Abstract
Wang et al. (J Operat Res Soc 62: 1898–1902, 2011) studied the m identical parallel-machine and unrelated parallel-machine scheduling with a deteriorating maintenance activity to minimize the total completion time. They showed that each problem can be solved in O(n 2m+3) time, where n is the number of jobs. In this note, we discuss the unrelated parallel-machine setting and show that the problem can be optimally solved by a lower order algorithm.
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Beyranvand, M.S., Reza Peyghami, M., Ghatee, M.: On the quadratic model for unrelated parallel machine scheduling problem with restrictive common due date. Optim. Lett. doi:10.1007/s11590-011-0385-0 (2011)
Brucker P.: Scheduling Algorithms. Springer-Verlag, Berlin (2007)
Cheng T.C.E., Hsu C.J., Yang D.L.: Unrelated parallel-machine scheduling with deteriorating maintenance activities. Comput. Indus. Eng. 60, 602–605 (2011)
Gawiejnowicz S.: Time-Dependent Scheduling. Springer-Verlag, Berlin (2008)
Kubzin M.A., Strusevich V.A.: Planning machine maintenance in two-machine shop scheduling. Operat. Res. 54, 789–800 (2006)
Lee C.Y., Leon V.J.: Machine scheduling with a rate-modifying activity. Eur. J. Operat. Res. 129, 119–128 (2001)
Lee C.Y., Yu G.: Parallel-machine scheduling under potential disruption. Optim. Lett. 2, 27–37 (2008)
Li C.L.: Viewpoints: a note on unrelated parallel machine scheduling with time-dependent processing times. J. Operat. Res. Soc. 59, 1696–1697 (2008)
Ma Y., Chu C., Zuo C.: A survey of scheduling with deterministic machine availability constraints. Comput. Indus. Eng. 58, 199–211 (2010)
Mosheiov G., Sidney J.B.: Scheduling a deteriorating maintenance activity on a single machine. J. Operat. Res. Soc. 61, 882–887 (2010)
Pardalos P.M.: Complexity in Numerical Optimization. World Scientific, Singapore (1993)
Ravetti M.G., Mateus G.R., Rocha P.L., Pardalos P.M.: A scheduling problem with unrelated parallel machines and sequence dependent setups. Int. J. Operat. Res. 2(4), 380–399 (2007)
Rocha P.L., Ravetti M.G., Mateus G.R., Pardalos P.M.: Exact algorithms for a scheduling problem with unrelated parallel machines and sequence and machine-dependent setup times. Comput. Operat. Res. 35(4), 1250–1264 (2008)
Setamaa-Karkkainen A., Miettinen K., Vuori J.: Heuristic for a new multiobjective scheduling problem. Optim. Lett. 1, 213–225 (2007)
Wang J.-J., Wang J.-B., Liu F.: Parallel machines scheduling with a deteriorating maintenance activity. J. Operat. Res. Soc. 62, 1898–1902 (2011)
Wang J.-B., Wang M.-Z.: Worst-case behavior of simple sequencing rules in flow shop scheduling with general position-dependent learning effects. Ann. Operat. Res. 191, 155–169 (2011)
Wang J.-B., Wang M.-Z.: Single-machine scheduling with nonlinear deterioration. Optim. Lett. 6, 87–98 (2012)
Wang, J.-B., Ji, P., Cheng, T.C.E., Wang, D.: Minimizing makespan in a two-machine flow shop with effects of deterioration and learning. Optim. Lett. doi:10.1007/s11590-011-0334-y (2011)
Wang, J.-B., Wang, X.-Y., Sun, L.-H., Sun, L.-Y.: Scheduling jobs with truncated exponential learning functions. Optim. Lett. doi:10.1007/s11590-011-0433-9 (2011)
Wang J.-B., Wei C.-M.: Parallel machines scheduling with a deteriorating maintenance activity and total absolute differences penalties. Appl. Math. Comput. 217, 8093–8099 (2011)
Wang J.-B., Wu Y.-B., Ji P.: A revision of some single-machine and m-machine flowshop scheduling problems with learning considerations. Inform. Sci. 190, 227–232 (2012)
Zhao C.-L., Tang H.-Y.: A note on two-machine no-wait flow shop scheduling with deteriorating jobs and machine availability constraints. Optim. Lett. 5, 183–190 (2011)
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Wang, LY., Huang, X., Ji, P. et al. Unrelated parallel-machine scheduling with deteriorating maintenance activities to minimize the total completion time. Optim Lett 8, 129–134 (2014). https://doi.org/10.1007/s11590-012-0472-x
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DOI: https://doi.org/10.1007/s11590-012-0472-x