Resource allocation in ordinal classification problems: A prescriptive framework utilizing machine learning and mathematical programming

Ordinal classification tasks that require the allocation of limited resources are prevalent in various real-world scenarios. Examples include assessing disease severity in the context of medical resource allocation and categorizing the quality of machines as good, medium, or bad to schedule maintenance treatment within capacity constraints. We propose a comprehensive analytic framework for scenarios that, in addition to including ordinal classification problems, also have constraints on the number of classified samples of classes due to resource limitations. The framework uses a probability matrix generated by a trained ordinal classifier as the input for an optimization model with a minimum misclassification cost objective and resource allocation constraints. We illustrated the equivalence between the formulation of the resource allocation problem into samples and the transportation problem, enabling the utilization of established transportation heuristics for our solution. To demonstrate the effectiveness and applicability of the framework, we applied it with various ordinal machine-learning models to both tabular data and image datasets. The proposed framework performs significantly better than the alternative common approach of using non-ordinal classifiers, achieving an average cost reduction of 1% with ordinal decision tree-based models and 4.4% with ordinal neural networks. Our results show that the proposed framework can provide an effective limited-resource allocation for ordinal classification problems. Our code is available at https://github.com/liorRabkin/hybrid-cost-sensitive-ml-optimization.