Scheduling with Time Dependent Utilities: Fairness and Efficiency

A team of computer scientists from Sapienza University of Rome and the University of Graz has published groundbreaking research on fair scheduling for AI agents with time-dependent utilities. The paper, "Scheduling with Time Dependent Utilities: Fairness and Efficiency," introduces a novel class of multi-agent single-machine scheduling problems where each job is controlled by a self-interested agent whose utility decreases with completion time. The researchers propose two primary objectives: maximizing the minimum utility across all agents (fairness) and maximizing the sum of utilities (efficiency). They developed a binary search procedure and exact greedy-based algorithms to find optimal solutions, providing mathematical frameworks for what they term "fairness-oriented objectives in competitive scheduling."

The research provides comprehensive complexity analysis across multiple problem variants. For the general case with arbitrary release dates, the problem is strongly NP-hard, making it computationally challenging. However, the team identified more tractable scenarios: problems with a single release date job are weakly NP-hard, and when all jobs share identical processing times, the problem becomes polynomially solvable. The paper also explores bi-level optimization where a leader (like a system designer) can modify utility functions to enforce target schedules while a follower computes fair solutions. This has direct applications in cloud computing resource allocation, autonomous vehicle scheduling, and multi-agent AI systems where fairness considerations are increasingly important alongside traditional efficiency metrics.