Abstract
This paper considers online scheduling on two unit flowshop machines, which there exists unbounded parallel-batch scheduling with incompatible job families and lookahead intervals. The unit flowshop machine means that the processing time of any job on each machine is unit processing time. The objective is to minimize the maximum completion time. The lookahead model means that an online algorithm can foresee the information of all jobs arriving in time interval \((t,t+\beta ]\) at time t. There exist incompatible job families, that is, jobs belonging to different families cannot be processed in the same batch. In this paper, we address the lower bound of the proposed problem, and provide a best possible online algorithm of competitive ratio \(1+\alpha _f\) for \(0\le \beta <1\), where \(\alpha _f\) is the positive root of the equation \({(f+1)} \alpha ^{2}+(\beta +2) \alpha +\beta -f=0\) and f is the number of incompatible job families which is known in advance.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Arman J, Philip MK (2021) Online scheduling to minimize total weighted (modified) earliness and tardiness cost. Journal of Scheduling 24:431–446
Chai X, Li WH, Zhu YJ (2021) Online scheduling to minimize maximum weighted flow-time on a bounded parallel-batch machine. Annals of Operations Research 298:79–93
Fu RY, Cheng TCE, Ng CT, Yuan JJ (2013) An optimal online algorithm for single parallel-batch machine scheduling with incompatible job families to minimize makespan. Operations Research Letters 216–219
Fu RY, Tian J, Yuan JJ (2009) On-line scheduling on an unbounded parallel batch machine to minimize makespan of two families of jobs. Journal of Scheduling 12:91–97
Fowler John W, Mönch Lars (2022) A survey of scheduling with parallel batch (p-batch) processing. European Journal of Operational Research 298:1–24
Jiao CW, Yuan JJ, Feng Q (2019) Online algorithms for scheduling unit length jobs on unbounded parallel-batch machines with linearly lookhead. Asia-Pacific Journal of Operational Research 36:1950024
Keskinocak P (1999) Online algorithms with lookahead. A survey, ISYE working paper
Lawler EL, Lenstra JK, Rinnooy Kan AHG, Shmoys DB (1993) Sequencing and scheduling: Algorithms and complexity. In Handbooks Operation Research and Management Science, Graves SC, Zipkin PH, Rinnooy Kan AHG (Eds.), Logistics of Production and Inventory, Vol. 4, pp. 445-522. Amsterdam: North-Holland
Li WH, Yuan JJ, Cao JF, Bu HL (2009) Online scheduling of unit length jobs on a batching machine to maximize the number of early jobs with lookahead. Theoretical Computer Science 410:5182–5187
Li WH, Yuan JJ, Yang SF (2014) Online scheduling of incompatible unit-length job families with lookahead. Theoretical Computer Science 543(10):120–125
Li WH, Zhai WN, Chai X, Gao C (2019) On-line bounded-batching scheduling of unit-length jobs with two incompatible families. Operations Research Transactions 23:105–110
Li WH, Zhang ZK, Yang SF (2012) Online algorithms for scheduling unit length jobs on parallel-batch machines with lookahead. Information Processing Letters 112:292–297
Lin R, Li WH, Chai X (2021) On-line scheduling with equal-length jobs on parallel-batch machines to minimise maximum flow-time with delivery times. Journal Of The Operational Research Society 72(8):1754–1761
Liu HL, Lu XW (2021) An Online Scheduling Problem on a Drop-Line Parallel Batch Machine with Delivery Times and Limited Restart. Asia-Pacific Journal of Operational Research 38(6):2150011
Mandelbaum M, Shabtay D (2011) Scheduling unit length jobs on parallel machines with lookahead information. Journal of Scheduling 14:335–350
Tian J, Cheng TCE, Ng CT, Yuan JJ (2009) Online scheduling on unbounded parallel-batch machines to minimize the makespan. Information Processing Letters 109:1211–1215
Xia Q, Zhang XG (2022) Online scheduling problem of two flow shop with lookahead interval and incompatible job family. Operations Research Transactions, https://kns.cnki.net/kcms/detail/31.1732.O1.20220424.1300.026.html
Yang SF, Li WH (2012) On-line scheduling on a machine of two families with lookahead. Operations Research Transactions 16:115–120
Zhang GC, Cai XQ, Wong CK (2001) On-line Algorithms for Minimizing Makespan on Batch Processing Machines. Naval Research Logistics 48:241–258
Zhang GC, Cai XQ, Wong CK (2003) Optimal online algorithms for scheduling on parallel batch processing machines. IIE Transactions 35:175–181
Zheng FF, Xu YF, Zhang E (2008) How much can lookahead help in online single machine scheduling. Information Processing Letters 106:70–74
Acknowledgements
This work was supported by the Natural Science Foundation of China [grant numbers 11991022, 11971443]; Key Research fund Projects of Chongqing Education [grant number KJZD-K202000501] and the Chongqing Municipal Science and Technology Commission of Natural Science Fund Projects[grant number cstc2021jcyj-msxmX0229].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Qian, X., Xingong, Z. Online scheduling of two-machine flowshop with lookahead and incompatible job families. J Comb Optim 45, 50 (2023). https://doi.org/10.1007/s10878-022-00974-8
Accepted:
Published:
DOI: https://doi.org/10.1007/s10878-022-00974-8