Job Block Scheduling with Dual Criteria and Sequence-Dependent Setup Time Involving Transportation Times

  • Deepak Gupta
  • Kewal Krishan Nailwal
  • Sameer Sharma
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 246)


A two-machine flowshop scheduling with sequence-dependent setup time (SDST), job block, and transportation time is considered with the objective of minimizing makespan and the rental cost of machines taken on rent under a specified rental policy. The processing time of attributes on these machines is associated with probabilities. To find the optimal or near-optimal solution for these objectives, a heuristic algorithm is developed. To test the efficiency of the proposed heuristic algorithm, a numerical illustration is given.


Scheduling Makespan Job block Sequence-dependent setup time Processing time Transportation time Rental cost Utilization time 


  1. 1.
    A. Allahverdi, J.N.D. Gupta, T. Aldowaisan, “A review of scheduling research involving setup considerations”, OMEGA, The International Journal of Management Sciences, 27, 1999, pp. 219–239.Google Scholar
  2. 2.
    A. Allahverdi, C.T. Ng, T.C.E. Cheng, M.Y. Kovalyov, “A survey of scheduling problems with setup times or costs”, European Journal of Operational Research, 187, 2008, pp. 985–1032.Google Scholar
  3. 3.
    P.C. Bagga and A. Bhambani, “Bicriteria in flow shop scheduling problem”, Journal of Combinatorics, Information and System Sciences, 22, 1999, pp. 63–83.Google Scholar
  4. 4.
    K.R. Baker, “Introduction to Sequencing and Scheduling”, Wiley: New York, 1974.Google Scholar
  5. 5.
    H.G. Campbell, R.A. Dudek, and M.L. Smith, “A heuristic algorithm for the n-job, m-machine sequencing problem”, Management Science, 16, 1970, pp. 630–637.Google Scholar
  6. 6.
    B.D. Crown and A.O. Esogbue, “Two machine flow shop scheduling problems with sequence dependent setup time: a dynamic programming approach”, Naval Research Logistics Quarterly, 21, 1974, pp. 515–523.Google Scholar
  7. 7.
    C. Gagne, W.L. Price, M. Gravel, “Comparing an ACO algorithm with other heuristics for the single machine scheduling problem with sequence-dependent setup times”, Journal of the Operational Research Society 53, 2002, pp. 895–906.Google Scholar
  8. 8.
    Y. Gajpal, C. Rajendran and H. Ziegler, “An ant colony algorithm for scheduling in flow shop with sequence dependent set times of jobs”, The international Journal of Advanced Manufacturing Technology, 30(5-6), 2006, pp. 416–424.Google Scholar
  9. 9.
    D. Gupta, S. Sharma, Seema and Shefali, “nx2 bicriteria flowshop scheduling under specified rental policy, processing time and setup time each associated with probabilities including job block”, European Journal of Business and Management, 3(3) (2012) pp. 268–286.Google Scholar
  10. 10.
    D. Gupta, S. Sharma, Seema and K.K. Nailwal, “A bicriteria two machine flowshop scheduling with sequence dependent setup time”, International Journal of Mathematical Sciences, 11(3-4), 2012, pp. 183–196.Google Scholar
  11. 11.
    D. Gupta, S. Sharma, Seema and K.K. Nailwal, “Bicriteria job block scheduling with sequence dependent setup time”, Proceedings of the International Conference on Optimization, Computing and Business Analytics, 2012, pp. 8-13.Google Scholar
  12. 12.
    J.N.D. Gupta and W.P. Darrow, “The two machine sequence dependent flowshop scheduling problem”, European Journal of Operational Research, 24(3) (1974) 439–446.Google Scholar
  13. 13.
    S.R. Gupta, J.S. Smith, “Algorithms for single machine total tardiness scheduling with sequence dependent setups”, European Journal of Operational Research, 175, 2006, pp. 722–739.Google Scholar
  14. 14.
    S.M. Johnson, “Optimal two and three stage production schedule with set up times included”, Naval Research Logistics Quarterly. 1(1) (1954) 61–68.Google Scholar
  15. 15.
    P.L. Maggu and G. Das, “Equivalent jobs for job block in job scheduling”, Opsearch, 14(4) (1977) 277–281.Google Scholar
  16. 16.
    P.L. Maggu P and G. Das, “Elements of Advanced Production Scheduling”, United Publishers and Periodical Distributors, 1985.Google Scholar
  17. 17.
    M. Nawaz, Jr.E.E. Enscore and I. Ham, “A heuristic algorithm for the m-machine n-job flowshop sequencing problem”, OMEGA, International Journal of Management Science, 11, 1983, pp. 91–95.Google Scholar
  18. 18.
    D.S. Palmer, “Sequencing jobs through a multi-stage process in the minimum total time - a quick method of obtaining a near-optimum”, Operational Research Quarterly, 16(1) (1965) 101–107.Google Scholar
  19. 19.
    M.L. Pinedo, “Scheduling: Theory, Algorithms, and Systems”, Third Edition, Springer, 2008.Google Scholar
  20. 20.
    G. Rabadi, M. Mollaghasemi, and G.C. Anagnostopoulos, “A branch-and-bound algorithm for the early/tardy machine scheduling problem with a common due-date and sequence dependent setup time”, Computers and Operations Research 31, 2004, pp. 1727–1751.Google Scholar
  21. 21.
    C. Rajendran, H. Ziegler, “A heuristic for scheduling to minimize the sum of weighted flowtime of jobs in a flowshop with sequence-dependent setup times of jobs”, Computers and Industrial Engineering 33, 1997, pp. 281–284.Google Scholar
  22. 22.
    R.Z. Rıos-Mercado, J.F. Bard, “A branch-and-bound algorithm for permutation flow shops with sequence-dependent setup times”, IIE Transactions 31, 1999, pp. 721–731.Google Scholar
  23. 23.
    K.C. Tan, R. Narasimhan, “Minimizing tardiness on a single processor with sequence-dependent setup times: A simulated annealing approach”, OMEGA, 25, 1997, pp. 619–634.Google Scholar
  24. 24.
    L.N. Van Wassenhove and L.F. Gelders, “Solving a bicriteria scheduling problem”, AIIE Tran 15 s, 1980, pp. 84–88.Google Scholar

Copyright information

© Springer India 2014

Authors and Affiliations

  • Deepak Gupta
    • 1
  • Kewal Krishan Nailwal
    • 2
  • Sameer Sharma
    • 3
  1. 1.M. M. University, MullanaAmbalaIndia
  2. 2.A. P. J. College of Fine ArtsJalandhar CityIndia
  3. 3.D. A. V. CollegeJalandhar CityIndia

Personalised recommendations