This chapter explores the critical decision-making process in selecting IT outsourcing service providers for public administrators, focusing on its impact on future public value creation. The research introduces a novel framework based on linear programming for stable matching, interval numbers and a Matrix Models procedure for addressing relational variables influencing service provider selection in public-private IT outsourcing. Drawing on empirical data from Mexico’s public administration, the study identifies trust and knowledge interfaces as pivotal factors shaping public value in outsourcing projects. The methodology correlates public value with service provider selection criteria, offering valuable insights for decision-makers and practitioners. Computational experiments validate the stability of this approach, providing recommendations for optimizing selection processes and enhancing outcomes for citizens and stakeholders. The study’s contributions extend beyond IT outsourcing, influencing discussions on methodologies for the service provider selection problem, outsourcing in public sector management, and value creation.