Multi-Organizational Scheduling: Individual Rationality, Optimality, and Complexity

Multi-Organizational Scheduling: Individual Rationality, Optimality, and Complexity

Jiehua Chen, Martin Durand, Christian Hatschka

Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence
Main Track. Pages 3780-3787. https://doi.org/10.24963/ijcai.2025/420

We investigate multi-organizational scheduling problems, building upon the framework introduced by Pascual et al. in 2009. In this setting, multiple organizations each own a set of identical machines and sequential jobs with distinct processing times. The challenge lies in optimally assigning jobs across organizations’ machines to minimize the overall makespan while ensuring no organization’s performance deteriorates. To formalize this fairness constraint, we introduce individual rationality, a game-theoretic concept that guarantees each organization benefits from participation. Our analysis reveals that finding an individually rational schedule with minimum makespan is ΘP2-hard, placing it in a complexity class strictly harder than both NP and coNP. We further extend the model by considering an alternative objective: minimizing the sum of job completion times, both within individual organizations and across the entire system. The corresponding decision variant proves to be NP-complete. Through comprehensive parameterized complexity analysis of both problems, we provide new insights into these computationally challenging multi-organizational scheduling scenarios.
Keywords:
Game Theory and Economic Paradigms: GTEP: Cooperative games
Planning and Scheduling: PS: Scheduling
Game Theory and Economic Paradigms: GTEP: Computational social choice
Game Theory and Economic Paradigms: GTEP: Mechanism design