# Single Machine Scheduling With Job Delivery To Minimize Makespan

## 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)

Registered author(s):

## 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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://www.worldscinet.com/cgi-bin/details.cgi?type=pdf&id=pii:S0217595908001596

File URL: http://www.worldscinet.com/cgi-bin/details.cgi?type=html&id=pii:S0217595908001596

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

## 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

as in new window
Handle: RePEc:wsi:apjorx:v:25:y:2008:i:01:p:1-10

Contact details of provider:
Web page: http://www.worldscinet.com/apjor/apjor.shtml

Order Information:
Email:

## Related research

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

## References

No references listed on IDEAS
You can help add them by filling out this form.

## Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

## Corrections

When requesting a correction, please mention this item's handle: RePEc:wsi:apjorx:v:25:y:2008:i:01:p:1-10. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Tai Tone Lim).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.