Multi-Organizational Scheduling: Individual Rationality, Optimality, and Complexity
Jiehua Chen, Martin Durand, Christian Hatschka
TL;DR
This work extends scheduling theory by introducing individual rationality (IR) to a multi-organizational setting where each organization owns machines and sequential jobs. It analyzes two core objectives—makespan ($\mathsf{C}_{\max}$) and sum of completion times ($\mathsf{C}_{\Sigma}$)—and establishes a sharp complexity separation: the decision version of $\mathsf{C}_{\max}$-MOS is $\Theta_2^{\text{P}}$-complete, while $\mathsf{C}_{\Sigma}$-MOS-Dec is NP-complete. The paper advances the algorithmic front with parameterized results: an $\mathsf{FPT}$ ILP-based approach for $k+\mathsf{p}_{\max}$, XP results in $\mathsf{m}$ and $\mathsf{m}+\mathsf{p}_{\max}$, and DP-based hardness for small $k$; analogous results hold for the $\mathsf{C}_{\Sigma}$ objective with $n$, $\tau$, and $\mathsf{p}_{\max}$-related parameters. Together, these findings illuminate the computational limits and tractable regimes of IR MOS, suggesting practical strategies and revealing fundamental trade-offs between fairness and global efficiency. The work has potential impact on resource sharing in distributed systems, grid computing, and collaborative research infrastructures where cooperative schedules must be individually rational and globally efficient.
Abstract
We investigate multi-organizational scheduling problems, building upon the framework introduced by Pascual et al.[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 $Θ_2^{\text{P}}$-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.