A Mathematical Model and a Firefly Algorithm for an Extended Flexible Job Shop Problem with Availability Constraints

  • Willian Tessaro LunardiEmail author
  • Luiz Henrique Cherri
  • Holger Voos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10841)


Manufacturing scheduling strategies have historically ignored the availability of the machines. The more realistic the schedule, more accurate the calculations and predictions. Availability of machines will play a crucial role in the Industry 4.0 smart factories. In this paper, a mixed integer linear programming model (MILP) and a discrete firefly algorithm (DFA) are proposed for an extended multi-objective FJSP with availability constraints (FJSP-FCR). Several standard instances of FJSP have been used to evaluate the performance of the model and the algorithm. New FJSP-FCR instances are provided. Comparisons among the proposed methods and other state-of-the-art reported algorithms are also presented. Alongside the proposed MILP model, a Genetic Algorithm is implemented for the experiments with the DFA. Extensive investigations are conducted to test the performance of the proposed model and the DFA. The comparisons between DFA and other recently published algorithms shows that it is a feasible approach for the stated problem.


Firefly algorithm Flexible job-shop scheduling Metaheuristics Mixed integer linear programming Availability constraints 


  1. 1.
    Bagheri, A., Zandieh, M., Mahdavi, I., Yazdani, M.: An artificial immune algorithm for the flexible job-shop scheduling problem. Future Gener. Comput. Syst. 26(4), 533–541 (2010)CrossRefGoogle Scholar
  2. 2.
    Demir, Y., İşleyen, S.K.: Evaluation of mathematical models for flexible job-shop scheduling problems. Appl. Math. Model. 37(3), 977–988 (2013)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Gao, J., Gen, M., Sun, L.: Scheduling jobs and maintenances in flexible job shop with a hybrid genetic algorithm. J. Intell. Manuf. 17(4), 493–507 (2006)CrossRefGoogle Scholar
  4. 4.
    Gao, K.Z., Suganthan, P.N., Chua, T.J., Chong, C.S., Cai, T.X., Pan, Q.K.: A two-stage artificial bee colony algorithm scheduling flexible job-shop scheduling problem with new job insertion. Expert Syst. Appl. 42(21), 7652–7663 (2015)CrossRefGoogle Scholar
  5. 5.
    Kacem, I., Hammadi, S., Borne, P.: Pareto-optimality approach for flexible job-shop scheduling problems: hybridization of evolutionary algorithms and fuzzy logic. Math. Comput. Simul. 60(3), 245–276 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Li, J.Q., Pan, Q.K., Gao, K.Z.: Pareto-based discrete artificial bee colony algorithm for multi-objective flexible job shop scheduling problems. Int. J. Adv. Manuf. Technol. 55(9), 1159–1169 (2011)CrossRefGoogle Scholar
  7. 7.
    Lunardi, W.T., Voos, H.: Comparative study of genetic and discrete firefly algorithm for combinatorial optimization. In: 33rd ACM/SIGAPP Symposium on Applied Computing, Pau, France, 9–13 April 2018 (2018)Google Scholar
  8. 8.
    Özgüven, C., Özbakır, L., Yavuz, Y.: Mathematical models for job-shop scheduling problems with routing and process plan flexibility. Appl. Math. Model. 34(6), 1539–1548 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Wang, S., Yu, J.: An effective heuristic for flexible job-shop scheduling problem with maintenance activities. Comput. Ind. Eng. 59(3), 436–447 (2010)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Xia, W., Wu, Z.: An effective hybrid optimization approach for multi-objective flexible job-shop scheduling problems. Comput. Ind. Eng. 48(2), 409–425 (2005)CrossRefGoogle Scholar
  11. 11.
    Xing, L.N., Chen, Y.W., Yang, K.W.: Multi-objective flexible job shop schedule: design and evaluation by simulation modeling. Appl. Soft Comput. 9(1), 362–376 (2009)CrossRefGoogle Scholar
  12. 12.
    Yuan, Y., Xu, H.: Multiobjective flexible job shop scheduling using memetic algorithms. IEEE Trans. Autom. Sci. Eng. 12(1), 336–353 (2015)CrossRefGoogle Scholar
  13. 13.
    Zhang, G., Shao, X., Li, P., Gao, L.: An effective hybrid particle swarm optimization algorithm for multi-objective flexible job-shop scheduling problem. Comput. Ind. Eng. 56(4), 1309–1318 (2009)CrossRefGoogle Scholar
  14. 14.
    Zribi, N., El Kamel, A., Borne, P.: Minimizing the makespan for the MPM job-shop with availability constraints. Int. J. Prod. Econ. 112(1), 151–160 (2008)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Interdisciplinary Centre for Security, Reliability and Trust (SnT)University of LuxembourgLuxembourg CityLuxembourg
  2. 2.Institute of Mathematics and Computer Sciences (ICMC)University of São PauloSão PauloBrazil

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