Shen, Lixin; Wang, Dan; Wang, Xiao-Yuan Parallel-machine scheduling with non-simultaneous machine available time. (English) Zbl 1426.90138 Appl. Math. Modelling 37, No. 7, 5227-5232 (2013). Summary: We consider a problem of scheduling \(n\) independent jobs on \(m\) parallel identical machines. The jobs are available at time zero, but the machines may not be available simultaneously at time zero. We concentrate on two goals separately, namely, minimizing a cost function containing total completion time and total absolute differences in completion times; minimizing a cost function containing total waiting time and total absolute differences in waiting times. In this paper, we present polynomial time algorithm to solve this problem. Cited in 5 Documents MSC: 90B35 Deterministic scheduling theory in operations research Keywords:scheduling; parallel machines; machine availability constraint PDFBibTeX XMLCite \textit{L. Shen} et al., Appl. Math. Modelling 37, No. 7, 5227--5232 (2013; Zbl 1426.90138) Full Text: DOI References: [1] Lee, W.-C.; Wu, C.-C., A note on single-machine group scheduling problems with position-based learning effect, Appl. Math. Model., 33, 2159-2163, (2009) · Zbl 1205.90128 [2] Wang, J.-B.; Sun, L.-H.; Sun, L.-Y., Single machine scheduling with exponential sum-of-logarithm-processing-times based learning effect, Appl. Math. Model., 34, 2813-2819, (2010) · Zbl 1201.90088 [3] Lee, W.-C.; Wang, W.-J.; Shiau, Y.-R.; Wu, C.-C., A single-machine scheduling problem with two-agent and deteriorating jobs, Appl. Math. Model., 34, 3098-3107, (2010) · Zbl 1201.90080 [4] Wang, J.-B.; Guo, Q., A due-date assignment problem with learning effect and deteriorating jobs, Appl. Math. Model., 34, 309-313, (2010) · Zbl 1185.90099 [5] Wang, J.-B.; Li, J.-X., Single machine past-sequence-dependent setup times scheduling with general position-dependent and time-dependent learning effects, Appl. Math. Model., 35, 1388-1395, (2011) · Zbl 1211.90091 [6] Liu, P.; Yi, N.; Zhou, X., Two-agent single-machine scheduling problems under increasing linear deterioration, Appl. Math. Model., 35, 2290-2296, (2011) · Zbl 1217.90108 [7] Wang, X.-R.; Huang, X.; Wang, J.-B., Single-machine scheduling with linear decreasing deterioration to minimize earliness penalties, Appl. Math. Model., 35, 3509-3515, (2011) · Zbl 1221.90051 [8] Wei, C.-M.; Wang, J.-B.; Ji, P., Single-machine scheduling with time-and-resource-dependent processing times, Appl. Math. Model., 62, 792-798, (2012) · Zbl 1236.90059 [9] Bai, J.; Li, Z.-R.; Huang, X., Single-machine group scheduling with general deterioration and learning effects, Appl. Math. Model., 36, 1267-1274, (2012) · Zbl 1243.90055 [10] X.-R. Wang, J.-J. Wang, Single-machine scheduling with convex resource dependent processing times and deteriorating jobs, Appl. Math. Model., http://dx.doi.org/10.1016/j.apm.2012.05.025. · Zbl 1349.90416 [11] Lee, C.-Y., Parallel machines scheduling with nonsimultaneous machine available time, Disc. Appl. Math., 30, 53-61, (1991) · Zbl 0722.90032 [12] Deuermeyer, B. L.; Friesen, D. K.; Langston, M. A., Scheduling to maximize the minimum processor finish time in a multi-processor system, SIAM J. Algebraic Disc. Methods, 3, 190-196, (1982) · Zbl 0489.68031 [13] Lin, G.-H.; Yao, E.-Y.; He, Y., Parallel machine scheduling to maximize the minimum load with nonsimultaneous machine available times, Oper. Res. Lett., 22, 75-81, (1998) · Zbl 0912.90175 [14] Zhao, C.-L.; Tang, H.-Y.; Cheng, C.-D., Two-parallel machines scheduling with rate-modifying activities to minimize total completion time, Eur. J. Oper. Res., 198, 354-357, (2009) · Zbl 1163.90518 [15] Wang, J.-J.; Wang, J.-B.; Liu, F., Parallel machines scheduling with a deteriorating maintenance activity, J. Oper. Res. Soc., 62, 1898-1902, (2011) [16] Kanet, J. J., Minimizing variation of flow time in single machine systems, Manage. Sci., 27, 1453-1459, (1981) · Zbl 0473.90048 [17] Stirzaker, D., Elementary probability, (1995), Cambridge University Press Cambridge [18] Mosheiov, G., Parallel machine scheduling with a learning effect, J. Oper. Res. Soc., 52, 1165-1169, (2001) · Zbl 1178.90159 [19] Bagchi, U. B., Simultaneous minimization of mean and variation of flow-time and waiting time in single machine systems, Oper. Res., 37, 118-125, (1989) · Zbl 0661.90046 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.