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

2025-05-18

AI Summary

This paper investigates multi-organizational cooperative scheduling: each organization possesses identical parallel machines and a sequence of jobs, aiming to minimize either the makespan or the total completion time, subject to individual rationality—that is, no organization’s performance degrades relative to standalone scheduling. It is the first work to formally incorporate individual rationality, a game-theoretic constraint, into multi-organizational scheduling. We rigorously establish that the makespan-minimization problem under individual rationality is Θ₂^P-complete—strictly harder than both NP and coNP—while the total completion time version is NP-complete. These complexity classifications are derived via computational complexity theory, parameterized analysis, and polynomial-time reductions. Our results provide the first decidable theoretical boundary for fairness in cross-organizational resource coordination and lay a foundational complexity-theoretic basis for cooperative scheduling.

Technology Category

• Game Theory and Economic Paradigms: Cooperative Game Theory
• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy

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 $Theta_2^{ ext{P}}$-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.

Problem

• Optimizing job assignment across organizations to minimize makespan
• Ensuring individual rationality to prevent organizational performance loss
• Analyzing complexity of scheduling problems with fairness constraints

Innovation

• Introduces individual rationality for fairness
• Analyzes Θ₂^P-hard complexity for makespan
• Extends model to minimize completion times