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

TL;DR

This paper studies multi-organizational scheduling with fairness constraints, revealing the problems' high computational complexity and analyzing their parameterized complexity for different objectives.

Contribution

It formalizes individual rationality in multi-organizational scheduling and analyzes the complexity of minimizing makespan and total completion time.

Findings

Finding an individually rational schedule with minimum makespan is $ ext{Theta}_2^{ ext{P}}$-hard.

Minimizing total completion time decision problem is NP-complete.

Provides parameterized complexity insights for these scheduling problems.

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 $\Theta_2^{\text{P}}$-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.