Advertisement

Journal of Intelligent Manufacturing

, Volume 26, Issue 6, pp 1085–1098 | Cite as

A mathematical model and genetic algorithm to cyclic flexible job shop scheduling problem

  • Amir Jalilvand-Nejad
  • Parviz FattahiEmail author
Article

Abstract

Product orders are usually released with a cyclic manner, in the part manufacturing industries. Hence, scheduling cyclic jobs instead of single jobs is more practical in the real manufacturing environment. In this paper, a flexible job shop scheduling problem with cyclic jobs is studied. In this problem, jobs must be delivered in determined batch sizes with definite time intervals. This problem is practical for many manufacturing systems such as automotive parts making industries. Whereas jobs are repeating infinitely during time, a framework is suggested to break down the infinite programming horizon to smaller periods. Then a mixed integer linear programming (MILP) model is presented to schedule jobs in this short term horizon. The goal of the proposed model is minimizing the total cost including delay costs, setup costs and holding costs. Since the problem is well-known as NP-hard class, the proposed MILP model is effective just for small size problems. Therefore, two algorithms based on genetic and simulated annealing (SA) algorithms are developed to solve real size problems. The numerical experiments are used to evaluate the performance of the developed algorithms. Results show that the proposed genetic algorithm (GA) has a better performance than the SA algorithm. Also some intelligent approaches are presented and examined in the proposed algorithms. Results show the efficiency of the presented intelligent approaches as mutation operators for the proposed GA.

Keywords

Cyclic scheduling problem Flexible job shop Mixed integer linear programming Genetic algorithm Simulated annealing 

References

  1. Bahroun, Z., Baptiste, P., Campagne, J. P., & Moalla, M. (1999). Production planning and scheduling in the context of cyclic delivery schedules. Computers and Industrial Engineering, 37(1), 3–7.Google Scholar
  2. Brucker, P., & Kampmeyer, T. (2008a). A general model for cyclic machine scheduling problems. Discrete Applied Mathematics, 156(13), 2561–2572.Google Scholar
  3. Brucker, P., & Kampmeyer, T. (2008b). Cyclic job shop scheduling problem with blocking. Journal of Intelligent Manufacturing, 159(1), 161–181.zbMATHMathSciNetGoogle Scholar
  4. Cavory, G., Dupas, R., & Goncalves, G. (2005). A genetic approach to solving the problem of cyclic job shop scheduling with linear constraints. European Journal of Operational Research, 161(1), 73–85.zbMATHMathSciNetCrossRefGoogle Scholar
  5. Fattahi, P., SaidiMehrabad, M., & Jolai, F. (2007). Mathematical modeling and heuristic approaches to flexible job shop scheduling problems. Journal of Intelligent Manufacturing, 18(3), 331–342.CrossRefGoogle Scholar
  6. Fattahi, P., Jolai, F., & Arkat, J. (2009). Flexible job shop scheduling with overlapping in operations. Applied Mathematical Modeling, 33(7), 3076–3087.zbMATHCrossRefGoogle Scholar
  7. Hanen, C. (1994). Study of a NP-hard cyclic scheduling problem: The recurrent job shop. European Journal of Operational Research, 72(1), 82–101.zbMATHCrossRefGoogle Scholar
  8. Hanen, C., & Munier, A. (1997). Cyclic scheduling on parallel processors: An overview. In P. Chretienne, E. G. Coffman, J. K. Lenstra, & Z. Liu (Eds.), Scheduling theory and its applications. New York: Wiley.Google Scholar
  9. Kacem, I., Hammadi, S., & Borne, P. (2002). Approach by localization and multiobjective evolutionary optimization for flexible job shop scheduling problems. IEEE Transactions on Systems, Man and Cybernetics, Part C, 32(1), 1–13.CrossRefGoogle Scholar
  10. Leung, J. (2004). Handbook of scheduling algorithms, models and performance analysis. Boca Raton, FL, USA: CRC Press.zbMATHGoogle Scholar
  11. Ouenniche, J., & Bertrand, J. W. M. (2001). The finite horizon economic lot sizing problem in job shops: The multiple cycle approach. International Journal of Production Economics, 74(1), 49–61.Google Scholar
  12. Pezzella, F., Morganti, G., & Ciaschetti, G. (2008). A genetic algorithm for the flexible job shop scheduling problem. Computers and Operations Research, 35(10), 3202–3212.zbMATHCrossRefGoogle Scholar
  13. Romanova, A. A., & Servakh, V. V. (2009). Optimization of processing identical jobs by means of cyclic schedules. Journal of Intelligent Manufacturing, 3(4), 496–504.MathSciNetGoogle Scholar
  14. Roundy, R. (1992). Cyclic schedules for job shops with identical jobs. Mathematics of Operations Research, 17(4), 842–865.zbMATHMathSciNetCrossRefGoogle Scholar
  15. Song, J.-S., & Lee, T.-E. (1998). Petri net modeling and scheduling for cyclic job shop with blocking. Computers and Industrial Engineering, 34(2), 281–295.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Industrial Engineering, Faculty of EngineeringBu-Ali Sina UniversityHamedanIran

Personalised recommendations