Annals of Operations Research

, Volume 229, Issue 1, pp 743–758 | Cite as

RETRACTED ARTICLE: OSGA: genetic-based open-shop scheduling with consideration of machine maintenance in small and medium enterprises

  • Shahaboddin ShamshirbandEmail author
  • Mohammad Shojafar
  • A. A. Rahmani Hosseinabadi
  • Maryam Kardgar
  • M. H. N. Md. Nasir
  • Rodina Ahmad


The problem of open-shop scheduling includes a set of activities which must be performed on a limited set of machines. The goal of scheduling in open-shop is the presentation of a scheduled program for performance of the whole operation, so that the ending performance time of all job operations will be minimised. The open-shop scheduling problem can be solved in polynomial time when all nonzero processing times are equal, becoming equivalent to edge coloring that has the jobs and workstations as its vertices and that has an edge for every job-workstation pair with a nonzero processing time. For three or more workstations, or three or more jobs, with varying processing times, open-shop scheduling is NP-hard. Different algorithms have been presented for open-shop scheduling so far. However, most of these algorithms have not considered the machine maintenance problem. Whilst in production level, each machine needs maintenance, and this directly influences the assurance reliability of the system. In this paper, a new genetic-based algorithm to solve the open-shop scheduling problem, namely OSGA, is developed. OSGA considers machine maintenance. To confirm the performance of OSGA, it is compared with DGA, SAGA and TSGA algorithms. It is observed that OSGA performs quite well in terms of solution quality and efficiency in small and medium enterprises (SMEs). The results support the efficiency of the proposed method for solving the open-shop scheduling problem, particularly considering machine maintenance especially in SMEs’.


Timing Open-shop Scheduling Genetic Algorithm 



This work has been partially sponsored by University Malaya Research Grant under the grant no: RG327-15AFR and Grant (No. RG316-14AFR). We thank the reviewers and associate editor for their comments which improved this manuscript


