A HYBRID MATHEMATICAL-MACHINE LEARNING FRAMEWORK FOR OPTIMIZING BUSINESS EFFICIENCY AND MANAGERIAL DECISION ACCURACY

The increasing complexity of contemporary business environments has intensified the need for intelligent analytical frameworks capable of improving operational efficiency, resource allocation, and managerial decision accuracy. Although conventional statistical and mathematical decision-support techniques provide structured approaches to business management, their effectiveness may be limited when addressing nonlinear relationships, multidimensional datasets, and dynamic operational conditions. This study proposes a hybrid mathematical-machine learning framework integrating predictive analytics, statistical evaluation, and constrained decision optimization to support evidence-based managerial decision-making. The research adopts a quantitative and comparative experimental design using two publicly accessible datasets from the UCI Machine Learning Repository: Bank Marketing, comprising 45,211 observations and 16 predictor variables, and Online Shoppers Purchasing Intention, comprising 12,330 observations and 17 predictor variables. Five analytical models, namely Logistic Regression, Random Forest, Support Vector Machine, Gradient Boosting, and Artificial Neural Networks, are selected for comparative evaluation. Predictive performance is assessed using accuracy, precision, recall, F1-score, and Receiver Operating Characteristic-Area under the Curve (ROC-AUC), while managerial decision effectiveness is evaluated through customer conversion outcomes, resource allocation efficiency, operational costs, and decision regret. The proposed hybrid framework integrates machine learning predictions with mathematical decision-support procedures to identify feasible managerial alternatives under predefined budgetary and operational constraints. Comparative analysis is designed to examine the effectiveness of conventional statistical approaches, standalone machine learning models, and hybrid decision-support strategies under consistent experimental conditions. Explainable artificial intelligence techniques are additionally incorporated to improve the transparency and interpretability of predictive recommendations. The study contributes a reproducible analytical framework for connecting predictive intelligence with structured managerial decision-making and establishes an empirical evaluation approach for examining potential improvements in business efficiency, cost effectiveness, and decision quality. The proposed framework offers practical implications for intelligent business management, customer targeting, operational planning, and sustainable organizational performance.