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Single Machine Scheduling With Job Delivery To Minimize Makespan

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Author Info

  • LINGFA LU

    ()
    (Department of Mathematics, Zhengzhou University, Zhengzhou, Henan 450052, People's Republic of China)

  • JINJIANG YUAN

    (Department of Mathematics, Zhengzhou University, Zhengzhou, Henan 450052, People's Republic of China)

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    Abstract

    In the single machine scheduling problem with job delivery to minimize makespan, jobs are processed on a single machine and delivered by a capacitated vehicle to their respective customers. We first consider the special case with a single customer, that is, all jobs have the same transportation time. Chang and Lee (2004) proved that this case is strongly NP-hard. They also provided a heuristic with the worst-case performance ratio $\frac{5}{3}$, and pointed out that no heuristic can have a worst-case performance ratio less than $\frac{3}{2}$ unless P = NP. In this paper, we provide a new heuristic which has the best possible worst-case performance ratio $\frac{3}{2}$. We also consider an extended version in which the jobs have non-identical transportation times and the transportation time of a delivery batch is defined as the maximum transportation time of the jobs contained in it. We provide a heuristic with the worst-case performance ratio 2 for the extended version, and show that this bound is tight.

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    Bibliographic Info

    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal Asia-Pacific Journal of Operational Research.

    Volume (Year): 25 (2008)
    Issue (Month): 01 ()
    Pages: 1-10

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    Handle: RePEc:wsi:apjorx:v:25:y:2008:i:01:p:1-10

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    Related research

    Keywords: Scheduling; job delivery; heuristic; worst-case performance ratio;

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