Scheduling with Time Dependent Utilities: Fairness and Efficiency

2026-03-26

AI Summary

This study addresses the trade-off between fairness and efficiency in single-machine multi-agent scheduling, where each self-interested agent’s utility decreases with job completion time. Focusing on settings with release times, deadlines, and processing time constraints, the work introduces—for the first time—the fairness objective of maximizing the minimum utility into time-dependent utility scheduling models. By integrating binary search with a greedy strategy, the authors develop polynomial-time exact algorithms and establish computational complexity boundaries—distinguishing between strongly and weakly NP-hard variants—for several problem formulations. The framework is further extended to novel scenarios involving tunable utility functions, rescheduling with inserted jobs, and bilevel optimization. The research elucidates how utility adjustments mediate the fairness–efficiency trade-off and provides an efficient solution methodology applicable across these generalized settings.

Abstract

A new class of multi agent single machine scheduling problems is introduced, where each job is associated with a self interested agent with a utility function decreasing in completion time. We aim to achieve a fair solution by maximizing the minimum utility across all agents. We study the problem's complexity and propose solution methods for several variants. For the general case, we present a binary search procedure to find the largest possible minimum utility, as well as an exact greedy based alternative. Variants with release and due dates are analyzed, showing strong NP hardness for arbitrary release dates, but weak NP hardness for a single release date job, and polynomial solvability when all jobs share processing times. For all these cases we also study the corresponding problem of finding efficient solutions where the sum of utilities is maximized. We also examine settings where linear utility functions can be adjusted within budget constraints, exploring the impact on optimal schedules when intercepts or slopes are modified. From a single agent perspective, we investigate the effect of improving one agent's utility in the overall solution. Adding a new job to be inserted with the best possible utility gives rise to rescheduling problems, where different lower bounds depending on the utilities of the original fair schedule are imposed. Finally, we consider a bi level setting where a leader wants to enforce a certain target schedule by modifying utility functions while the follower computes a fair solution for the modified instance. Our work contributes to scheduling theory, multi agent systems, and algorithmic fairness, highlighting fairness oriented objectives in competitive scheduling.

Problem

• scheduling
• fairness
• multi-agent systems
• time-dependent utilities
• algorithmic fairness

Innovation

• time-dependent utility
• max-min fairness
• multi-agent scheduling
• bilevel optimization
• rescheduling