Optimizing Student Seating Arrangements with Conflict Minimization and Mandatory Adjacency Constraints

This study explored the Student Seat Allocation Problem (SSAP) by integrating conflict mitigation and pedagogical proximity. The proposed model enforces mandatory adjacency between selected student pairs and evaluates spare seating capacity. The formulation is assessed on three real classrooms under progressive proximity levels and two capacity settings. Low proximity requirements are absorbed with no cost across all classrooms, whereas higher requirements cause one classroom to retain active conflicts and another to lose feasibility. This behavior is governed by the interaction between mandatory adjacency and classroom geometry rather than conflict density alone. Spare seats did not degrade feasibility and recovered it in one scenario. Results show that pedagogical requirements depend strongly on physical classroom layout, though future validation with teacher-supplied proximity data is recommended for practical application.