Classification Tasks with Local and Global Resource Allocation Constraints

Efficiently allocating limited resources in classification problems is an important task in many real-world applications. We propose a two-phase framework consisting of machine learning and optimization models to address this challenge. In the first phase, a machine learning model is used to obtain a probability matrix for potential classifications. In the second phase, the probability matrix is used as input for a linear programming model, which is designed to minimize misclassification costs while considering resource constraints. This study addresses both local and global resource availability constraints, which we define in the context of classification problems as: Target-based constraints-limiting the total number of entities that can be assigned to various classes; and feature-based constraints-limiting the number of entities from each subgroup, defined by a specific feature value, that can be assigned to various classes (e.g., geographic-based limitations). We prove that the coefficient constraint matrix in the linear programming model is totally unimodular, guaranteeing that integer optimal solutions can be obtained using efficient linear programming algorithms. An experimental study illustrates the effectiveness of the proposed framework in terms of time and performance in resource allocation compared to the commonly used conventional method. This two-phase approach advances the application of machine learning and operations research in resource-constrained environments, offering a scalable framework for solving complex classification problems under various constraints.