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Online scheduling on two parallel machines with release dates and delivery times

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Abstract

We consider an online scheduling problem where jobs arrive over time. A set of independent jobs has to be scheduled on two parallel machines, where preemption is not allowed and the number of jobs is unknown in advance. The characteristics of each job, i.e., processing time and delivery time, become known at its release date. Each job is delivered to the destination independently and immediately at its completion time on the machines. The objective is to minimize the time by which all jobs have been delivered. We present an online algorithm which has a competitive ratio of \((1+\sqrt{5})/2\approx 1.618\). Finally, our experimental results show that, in practice, the worst case error ratio is much better than the theoretical bound.

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Acknowledgments

The authors would like to thank anonymous referees whose comments helped a lot to improve this paper. This work was supported by the National Nature Science Foundation of China (11101147, 11371137) and the Fundamental Research Funds for the Central Universities.

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Authors and Affiliations

  1. Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, China

    Peihai Liu & Xiwen Lu

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  1. Peihai Liu
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  2. Xiwen Lu
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Correspondence to Peihai Liu.

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Liu, P., Lu, X. Online scheduling on two parallel machines with release dates and delivery times. J Comb Optim 30, 347–359 (2015). https://doi.org/10.1007/s10878-014-9760-y

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