Abstract
In this paper we deal with different models of production lines of factories and consider the makespan optimization problem based on these models. We consider state-of-the-art and novel mathematical optimizers including exact and heuristic methods. We apply these optimizers to both standard academic and industrial data sets. We see that in a large rate of the considered cases the novel exact optimizers converged to the optimum fast which is surprising being the problems NP-hard and the problem sizes big. This shows the importance of exploiting the structure present in the industrial data using standardized industrial data sets for testing mathematical algorithms devoted to solve industrial problems and that some provided exact mathematical optimizers are fast and perform accurately on the considered industrial problems.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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
Baker, K.R.: Introduction to Sequencing and Scheduling. Wiley, New York (1974)
Hajba, T., Horváth, Z.: New effective MILP models for PFSPs arising from real applications. Cent. J. Oper. Res. 21, 729–744 (2012)
Hajba, T., Horváth, Z.: MILP models for the optimization of real production lines. Cent. J. Oper. Res. 23, 899–912 (2015)
Johnson, S.M., Optimal two -and three stage production schedules with setup times included. Nav. Res. Logist. Q. 1(1), 61–68 (1954)
Jósvai, J.: Production process modeling and planning with simulation method, mounting process optimisation. In: The International Conference on Modeling and Applied Simulation. Universidad de La Laguna, 23–25 September 2009, pp. 240–245 (2009)
Kan, A.H.G.R.: Machine Scheduling Problems: Classifications, Complexity and Computation. Nijhoff, The Hague (1976)
Lageweg, B.J., Lenstra, J.K., Kan, A.H.G.R.: A general bounding scheme for the permutation flow-shop problem. Oper. Res. 26, 53–67 (1978)
Liao, C.L., You, C.T.: An improved formulation for the job-shop scheduling problem. J. Oper. Res. Soc. 43, 1047–1054 (1992)
Manne, A.S.: On the job-shop scheduling problem. Oper. Res. 8, 219–223 (1960)
Nawaz, M., Enscore, E.E., Ham, I.: A heuristic algorithm for the m-machine n-job flow-shop sequencing problem. Omega 11, 91–95 (1983)
Nowicki, E., Smutnicki, C.: A fast tabu search algorithm for the permutation flow-shop problem. Eur. J. Oper. Res. 91, 160–175 (1996)
Pan, C.H.: A study of integer programming formulations for scheduling problems. Int. J. Sys. Sci. 28, 33–41 (1997)
Rajendran, C., Ziegler, H.: Ant-colony algorithms for permutation flowshop scheduling to minimize total makespan/total flowtime of jobs. Eur. J. Oper. Res. 155, 426–438 (2004)
Stafford, E.F.: On the development of a mixed-integer linear programming model for the flowshop sequencing problem. J. Oper. Res. Soc. 39, 1163–1174 (1988)
Stafford, E.F., Tseng, F.T.: On the Strikar-Gosh MILP model for the N × M SDST flowshop problem. Int. J. Prod. Res. 28, 1817–1830 (1990)
Stafford, E.F., Tseng, F.T.: Two models for a family of flowshop sequencing problems. Eur. J. Opr. Res. 142, 282–293 (2002)
Stafford, E.F., Tseng, F.T.: New MILP models for the permutation flowshop problem. J. Oper. Res. Soc. 59, 1373–1386 (2008)
Stafford, E.F., Tseng, F.T., Gupta, N.D.: An empirical anlysis of integer programming formulations for the permutation flowshop. Omega 32, 285–293 (2004)
Stafford, E.F., Tseng, F.T., Gupta, N.D.: Comparative evaluation of the MILP Flowshop models. J. Opr. Res. Soc. 56, 88–101 (2005)
Taillard, E.: Benchmarks for basic scheduling problems. Eur. J. Oper. Res. 64, 278–285 (1993)
VDI: Digital Factory Fundamentals. VDI 4499 Guideline, Düsseldorf (2008)
Wagner, H.M.: An integer linear-programming model for machine scheduling. Nav. Res. Log. Q. 6, 131–140 (1959)
Wilson, J.M.: Alternative formulations of a flow-shop scheduling problem. J. Oper. Res. Soc. 40, 395–399 (1989)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Hajba, T., Horváth, Z., Kiss-Tóth, C., Jósvai, J. (2017). Production Line Optimization with Model Based Methods. In: Ghezzi, L., Hömberg, D., Landry, C. (eds) Math for the Digital Factory. Mathematics in Industry(), vol 27. Springer, Cham. https://doi.org/10.1007/978-3-319-63957-4_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-63957-4_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-63955-0
Online ISBN: 978-3-319-63957-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)