A SPARSE ANP FORMALIZATION WITH DATA-DRIVEN BINARY COMPARISONS AMONG HOMOGENEOUS COMPONENTS FOR RESOURCE ALLOCATION PRIORITIZATION

Background. Resource allocation problems involving interdependent homogeneous entities arise in many practical settings, including competitive project funding, peer-based evaluation, and proportional budget distribution under limited resources. In such contexts, the relative importance of entities is shaped not only by their individual performance but also by mutual influences within the system. Classical Analytic Network Process (ANP) models are well suited to capture interdependencies, yet they typically rely on expert-based pairwise comparisons and dense influence structures, which become impractical when the number of entities is large or when expert judgment is costly or unreliable. These limitations motivate the development of sparse, data-driven ANP formalization that preserve network feedback while reducing elicitation complexity. Objective. The objective of this study is to propose a sparse ANP approach based on data-driven binary comparisons among homogeneous components, aimed at prioritizing entities for resource allocation while explicitly accounting for interdependence. The goal is to obtain a unique and interpretable global priorities vector that can support ranking, selection, or proportional allocation decisions without relying on subjective expert assessments. Methods. A network of homogeneous components is considered, where each component is influenced by exactly two peer components, resulting in pairwise influence comparison matrices (PICMs). These matrices are constructed deterministically from observed or reported evaluation scores using ratio-based comparisons, without restricting the scale to Saaty’s classical judgments. The resulting supermatrix is sparse, column-stochastic, and strongly connected. Existence and uniqueness of the global priorities vector are established via strict positivity of observed scores, strong connectivity of the induced influence network, and stochastic normalization, and the priorities are obtained as the stationary distribution of the supermatrix. Results. The proposed formalization yields a well-defined global priorities vector despite the minimal local comparison structure. The sparse influence topology ensures computational efficiency and scalability, while the data-driven construction guarantees local consistency of all PICMs. The resulting priorities reflect both individual performance scores and systemic interdependencies, enabling fair and transparent prioritization even when direct expert comparison among all entities is infeasible. Conclusions. The sparse data-driven ANP approach provides an effective decision support framework for resource allocation problems involving interdependent homogeneous entities. By combining network-based feedback modeling with minimal, observation-based binary comparisons, the method bridges classical ANP methodology and data-oriented evaluation settings. Its advantages include reduced subjectivity, guaranteed consistency, and analytical tractability, while its applicability is best suited to contexts with homogeneous alternatives and structured interdependence.