Abstract
We investigate a single machine scheduling problem with job delivery to multiple customers. In this problem, each job needs to be processed on the single machine, and then delivered by a single vehicle to its customer, where the job has a physical size representing the fraction of space it occupies on the vehicle. The vehicle delivers a shipment from the machine to a customer and has to return back to the machine for delivering the next shipment. It takes different constant time for the round trips between the machine and the different customers. The goal is to minimize the makespan, by that time all the jobs are processed and delivered to their respective customers, and the vehicle returns back to the machine. We propose a 2-approximation algorithm for the general case; when there are only two customers, we present an improved 5/3-approximation algorithm. The design and performance analysis of these two algorithms integrate several known results and techniques for the single machine scheduling problem, the bin-packing problem, and the knapsack problem.
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Acknowledgements
The authors are grateful to the anonymous referees for their numerous helpful comments that improve the presentation. Dong is supported by the NNSF of China (Grant No. 11501512) and the Science Foundation of ZSTU (Grant No. 13062171-Y); Hu is supported by the NNSF of China (Grant No. 11271324 and 11471286); Lin is supported by the NSERC Canada, the Science Foundation of ZSTU (Grant No. 14062170-Y), and NNSF of China (Grant No. 61672323). Lin’s work was mostly done during his sabbatical leave at the ZSTU.
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Dong, J., Wang, X., Hu, J. et al. Single machine scheduling with job delivery to multiple customers. J Sched 21, 337–348 (2018). https://doi.org/10.1007/s10951-017-0508-2
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DOI: https://doi.org/10.1007/s10951-017-0508-2