Semi-online scheduling on 2 machines under a grade of service provision with bounded processing times

  • Authors:

  • Ming Liu;Chengbin Chu;Yinfeng Xu;Feifeng Zheng

  • Affiliations:

  • School of Management, Xi'an Jiaotong University, Xi'an, P.R. China 710049 and Laboratoire Génie Industriel, Ecole Centrale Paris, Châtenay-Malabry Cedex, France 92295;School of Management, Xi'an Jiaotong University, Xi'an, P.R. China 710049 and Laboratoire Génie Industriel, Ecole Centrale Paris, Châtenay-Malabry Cedex, France 92295;School of Management, Xi'an Jiaotong University, Xi'an, P.R. China 710049;School of Management, Xi'an Jiaotong University, Xi'an, P.R. China 710049

  • Venue:
  • Journal of Combinatorial Optimization
  • Year:
  • 2011

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Abstract

We study the problem of semi-online scheduling on 2 machines under a grade of service (GoS). GoS means that some jobs have to be processed by some machines to be guaranteed a high quality. The problem is online in the sense that jobs are presented one by one, and each job shall be assigned to a time slot on its arrival. Assume that the processing time p i of every job J i is bounded by an interval [a,驴 a], where a0 and 驴1 are two constant numbers. By knowing the bound of jobs' processing times, we denote it by semi-online problem. We deal with two semi-online problems.The first one concerns about bounded processing time constraint. First, we show that a lower bound of competitive ratio is: (1) $\frac{1+\alpha}{2}$ in the case where 1驴 $\frac{3}{2}$ in the case where 2驴驴 $\frac{4+\alpha}{6}$ in the case where 5驴驴B-ONLINE, and prove that in the case where $\frac{25}{14}\leq \alpha$ and the optimal makespan C OPT 驴20a, B-ONLINE algorithm is optimal.For the second problem, we further know the sum of jobs' processing times Σ in advance. We first show a lower bound $\frac{1+\alpha}{2}$ in the case where 1驴B-SUM-ONLINE which is optimal in the case where $\Sigma \geq \frac{2\alpha}{\alpha-1}a$ and 1驴