The Hybrid Flow Shop

  • Hamilton Emmons
  • George Vairaktarakis
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 182)


In this chapter we organize the literature on the hybrid flow shop scheduling problem that has appeared since the late 1950’s. We see a number of interesting and diverse industrial applications of this system, and find that the majority of research focuses on the makespan objective. Our coverage of results is exhaustive and categorized along concepts such as complexity, error-bound analyses, computational experiments and choice of objective. Several new results are included that have not appeared in the literature before. Surprisingly, existing research does not focus on the deterministic version of the problem alone, but also on the case of stochastic processing times.


Completion Time Idle Time Flow Shop Quay Crane Flow Shop Schedule Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Bish, E.K., F.Y. Chen, Y.T. Leong, B.L. Nelson, J.W.C. Ng and D. Simchi-Levi (2005) Dispatching Vehicles in a Mega Container Terminal, OR Spectrum, 27, 491–506.CrossRefGoogle Scholar
  2. 2.
    Brah, S.A. and J.L. Hunsucker (1991) Branch and Bound Algorithm for the Flow shop with Multiple Processors, European Journal of Operational Research, 51, 88–99.CrossRefGoogle Scholar
  3. 3.
    Buten, R.E. and V.Y. Shen (1973) A Scheduling Model for Computer Systems with Two Classes of Processors, Proceedings of the Sagamore Computer Conference on Parallel Processing, 130–138.Google Scholar
  4. 4.
    Campbell, H.G., R.A. Dudek and M.L. Smith (1970) A Heuristic Algorithm for the n Jobm Machine Sequencing Problem, Management Science, 16, B630–B637.CrossRefGoogle Scholar
  5. 5.
    Chang, S.-C. and D.-Y. Liao (1994) Scheduling Flexible Flow Shops with no Setup Effects, IEEE Transactions on Robotics and Automation, 10, 112–122.CrossRefGoogle Scholar
  6. 6.
    Chen, B. (1994) Scheduling Multiprocessor Flow Shops, New Advances in Optimization and Approximation, D.-Z. Du and J. Sun (Editors), Kluwer, Dordrecht, 1–8.Google Scholar
  7. 7.
    Chen, B. (1995) Analysis of Classes of Heuristics for Scheduling a Two-Stage Flow Shop with Parallel Machines at One Stage, Journal of the Operational Research Society, 46, 234–244.Google Scholar
  8. 8.
    Coffman, E.G. Jr. and E.N. Gilbert (1985) On the Expected Relative Performance of List Scheduling, Operations Research, 33, 548–561.CrossRefGoogle Scholar
  9. 9.
    Gonzalez, T. and S. Sahni (1978) Flowshop and Jobshop Schedules: Complexity and Approximation, Operations Research, 26, 36–52.CrossRefGoogle Scholar
  10. 10.
    Graham, R.L. (1966) Bounds for Certain Multiprocessing Anomalies, Bell System Technical Journal, 45, 1563–1581.Google Scholar
  11. 11.
    Guinet, A.G. and M.M. Solomon (1996) Scheduling Hybrid Flow Shops to Minimize Maximum Tardiness or Maximum Completion Time, International Journal of Production Research, 34, 1643–1654.CrossRefGoogle Scholar
  12. 12.
    Guinet, A.G., M.M. Solomon, P. Kedia and A. Dussachoy (1996) Computational Study of Heuristics for Two-stage Flexible Flow Shops, International Journal of Production Research, 34, 1399–1415.CrossRefGoogle Scholar
  13. 13.
    Gupta, J.N.D. (1988) Two-Stage, Hybrid Flowshop Scheduling Problem, Journal of the Operational Research Society, 39, 359–364.Google Scholar
  14. 14.
    Gupta, J.N.D. and E.A. Tunc (1991) Schedules for a Two-Stage Hybrid Flowshop with Parallel Machines at the Second Stage, International Journal of Production Research, 29, 1489–1502.CrossRefGoogle Scholar
  15. 15.
