Abstract
This paper considers two uniform parallel machine scheduling problems with fixed machine cost under the background of cloud manufacturing. The goal is to minimize the makespan with a given budget of total cost, \(\hat{U}\). All the jobs are homogeneous, i.e., the processing times of the jobs are identical. Non-preemptive and preemptive problems are studied. For the non-preemptive problem, we give a \(2[1+1{/}(h-1)]\)-approximation algorithm, where h is the number of the machine which can not be selected the first time. For the preemptive problem, we give an algorithm whose worst-case bound equals to \(1+1{/}(h-1)\). Preliminary experimental results indicate that the proposed algorithms are reasonably accurate compared with the lower bounds.
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Acknowledgements
This work was supported by the fund from National Natural Science Foundation of China under Grant Nos. 71471052, 71521001, and 71531008. P.M. Pardalos was partially supported by a project of Distinguished International Professor by the Chinese Ministry of Education under Grant MS2014HFGY026.
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Li, K., Zhang, HJ., Cheng, BY. et al. Uniform parallel machine scheduling problems with fixed machine cost. Optim Lett 12, 73–86 (2018). https://doi.org/10.1007/s11590-016-1096-3
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DOI: https://doi.org/10.1007/s11590-016-1096-3