Online scheduling of equal-length jobs with incompatible families on multiple batch machines to maximize the weighted number of early jobs

  • Authors:

  • Wenjie Li;Zhenkun Zhang;Hailing Liu;Jinjiang Yuan

  • Affiliations:

  • Department of Mathematics, Zhengzhou University, Zhengzhou, Henan 450001, Peoples Republic of China;Department of Mathematics, Huanghuai University, Zhumadian, Henan 463000, Peoples Republic of China;Department of Mathematics, Zhengzhou University, Zhengzhou, Henan 450001, Peoples Republic of China and Department of Mathematical and Physical Science, Henan Institution of Engineering, Zhengzhou ...;Department of Mathematics, Zhengzhou University, Zhengzhou, Henan 450001, Peoples Republic of China

  • Venue:
  • Information Processing Letters
  • Year:
  • 2012

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Abstract

This paper studies the online scheduling of equal-length jobs with incompatible families on multiple batch machines which can process the jobs from a common family in batches, where each batch has a capacity b with b=~ in the unbounded batching and b0, an integral release time r(J)=0, an integral deadline d(J)=0 and a real weight w(J)=0. The goal is to determine a preemptive schedule with restart which maximizes the weighted number of early jobs. When p=1, we show that a simple greedy online algorithm has a competitive ratio 2, and establish the lower bound 2-1/b. This means that the greedy algorithm is of the best possible for b=~. When p is any positive integer, we provide an online algorithm of competitive ratio 3+22 for both b=~ and b