  1. Alcaide, D., Sicilia, J., & Vigo, D. (1997). Atabu search algorithmfor the open-shop problem. Top, 5, 283–286.CrossRefGoogle Scholar
  2. Andresen, M., Brasel, H., Morig, M., Tusch, J., Werner, F., & Willenius, P. (2008). Simulated annealing and genetic algorithms for minimizing mean flow time in an open shop. Mathematical and Computer Modelling, 48, 1279–1293.CrossRefGoogle Scholar
  3. Baccarelli, E., Cordeschi, N., & Patriarca, T. (2012). QoS stochastic traffic engineering for the wireless support of real-time streaming applications. Computer Networks, 56(1), 287–302.CrossRefGoogle Scholar
  4. Baccarelli, E., Cordeschi, N., & Polli, V. (2013). Optimal self-adaptive qos resource management in interference-affected multicast wireless networks. IEEE/ACM Transactions on Networking (TON), 21(6), 1750–1759.CrossRefGoogle Scholar
  5. Brasel, H., Tautenhahn, T., & Werner, F. (1993). Constructive heuristic algorithms for the open-shop problem. Computing, 51, 95–110.CrossRefGoogle Scholar
  6. Brucker, P., Hurink, J., Jurish, B., & Wostmann, B. (1997). A branch and bound Algorithm for the open-shop problem. Discrete Applied Mathematics, 76, 43–59.CrossRefGoogle Scholar
  7. Chan, F. T. S., Chung, S. H., Chan, L. Y., Finke, G., & Tiwari, M. K. (2006). Solving distributed FMS scheduling problems subject to maintenance: Genetic algorithms approach. Robotics and Computer Integrated Manufacturing, 22, 5–6.Google Scholar
  8. Cheng, R., Gen, M., & Tsujimura, Y. (1996). A tutorial survey of job-shop scheduling problems using genetic algorithms-I. representation. Computers & Industrial Engineering, 30, 983–997.CrossRefGoogle Scholar
  9. Dorndorf, U., Pesch, E., & Phan-Huy, T. (2001). Solving the open-shop scheduling problem. Journal of Scheduling, 4, 157–174.CrossRefGoogle Scholar
  10. Glover, F., & Laguna, M. (1997). Tabu search. Norwell, MA: Kluwer Academic Publishers.CrossRefGoogle Scholar
  11. Gonzalez, S., & Sahni, T. (1976). Open-shop scheduling to minimize finish time. Journal of the Assooauon for Computing Machinery, 23, 665–679.CrossRefGoogle Scholar
  12. Gueret, C., & Prins, C. (1998). Classical and new heuristics for theshop problem: A computational evaluation. European Journal of Operational Research, 107, 306–314.CrossRefGoogle Scholar
  13. Hosseinabadi, A. A. R., Kardgar, M., Shojafar, M., Shamshirband, S., & Abraham, A. (2014a). GELS-GA: Hybrid metaheuristic algorithm for solving multiple travelling salesman problem (pp. 76–81). 14th IEEE ISDA.Google Scholar
  14. Hosseinabadi, A. A. R., Siar, H., Shamshirband, S., Shojafar, M., & Nasir M. H. N. M. (2014b). Using the gravitational emulation local search algorithm to solve the multi-objective flexible dynamic job shop scheduling problem in Small and Medium Enterprises. Annals of Operations Research, 1–24.Google Scholar
  15. Kordon, A. M., & Rebaine, D. (2010). The two-machine open-shop problem with unit-time operations and time delays to minimize the makespan. European Journal of Operational Research, 203, 42–29.CrossRefGoogle Scholar
  16. Kubiak, W., Sriskandarajah, C., & Zaras, V. (1991). A note on the complexity of open-shop scheduling problems. INFOR, 29, 284–294.Google Scholar
  17. Laarhoven, P. J. M., & Aarts, E. H. L. (1987). Simulated annealing: Theory and applications. Norwell, MA: Kluwer Academic Publishers.CrossRefGoogle Scholar
  18. Liaw, C. F. (2000). A hybrid genetic algorithm for the open-shop scheduling problem. European Journal of Operational Research, 124, 28–42.CrossRefGoogle Scholar
  19. Lina, H., Leeb, H., & Pan, W. (2008). Heuristics for scheduling in a no-wait open shop withmovable dedicated machines. International Journal of Production Economics, 111, 368–377.CrossRefGoogle Scholar
  20. Liu, C. Y., & Bulfin, R. L. (1987). Scheduling ordered open-shops. Computers & Operations Research, 14, 257–264.CrossRefGoogle Scholar
  21. Low, C., & Yeh, Y. (2009). Genetic algorithm-based heuristics for an open shop scheduling problem with setup, processing, and removal times separated. Robotics and Computer-Integrated Manufacturing, 25, 314–322.CrossRefGoogle Scholar
  22. Matta, M. E. (2009). A genetic algorithm for the proportionate multiprocessor open shop. Computers & Operations Research, 36, 2601–2618.CrossRefGoogle Scholar
  23. Matta, M. E., & Elmaghraby, S. E. (2010). Polynomial time algorithms for two special classes of the proportionate multiprocessor open shop. European Journal of Operational Research, 201, 720–728.CrossRefGoogle Scholar
  24. Panahi, H., & Moghaddam, R. T. (2011). Solving a multi-objective open shop scheduling problem by a novel hybrid ant colony optimization. Expert Systems with Applications, 38, 2817–2822.CrossRefGoogle Scholar
  25. Pinedo, M. (1995). Scheduling: Theory algorithms and systems. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
  26. Pooranian, Z., Harounabadi, A., Shojafar, M., & Hedayat, N. (2011). New hybrid algorithm for task scheduling in grid computing to decrease missed task. World Academy of Science, Engineering and Technology, 55, 924–928.Google Scholar
  27. Prins, C. (1994). An overview of scheduling problems arising in satellite communications. The Journal of the Operational Research Society, 45, 611–623.CrossRefGoogle Scholar
  28. Prins, C. (2000). Competitive genetic algorithms for the open-shop scheduling problem. Mathematical Methods of Operations Research, 52, 389–411.CrossRefGoogle Scholar
  29. Sha, D. Y., & Hsu, Ch Y. (2008). A new particle swarm optimization for the open shop scheduling problem. Computers & Operations Research, 35, 324–3261.CrossRefGoogle Scholar
  30. Taillard, E. (1993). Benchmarks for basic scheduling problems. European Journal of Operational Research, 64, 278–285.CrossRefGoogle Scholar
  31. Yadollahi, M., & Rahmani, A. M. (2009). Solving distributed flexible manufacturing systems scheduling problems subject to maintenance: Memetic algorithms approach. International Conference on Computer and Information Technology, 1, 36–41.Google Scholar
  32. Yu, W., Liu, Zh, Wang, L., & Fan, T. (2011). Routing open shop and flow shop scheduling problems. European Journal of Operational Research, 213, 24–36.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Shahaboddin Shamshirband
    • 1
    Email author
  • Mohammad Shojafar
    • 2
  • A. A. Rahmani Hosseinabadi
    • 3
  • Maryam Kardgar
    • 3
  • M. H. N. Md. Nasir
    • 4
  • Rodina Ahmad
    • 4
  1. 1.Department of Computer System and Technology, Faculty of Computer Science and Information TechnologyUniversity of MalayaKuala LumpurMalaysia
  2. 2.Department of Information Engineering Electronics and Telecommunications (DIET)Sapienza University of RomeRomeItaly
  3. 3.Young Research Club, Behshahr BranchIslamic Azad UniversityBehshahrIran
  4. 4.Department of Software Engineering, Faculty of Computer Science and Information TechnologyUniversity of Malaya (UM)Kuala LumpurMalaysia

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