Bounding the Price of Anarchy of Weighted Shortest Processing Time Policy on Uniform Parallel Machines

Abstract

This article investigates the performance of the Weighted Shortest Processing Time (WSPT) rule as a local sequencing policy in a scheduling game for uniformly related parallel machines, where the social objective is the total weighted completion time. Our research aims to establish improved upper bounds for the price of anarchy in this game. We determine two bounds, incorporating parameters that characterize the instance family, such as the speed of the fastest machine (sm) and the number of machines (m). One bound establishes a fixed upper bound for the price of anarchy, while the other outperforms the parametric upper bound found in the existing literature. These newly derived bounds provide better insights into the performance of the scheduling game under study, proving that the price of anarchy is upper bounded by minsm1+1/2sm−1/2m,m,4.