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arXiv · 2401.05740

An improved bound for the price of anarchy for related machine scheduling

Andre Berger·Arman Rouhani·Marc Schröder
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Abstract

In this paper, we introduce an improved upper bound for the efficiency of Nash equilibria in utilitarian scheduling games on related machines. The machines have varying speeds and adhere to the Shortest Processing Time (SPT) policy as the global order for job processing. The goal of each job is to minimize its completion time, while the social objective is to minimize the sum of completion times. Our main result provides an upper bound of $2-\frac{1}{2\cdot(2m-1)}$ on the price of anarchy for the general case of $m$ machines. We improve this bound to 3/2 for the case of two machines, and to $2-\frac{1}{2\cdot m}$ for the general case of $m$ machines when the machines have divisible speeds.

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Andre Berger, Arman Rouhani, Marc Schröder. 2024-01-11. An improved bound for the price of anarchy for related machine scheduling. https://arxiv.org/abs/2401.05740

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