Journal of Combinatorial Optimization ( IF 0.9 ) Pub Date : 2024-10-11 , DOI: 10.1007/s10878-024-01212-z Bo Hou, Tianjiao Guo, Suogang Gao, Guanghua Wang, Weili Wu, Wen Liu
In this paper, we consider the W-prize-collecting scheduling problem on parallel machines. In this problem, we are given a set of n jobs, a set of m identical parallel machines and a value W. Each job \(J_j\) has a processing time, a profit and a rejection penalty. Each job is either accepted and processed on one of the machines without preemption, or rejected and paid a rejection penalty. The objective is to minimize the sum of the makespan of accepted jobs and the penalties of rejected jobs, and at the same time the total profit brought by accepted jobs is not less than W. We design a 2-approximation algorithm for the problem based on the greedy method and the list scheduling algorithm.
中文翻译:
并行机器上的 W 奖品收集调度问题
在本文中,我们考虑了并行机器上的 W 奖品收集调度问题。在这个问题中,我们得到了一组 n 个作业、一组 m 个相同的并行机器和一个值 W。每个作业 \(J_j\) 都有一个处理时间、一个利润和一个拒绝惩罚。每个作业要么在其中一台机器上被接受和处理而没有优先权,要么被拒绝并支付拒绝罚款。目标是最小化被接受的工作的 makespan 和被拒绝的 jobs 的惩罚之和,同时被接受的工作带来的总利润不小于 W。我们基于贪婪方法和列表调度算法为问题设计了一种 2 近似算法。