Mathematics and Artificial Intelligence for Industry Bridging Small Businesses and Large Enterprises with an Application to Biscuit Manufacturing

Abstract

Mathematical modeling and artificial intelligence (AI) are increasingly fundamental to industrial competitiveness, but their adoption differs markedly between small and medium-sized enterprises (SMEs) and large manufacturing companies. Food manufacturing, and in particular cookie production, offers an ideal setting to analyze this gap, given that production involves measurable and repeatable physical and chemical processes. This article develops a conceptual and applied framework that links the main branches of mathematics (statistics, optimization, and calculus-based process modeling) with AI methods (predictive analytics, computer vision, and anomaly detection), and examines how this framework adapts from SMEs to large companies, using cookie manufacturing as an illustrative case. A narrative and thematic synthesis of the literature was combined with the formulation of a mathematical model and a comparison of illustrative operational cases. The sources were obtained from peer-reviewed literature on manufacturing, SMB adoption, and food quality control, published primarily between 2014 and 2026. The synthesis identifies four recurring layers of mathematical AI relevant to cookie manufacturing: demand forecasting (regression/time series models), recipe and batch optimization (linear and mixed-integer programming), computer vision-based defect detection (CNN/YOLO architectures), and predictive maintenance (statistical process control combined with machine learning classifiers). Defect detection accuracies reported in the literature range from approximately 90% to 99.2%, and SMEs can achieve comparable per-unit accuracy through lower-cost cloud-based tools, albeit with lower throughput and integration depth than large enterprises. A common mathematical core underlies AI applications in companies of all sizes; the main difference lies in computational scale, data infrastructure, and integration, rather than the underlying mathematics itself. The framework offers a practical reference for manufacturers and researchers seeking to align AI ambitions with enterprise-level resource constraints.