    Gupta, J.N.D., A.M.A. Hariri and C.N. Potts (1997) Scheduling a Two-Stage Hybrid Flow Shop with Parallel Machines at the First Stage, Annals of Operations Research, 69, 171–191.CrossRefGoogle Scholar
  16. 16.
    Hall, L.A. (1995) Approximability of Flow Shop Scheduling, Proceedings of the 36th IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamos, CA, 82–91.Google Scholar
  17. 17.
    Haouari, M. and R. M’Hallah (1997) Heuristic Algorithms for the Two-Stage Hybrid Flowshop Problem, Operations Research Letters, 21, 43–53.CrossRefGoogle Scholar
  18. 18.
    Hoogeveen, J.A., J.K. Lenstra and B. Veltman (1996) Preemptive Scheduling in a Two-stage Multiprocessor Flow Shop is NP-hard, European Journal of Operational Research, 89, 172–175.Google Scholar
  19. 19.
    Koulamas, C. and G.J. Kyparisis (2000) Asymptotically Optimal Linear Time Algorithms for Two-stage and Three-stage Flexible Flow Shops, Naval Research Logistics, 47, 259–268.CrossRefGoogle Scholar
  20. 20.
    Langston, M.A. (1987) Interstage Transportation Planning in the Deterministic Flow Shop Environment, Operations Research, 34, 556–564.CrossRefGoogle Scholar
  21. 21.
    Lee, C.-Y. and G.L. Vairaktarakis (1994) Minimizing Makespan in Hybrid Flow Shops, Operations Research Letters, 16, 149–158.CrossRefGoogle Scholar
  22. 22.
    Li, C.-L. and G.L. Vairaktarakis (2004) Loading and Unloading Operations in Container Terminals, IIE Transactions, 36, 287–297.CrossRefGoogle Scholar
  23. 23.
    Nawaz, M., E. Enscore and I. Ham (1983) A Heuristic Algorithm for the m Machine n Job Flow Shop Sequencing Problem, Omega, 11, 91–95.CrossRefGoogle Scholar
  24. 24.
    Paul, R.J. (1979) A Production Scheduling Problem in the Glass-container Industry, Operations Research, 22, 290–302.CrossRefGoogle Scholar
  25. 25.
    Rajendran, C. and D. Chaudhuri (1992) Scheduling in n-job, m-stage Flow Shop with Parallel Processors to Minimize Makespan, International Journal of Production Economics, 27, 137–143.CrossRefGoogle Scholar
  26. 26.
    Salvador, M.S. (1973) A Solution to a Special Case of Flow Shop Scheduling Problems, Symposium of the Theory of Scheduling and Applications, edited by S.E. Elmaghraby, Springer-Verlag, New York, 83–91.Google Scholar
  27. 27.
    Schuurman, P. and G.J. Woeginger (2000) A Polynomial Time Approximation Scheme for the Two-Stage Multiprocessor Flow Shop Problem, Theoretical Computer Science, 237, 105–122.CrossRefGoogle Scholar
  28. 28.
    Sevast’janov, S.V. (1995) Vector Summation in Banach Space and Polynomial Algorithms for Flow Shops and Open Shops, Mathematics of Operations Research, 20, 90–103.CrossRefGoogle Scholar
  29. 29.
    Sevast’janov, S.V. (1997) Nonstrict Vector Summation in the plane and its Applications to Scheduling Problems, Operations Research and Discrete Analysis, A.D. Korshunov (Editor), Kluwer, Dordrecht, 241–272.Google Scholar
  30. 30.
    Sriskandarajah, C. and S.P. Sethi (1989) Scheduling Algorithms for Flexible Flowshops: Worst and Average Case Performance, European Journal of Operational Research, 43, 143–160.CrossRefGoogle Scholar
  31. 31.
    Townsend, D.W. (1977) Sequencing n Jobs onm Machines to Minimize Tardiness: A Branch and Bound Solution, Management Science, 23, 1016–1019.CrossRefGoogle Scholar
  32. 32.
    Williamson, D.P., L.A. Hall, J.A. Hoogeveen, C.A.J. Hurkens, J.K. Lenstra, S.V. Sevastianov and D.B. Shmoys (1997) Short Shop Schedules, Operations Research, 45, 288–294.CrossRefGoogle Scholar

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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Weatherhead School of ManagementCase Western Reserve UniversityClevelandUSA

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