A best on-line algorithm for the single machine parallel-batch scheduling with restricted delivery times

Jinjiang Yuan (), Shisheng Li, Ji Tian and Ruyan Fu
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Jinjiang Yuan: Zhengzhou University
Shisheng Li: Zhengzhou University
Ji Tian: Zhengzhou University
Ruyan Fu: Zhengzhou University

Journal of Combinatorial Optimization, 2009, vol. 17, issue 2, No 6, 206-213

Abstract: Abstract We consider a single batch machine on-line scheduling problem with delivery times. In this paper on-line means that jobs arrive over time and the characteristics of jobs are unknown until their arrival times. Once the processing of a job is completed it is delivered to the destination. The objective is to minimize the time by which all jobs have been delivered. For each job J j , its processing time and delivery time are denoted by p j and q j , respectively. We consider two restricted models: (1) the jobs have small delivery times, i.e., for each job J j , q j ≤p j ; (2) the jobs have agreeable processing and delivery times, i.e., for any two jobs J i and J j , p i >p j implies q i ≥q j . We provide an on-line algorithm with competitive ratio $(\sqrt{5}+1)/2$ for both problems, and the results are the best possible.

Keywords: Scheduling; On-line algorithm; Parallel-batching; Delivery time (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (9)

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DOI: 10.1007/s10878-007-9108-y

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