An approximation algorithm for multi-agent scheduling on two uniform parallel machines

• Published in: Optimization letters Vol. 13; no. 4; pp. 907 - 933
• Main Authors: Gu, Manzhan, Lu, Xiwen, Gu, Jinwei
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2019
• Subjects: Computational Intelligence; Mathematics; Mathematics and Statistics; Numerical and Computational Physics; Operations Research/Decision Theory; Optimization; Original Paper; Simulation; Multi-agent; LPT; Scheduling; Makespan
• ISSN: 1862-4472; 1862-4480
• DOI: 10.1007/s11590-018-1298-y

This paper considers a multi-agent scheduling problem, in which each agent has a set of non-preemptive jobs, and all jobs are to be processed on two uniform parallel machines with the objective to minimize the makespan of each agent. Given an instance of the multi-agent scheduling problem, we first devise a measure on the optimal makespan of the single-agent instance for each agent. Then an approximation algorithm is proposed for the multi-agent scheduling problem, in which agents are scheduled in the non-decreasing order of the measure values, and all jobs of each agent are scheduled generally subject to the longest processing time first (LPT) rule. In the obtained schedule, we prove the makespan of the i th completed agent is at most i + 17 - 3 4 times its optimal makespan, in which 17 - 3 4 is the relative error of the LPT rule for the single-agent problem Q 2 | | C max . Furthermore, an example is introduced to show the tightness of the performance analysis.