Abstract
The paper establishes the NP-hardness in the strong sense of a two-machine flow shop scheduling problem with unit execution time (UET) operations, dynamic storage availability, job dependent storage requirements, and the objective to minimise the time required for the completion of all jobs, i.e. to minimise the makespan. Each job seizes the required storage space for the entire period from the start of its processing on the first machine till the completion of its processing on the second machine. The considered scheduling problem has several applications, including star data gathering networks and certain supply chains and manufacturing systems. The NP-hardness result is complemented by a polynomial-time approximation scheme (PTAS) and several heuristics. The presented heuristics are compared by means of computational experiments.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Berlińska, J.: Scheduling for data gathering networks with data compression: Berlińska. J. Eur. J. Oper. Res. 246, 744–749 (2015)
Berlińska, J.: Scheduling data gathering with maximum lateness objective. In: Wyrzykowski, R. et al. (eds.) PPAM 2017, Part II. LNCS, vol. 10778, pp. 135–144. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78054-2_13
Berlińska, J.: Heuristics for scheduling data gathering with limited base station memory. Ann. Oper. Res. (2019). https://doi.org/10.1007/s10479-019-03185-3. In press
Błażewicz, J., Kubiak, W., Szwarcfiter, J.: Scheduling unit-time tasks on flow-shops under resource constraints. Ann. Oper. Res. 16, 255–266 (1988)
Błażewicz J., Lenstra, J.K., Rinnooy Kan, A.H.G.: Scheduling subject to resource constraints: classification and complexity. Discret. Appl. Math. 5, 11–24 (1983)
Fernandez de la Vega, W., Lueker, G.S.: Bin packing can be solved within \(1+ \varepsilon \) in linear time. Combinatorica 1(4), 349–355 (1981)
Fung, J., Zinder, Y.: Permutation schedules for a two-machine flow shop with storage. Oper. Res. Lett. 44(2), 153–157 (2016)
Garey, M.R., Johnson, D.S.: Computers and intractability: a guide to the theory of NP-completeness. Freeman, San Francisco (1979)
Gu, H., Memar, J., Kononov, A., Zinder, Y.: Efficient Lagrangian heuristics for the two-stage flow shop with job dependent buffer requirements. J. Discret. Algorithms 52–53, 143–155 (2018)
Luo, W., Xu, Y., Gu, B., Tong, W., Goebel, R., Lin, G.: Algorithms for communication scheduling in data gathering network with data compression. Algorithmica 80(11), 3158–3176 (2018)
Röck, H.: Some new results in no-wait flow shop scheduling. Z. Oper. Res. 28(1), 1–16 (1984)
Süral, H., Kondakci, S., Erkip, N.: Scheduling unit-time tasks in renewable resource constrained flowshops. Z. Oper. Res. 36(6), 497–516 (1992)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Berlińska, J., Kononov, A., Zinder, Y. (2020). Two-Machine Flow Shop with a Dynamic Storage Space and UET Operations. In: Le Thi, H., Le, H., Pham Dinh, T. (eds) Optimization of Complex Systems: Theory, Models, Algorithms and Applications. WCGO 2019. Advances in Intelligent Systems and Computing, vol 991. Springer, Cham. https://doi.org/10.1007/978-3-030-21803-4_112
Download citation
DOI: https://doi.org/10.1007/978-3-030-21803-4_112
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-21802-7
Online ISBN: 978-3-030-21803-4
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)