Abstract
In this study, one variant of multi-product scheduling problem is considered. The problem asks to find the optimal selection of a set of tasks to produce a given number of products in required amounts, to allocate the task on units, and to find the order of execution of tasks for each unit. The production rates for each task, the task-unit suitability matrix, and the sequence dependent changeover times for task pairs are given.
For the one-unit problem, two combinatorial algorithms are proposed: a branch-and-bound algorithm and a parallel dynamic programming algorithm. The last one is implemented using the CUDA library for running on a Graphical Processing Unit (GPU). For the multiple-units problem, both approaches are combined in a branch-and-bound algorithm with bounds provided by the dynamic programming procedure.
The algorithms are compared with CPLEX solver applied to the considered problem formulated as a mixed integer linear program. Although, the main limitation of using the proposed algorithms is a requirement of large amount of memory, the experiments showed their superior performance over CPLEX in terms of running time for rather large sized instances. The advantage of parallelization and using the GPU is also demonstrated.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Allahverdi, A., Ng, C.T., Cheng, T.C.E., Kovalyov, M.Y.: A survey of scheduling problems with setup times or costs. Eur. J. Oper. Res. 187, 985–1032 (2008)
Berger, K.-E., Galea, F.: An efficient parallelization strategy for dynamic programming on GPU. In: 2013 IEEE 27th International Symposium on Parallel and Distributed Processing Workshops and PhD Forum, Boston, USA, pp. 1797–1806 (2013)
Borisovsky, P.A.: A genetic algorithm for one production scheduling problem with setup times. In: Proceedings of XIV Baikal International School-seminar Optimization Methods and Their Applications, vol. 4, pp. 166–172. Melentiev Energy Systems Institute SB RAS, Irkutsk, Russia (2008). (In Russian)
Borisovsky, P.A.: A Branch-and-Bound algorithm for one multi-product single-machine scheduling problem. In: Proceeding of 11 International Workshop on CSIT (CSIT 2009), vol 2, pp. 223–227. UFA: USATU Editorial-Publishing Office, Russia (2009)
Borisovsky, P.A., Eremeev, A.V., Kallrath, J.: On hybrid method for medium-term multi-product continuous plant scheduling. In: Proceedings of 2017 International Multi-Conference on Engineering, Computer and Information Sciences (SIBIRCON), Novosibirsk, Russia, pp. 42–47 (2017)
Dolgui, A., Eremeev, A.V., Kovalyov, M.Y., Kuznetsov, P.M.: Multi-product lot sizing and scheduling on unrelated parallel machines. IIE Trans. 42(7), 514–524 (2010)
Held, M., Karp, R.M.: A dynamic programming approach to sequencing problems. J. Soc. Ind. Appl. Math. 10, 196–210 (1962)
Ierapetritou, M.G., Floudas, C.A.: Effective continuous-time formulation for short-term scheduling: I. Multipurpose batch processes. Ind. Eng. Chem. Res. 37, 4341–4359 (1998)
Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G., Shmoys, D.B.: The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization. Wiley, Chichester (1985)
Shaik, M.A., Floudas, C.A., Kallrath, J., Pitz, H.-J.: Production scheduling of a large-scale industrial continuous plant: short-term and medium-term scheduling. Comput. Chem. Eng. 33, 670–686 (2009)
Acknowledgments
The work was supported by the program of fundamental scientific research of the SB RAS No. I.5.1., project No. 0314-2016-0019.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Borisovsky, P. (2018). Exact Solution of One Production Scheduling Problem. In: Eremeev, A., Khachay, M., Kochetov, Y., Pardalos, P. (eds) Optimization Problems and Their Applications. OPTA 2018. Communications in Computer and Information Science, vol 871. Springer, Cham. https://doi.org/10.1007/978-3-319-93800-4_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-93800-4_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-93799-1
Online ISBN: 978-3-319-93800-4
eBook Packages: Computer ScienceComputer Science (R0)