Designing a Fuzzy Logic-based Carbon Emission Cost-incorporated Inventory Model: A Comparative Analysis of Different Machine Learning Algorithms for Demand Forecasting with Memory Effects

Inventory control is a widely discussed topic in the real world, with organisations increasingly turning to Machine Learning models to manage stock levels based on specific product demand.This article presents an inventory model that addresses imperfect and deteriorating products within a fuzzy environment.It allows for shortages, which may be partially backlogged, and connects closely with concerns about carbon emissions and global warming.Traditional inventory models, often based on integer-order differential equations, typically overlook the system's memory aspect.Addressing inventory management is crucial in our efforts to combat global warming.This paper introduces a novel approach by integrating carbon emission costs within a fuzzy environment.To capture the memory effect of the system, Fractional Calculus is a powerful mathematical tool is employed.In the real world, entrepreneurs frequently face challenges in pinpointing exact parameter values.Therefore, this study considers uncertain factors such as ordering costs, deterioration rates, and demand rates, treating them as triangular fuzzy numbers.The objective is to determine the optimal ordering quantity and replenishment period to minimise average overall costs, including carbon emissions.The defuzzification process utilises the Graded mean integration method (GMIM), Centroid methods (CM), and Signed Distance method (SDM).Seasonal demand forecasting is approached using Machine Learning methodologies.Numerical results are analysed through the lens of memory concepts to validate the proposed mathematical model.