This article considers the single-machine serial-batching scheduling problem with a machine availability constraint, position-dependent processing time, and time-dependent set-up time. The objective of this problem is to make the decision of batching jobs and sequencing batches to minimize the makespan. To solve the problem, three cases of machine non-availability periods are considered, and the structural properties of the optimal solution are derived for each case. Based on these structural properties, an optimization algorithm is developed and an example is proposed to illustrate this algorithm.
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This work is supported by the National Natural Science Foundation of China (Nos. 71601065, 71231004, 71501058, 71131002, 71471052, 71521001, 71571058), the Humanities and Social Sciences Foundation of the Chinese Ministry of Education (No. 15YJC630097), Anhui Province Natural Science Foundation (No. 1608085QG167), and the Fundamental Research Funds for the Central Universities (Nos. JZ2016HGTA0709, JZ2016HGTB0727). Panos M. Pardalos is partially supported by the project of “Distinguished International Professor by the Chinese Ministry of Education” (MS2014HFGY026).
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Pei, J., Liu, X., Pardalos, P.M. et al. Single-machine serial-batching scheduling with a machine availability constraint, position-dependent processing time, and time-dependent set-up time. Optim Lett 11, 1257–1271 (2017). https://doi.org/10.1007/s11590-016-1074-9
- Availability constraint
- Position-dependent processing time