Flow Shop Scheduling Problem of Minimizing Makespan with Bounded Processing Parameters

  • Meenakshi Sharma
  • Manisha Sharma
  • Sameer SharmaEmail author
  • Amit Kumar
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1138)


A three-machine flow shop scheduling problem of minimum makespan is addressed in this paper. The setup time and transportation time are considered as independent parameters of processing. Further, setup time, processing time and transportation time are considered to be stochastic rather than deterministic. It is observed that the actual value of these cannot be estimated in advance unless the processing of jobs is completed on each of the available machines and only prior information of lower and upper bounds is available. Since the exact value of the time required is not known in advance, there may not exist a unique optimal schedule of jobs. Therefore, it is desired to obtain the set of all dominating schedules and reduce the cardinality of solution set. To meet the claimed objective, the local and global dominance relations have been developed and the use of these relations is represented by numerical illustration.


Flow shop scheduling Dominance relation Bounded processing time Bounded setup and transportation time Makespan 



One of authors (Meenakshi Sharma) acknowledges the financial support provided by council of scientific and industrial research, New Delhi, India, in the form of SRF through grant number 09/135(0766)/2017-EMR-I.


  1. 1.
    S. Aggarwal, A. Gautam, D.K. Chauhan, L.M. Tiwari, S. Kapoor, A flow shop scheduling problem with transportation time and separated setup time of jobs. Procedia Eng. 38, 1327–1332 (2012)Google Scholar
  2. 2.
    A. Allahverdi, The third comprehensive survey on scheduling problems with setup times/costs. Eur. J. Oper. Res. 246, 345–378 (2015)MathSciNetCrossRefGoogle Scholar
  3. 3.
    A. Allahverdi, Three-machine flowshop scheduling problem to minimize total completion time with bounded setup and processing times. Decis. Mak. Manuf. Serv. 1(1–2), 5–23 (2017)Google Scholar
  4. 4.
    A. Allahverdi, F. Al-Anzi, A branch-and-bound algorithm for three-machine flowshop scheduling problem to minimize total completion time with separate setup times. Eur. J. Oper. Res. 169, 767–780 (2006)MathSciNetCrossRefGoogle Scholar
  5. 5.
    A. Allahverdi, Y.N. Sotskov, Two machine flowshop minimum length scheduling problem with random and bounded processing times. Int. Trans. Oper. Res. 10, 65–76 (2003)MathSciNetCrossRefGoogle Scholar
  6. 6.
    P.C. Bagga, K. Khurana, Two-machine flowshop with separated sequence-independent setup times: mean completion time criterion. Indian J. Manag. Syst. 2, 47–57 (1986)Google Scholar
  7. 7.
    A.B. Chandramauli, Heuristic approach for n-job 3 machine flow shop scheduling problem involving transportation time, breakdown and weights of jobs. Math. Comput. Appl. 10(2), 301–305 (2005)Google Scholar
  8. 8.
    X. Dong, H. Huang, P. Chen, An improved NEH-based heuristic for permutation flow shop problem. Comput. Oper. Res. 35, 3962–3968 (2008)CrossRefGoogle Scholar
  9. 9.
    R. Gangadharan, C. Rajendran, A simulated annealing heuristic for scheduling in a flowshop with bicriteria. Comput. Ind. Eng. 27, 473–476 (1994)CrossRefGoogle Scholar
  10. 10.
    M.R. Garey, J.R. Johnson, R. Sethi, The complexity of flowshop and jobshop scheduling. Math. Oper. Res. 1(2), 117–129 (1986)MathSciNetCrossRefGoogle Scholar
  11. 11.
    D. Gupta, S. Sharma, S. Sharma, Heuristic approach for n-jobs, 3-machines flow shop scheduling problem, processing time associated with probabilities involving transportation time, break-down interval, weightage of jobs and job block criteria. Math. Theory Model. 1(1), 30–36 (2011)Google Scholar
  12. 12.
    S.M. Johnson, Optimal two and three stage production schedules with setup time included. Naval Res. Log. Q. 1, 69–81 (1954)CrossRefGoogle Scholar
  13. 13.
    P.J. Kalczynski, J. Kamburowski, An improved NEH heuristic to minimize makespan in permutation flow shops. Comput. Oper. Res. 35, 3001–3008 (2009)MathSciNetCrossRefGoogle Scholar
  14. 14.
    W. Liu, Y. Jin, M. Price, A new improved NEH heuristic for permutation flowshop scheduling problems. Int. J. Product. Econ. 193, 21–30 (2017)CrossRefGoogle Scholar
  15. 15.
    P.L. Maggu, G. Das, Elements of Advanced Production Scheduling (UPPD, New Delhi, 1980)Google Scholar
  16. 16.
    A. Mittal, S. Agarwal, S. Prasad, S.R. Ansari, Heuristic approach for n jobs, 3 machines flow shop scheduling problem involving transportation time, equivalent job block, weight of jobs and break down internval. Int. J. Appl. Math. Appl. 3(1), 77–84 (2011)Google Scholar
  17. 17.
    M. Nawaz, E.E. Enscore, I. Ham, A heuristic algorithm for the m-machine, n-job flow-shop sequencing problem. Omega. 11(1), 91–95 (1983)Google Scholar
  18. 18.
    C. Rajendran, H. Ziegler, Ant colony algorithms for permutation flow shop scheduling to minimize makespan/ total flowtime of jobs. Eur. j. op. Res. 155(2), 426–438 (2004)Google Scholar
  19. 19.
    R. Ruiz, T. Stutzle. An iterated greedy algorithm for permutation flow shop scheduling problem. Eur. J. Oper. Res. 177(3), 2033-2049 (2007)Google Scholar
  20. 20.
    Y.N. Sotskov, A. Allahverdi, T.C. Lai, Flowshop scheduling problem to minimize total completion time with random and bounded processing times. J. Oper. Res. Soc. 55, 277–286 (2004)CrossRefGoogle Scholar
  21. 21.
    L. Wang, D.Z. Zheng, An effective hybrid heuristic for flow shop scheduling. Int. J. Adv. Manuf. Tech. 21, 38–44 (2003)CrossRefGoogle Scholar
  22. 22.
    K.C. Ying, S.-W. Lin, A high-performing constructive heuristic for minimizing makespan in permutation flowshops. Int. J. Product. Ind. Eng. 36(6), 355–362 (2014)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  • Meenakshi Sharma
    • 1
  • Manisha Sharma
    • 1
  • Sameer Sharma
    • 2
    Email author
  • Amit Kumar
    • 2
  1. 1.Department of MathematicsPanjab UniversityChandigarhIndia
  2. 2.Department of MathematicsD.A.V. CollegeJalandharIndia

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