Abstract
We consider the problem of scheduling a set of jobs with different processing times and sizes on a single bounded parallel-batch machine with periodic maintenance. Because the machine is in batch-processing model and the capacity is fixed, several jobs can be processed simultaneously in a batch provided that the total size of the jobs in the batch doesn’t exceed the machine capacity. And the processing time of a batch is the largest processing time of the jobs contained in the batch. Meanwhile, the production of each batch is non-resumable, that is, if a batch cannot be completed processing before some maintenance, that batch needs to be processed anew once the machine returns available. Our goal is to minimize the makespan. We first consider two special cases where the jobs have the same sizes or the same processing times, both of which are strongly NP-hard. We present two different approximation algorithms for them and show that these two algorithms have the same tight worst-case ratio of 2. We then consider the general case where the jobs have the arbitrary processing times and arbitrary sizes, for which we propose a 17/5-approximation algorithm.
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References
Cheng BY, Leung JYT, Li K, Yang SL (2015) Single batch machine scheduling with deliveries. Naval Res Logist 62:470–482
Dosa G, Li R, Han X, Tuza Z (2013) Tight absolute bound for first fit decreasing bin packing. Theor Comput Sci 510:13–61
Dosa G, Tan ZY, Tuza Z, Yan YJ, Lányi CS (2014) Improved bounds for batch scheduling with nonidentical job sizes. Naval Res Logist 61:351–358
Fan J, Lu XW (2015) Supply chain scheduling problem in the hospital with periodic working time on a single machine. J Comb Optim 30:892–905
Fan J, Ng CT, Cheng TCE, Shi H (2020) Single bounded parallel-batch machine scheduling with an unavailability constraint and job delivery, AAIM 2020. Lect Notes Comput Sci 12290:525–536
He Y, Ji M, Cheng TCE (2005) Single machine scheduling with a restricted rate-modifying activity. Naval Res Logist 52:361–369
Ji M, He Y, Cheng TCE (2007) Single-machine scheduling with periodic maintenance to minimize makespan. Comput Oper Res 34:1764–1770
Lee CY (1996) Machine scheduling with an availability constraints. J Global Optim 9:395–416
Liao CJ, Chen WJ (2003) Single-machine scheduling with periodic maintenance and nonresumable jobs. Comput Oper Res 30:1335–1347
Li WH, Chai X (2019) The medical laboratory scheduling for weighted flow-time. J Comb Optim 37:83–94
Liu LL, Fu CY (2020) A batch scheduling problem of automatic drug dispensing system in outpatient pharmacy, AAIM 2020. Lect Notes Comput Sci 12290:537–543
Low CY, Ji M, Hsu CJ, Su CT (2010) Minimizing the makespan in a single machine scheduling problems with flexible and periodic maintenance. Appl Math Model 34:334–342
Ma Y, Chu CB, Zuo CR (2010) A survey of scheduling with deterministic machine availability constraints. Comput Ind Eng 58:199–211
Uzsoy R (1994) A single batch processing machine with nonidentical job sizes. Int J Prod Res 32:1615–1635
Xu DH, Sun KB, Li HX (2008) Parallel machine scheduling with almost periodic maintenance and non-preemptive jobs to minimize makespan. Comput Oper Res 35:1344–1349
Yu XY, Zhang YL, Steiner G (2014) Single-machine scheduling with periodic maintenance to minimize makespan revisited. J Sched 17:263–270
Zade AE, Fakhrzad MB (2013) A dynamic genetic algorithm for solving a single machine scheduling problem with periodic maintenance. ISRN Ind Eng 5:1–11
Zhang GC, Cai XQ, Lee CY, Wong CK (2001) Minimizing makespan on a single batch processing machine with nonidentical job sizes. Naval Res Logist 48:226–240
Acknowledgements
The first author is also supported by the key discipline “Applied Mathematics”of Shanghai Polytechnic University (No.XXKPY1604).
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This research is supported in part by NSF of China (Grant Nos. 11601316 and 71520107003).
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Fan, J., Shi, H. Non-resumable scheduling on a single bounded parallel-batch machine with periodic maintenance. J Comb Optim 43, 1645–1654 (2022). https://doi.org/10.1007/s10878-021-00715-3
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DOI: https://doi.org/10.1007/s10878-021-00715-3