de variáveis, incluindo regressões lineares e a regressão Lasso, e a comparação entre diferentes modelos de previsão. O modelo principal estudado foi o SARIMAX (Seasonal AutoRegressive Integrated Moving Average with eXogenous regressors), permitindo incorporar variáveis exógenas na previsão da procura. As previsões obtidas foram comparadas com as provenientes de um modelo de Alisamento Exponencial, recorrendo à análise sistemática de métricas de erro e à verificação dos pressupostos através da avaliação dos resíduos. Os resultados evidenciaram que a integração de variáveis exógenas, aliada a um processo rigoroso de seleção de preditores, melhorou de forma consistente a precisão das previsões. O estudo reforça, assim, a importância de abordagens multivariadas e estatisticamente sustentadas na otimização do planeamento da procura e na gestão eficiente de cadeias de abastecimento.
Abstract This report describes the project developed as part of the curricular internship of the Master’s in Applied Mathematics for Industry, focused on improving demand planning through quantitative methodologies. The work addresses the need to strengthen the statistical foundations supporting the selection of explanatory variables and the development of forecasting models applied to time series. The investigation focused on the analysis of historical sales data for several products from four distinct families, with the main objective of identifying relevant predictors and assessing the impact of their inclusion in forecasting models. To achieve this, a structured methodological approach was implemented, integrating descriptive analysis, three complementary variable selection techniques, including linear regressions and the Lasso regression, and the comparison of multiple forecasting models. The main forecasting model studied was SARIMAX (Seasonal AutoRegressive Integrated Moving Average with eXogenous regressors), which enables the incorporation of exogenous variables into demand forecasting. Its results were compared with those obtained from an Exponential Smoothing model, using systematic error metric evaluation and residual diagnostics to assess model adequacy. The results showed that integrating exogenous variables, combined with a rigorous predictor selection process, consistently improved forecasting accuracy. The study therefore highlights the importance of multivariate and statistically grounded approaches in optimizing demand planning and enhancing the efficiency of supply chain management.
Abstract This report describes the project developed as part of the curricular internship of the Master’s in Applied Mathematics for Industry, focused on improving demand planning through quantitative methodologies. The work addresses the need to strengthen the statistical foundations supporting the selection of explanatory variables and the development of forecasting models applied to time series. The investigation focused on the analysis of historical sales data for several products from four distinct families, with the main objective of identifying relevant predictors and assessing the impact of their inclusion in forecasting models. To achieve this, a structured methodological approach was implemented, integrating descriptive analysis, three complementary variable selection techniques, including linear regressions and the Lasso regression, and the comparison of multiple forecasting models. The main forecasting model studied was SARIMAX (Seasonal AutoRegressive Integrated Moving Average with eXogenous regressors), which enables the incorporation of exogenous variables into demand forecasting. Its results were compared with those obtained from an Exponential Smoothing model, using systematic error metric evaluation and residual diagnostics to assess model adequacy. The results showed that integrating exogenous variables, combined with a rigorous predictor selection process, consistently improved forecasting accuracy. The study therefore highlights the importance of multivariate and statistically grounded approaches in optimizing demand planning and enhancing the efficiency of supply chain management.
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Seleção de preditores SARIMAX Planeamento da procura Modelos de previsão Predictor selection Demand planning Forecasting models