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  • YIWEI JIANG (a1) (a2), PING ZHOU (a3), HUIJUAN WANG (a2) and JUELIANG HU (a2)


We study a nonpreemptive scheduling on two parallel identical machines with a dedicated loading server and a dedicated unloading server. Each job has to be loaded by the loading server before being processed on one of the machines and unloaded immediately by the unloading server after its processing. The loading and unloading times are both equal to one unit of time. The goal is to minimize the makespan. Since the problem is NP-hard, we apply the classical list scheduling and largest processing time heuristics, and show that they have worst-case ratios, $8/5$ and $6/5$ , respectively.


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[1] Batur, G., Karasan, O. and Akturk, M., “Multiple part-type scheduling in flexible robotic cells”, Int. J. Product. Econ. 135 (2012) 726740; doi:10.1016/j.ijpe.2011.10.006.
[2] Brucker, P., Dhaenens-Flipo, C., Knust, S., Kravchenko, S. A. and Werner, F., “Complexity results for parallel machine problems with a single server”, J. Sched. 5 (2002) 429457; doi:10.1002/jos.120.
[3] Hall, N., Potts, C. and Sriskandarajah, C., “Parallel machine scheduling with a common server”, Discrete Appl. Math. 102 (2000) 223243; doi:10.1016/S0166-218X(99)00206-1.
[4] Jiang, Y., Dong, J. and Ji, M., “Preemptive scheduling on two parallel machines with a single server”, Comput. Ind. Eng. 66 (2013) 514518; doi:10.1016/j.cie.2013.07.020.
[5] Jiang, Y., Wang, H. and Zhou, P., “An optimal preemptive algorithm for the single-server parallel-machine scheduling with loading and unloading times”, Asia-Pac. J. Oper. Res. 32 (2014) 11 pages; doi:10.1142/S0217595914500390.
[6] Jiang, Y., Yu, F., Zhou, P. and Hu, J., “Online algorithms for scheduling on two parallel machines with a single server”, Int. Trans. Oper. Res. 22 (2015) 913927; doi:10.1111/itor.12136.
[7] Jiang, Y., Zhang, Q., Hu, J., Dong, J. and Ji, M., “Single-server parallel-machine schduling with loading and unloading times”, J. Comb. Optim. 30 (2015) 201213; doi:10.1007/s10878-014-9727-z.
[8] Kim, M. Y. and Lee, Y. H., “MIP models and hybrid algorithm for minimizing the makespan of parallel machines scheduling problem with a single server”, Comput. Oper. Res. 39 (2012) 24572468; doi:10.1016/j.cor.2011.12.011.
[9] Koulamas, C., “Scheduling two parallel semiautomatic machines to minimize machine interference”, Comput. Oper. Res. 23 (1996) 945956; doi:10.1016/0305-0548(96)00011-1.
[10] Kravchenko, S. and Werner, F., “Parallel machine scheduling problems with a single server”, Math. Comput. Modelling 26 (1997) 111; doi:10.1016/S0895-7177(97)00236-7.
[11] Ou, J., Qi, X. and Lee, C., “Parallel machine scheduling with multiple unloading servers”, J. Sched. 13 (2010) 213226; doi:10.1007/s10951-009-0104-1.
[12] Su, C., “Online LPT algorithms for parallel machines scheduling with a single server”, J. Comb. Optim. 26 (2013) 480488; doi:10.1007/s10878-011-9441-z.
[13] Wang, G. and Cheng, T. C. E., “An approximation algorithm for parallel machine scheduling with a common server”, J. Oper. Res. Soc. 52 (2001) 234237; doi:10.1057/palgrave.jors.2601074.
[14] Werner, F. and Kravchenko, S., “Scheduling with multiple servers”, Autom. Remote Control 71 (2010) 21092121; doi:10.1134/S0005117910100103.
[15] Xie, X., Li, Y., Zhou, H. and Zheng, Y., “Scheduling parallel machines with a single server”, in: Measurement, information and control (MIC) (IEEE, Harbin, China, 2012) 453456; doi:10.1109/MIC.2012.6273340.
[16] Zhang, L. and Wirth, A., “On-line scheduling of two parallel machines with a single server”, Comput. Oper. Res. 36 (2009) 15291553; doi:10.1016/j.cor.2008.02.015.
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