A Two-Stage Flexible Flowshop Problem with Deterioration

  • Hua Gong
  • Lixin Tang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5092)


We study a scheduling problem under considering deterioration on a two-stage flexible flowshop of particular structure (parallel machines in the first stage and a single batching machine in the second stage). The deterioration of a job means that its processing time on the batching machine is dependent on its waiting time, i.e., the time between the completion of the job in the first stage and the start of the job in the second stage. The objective is to minimize the makespan plus the total penalty cost of batching-machine utilization ratio. First, we prove the problem is strongly NP-hard. An efficient heuristic algorithm for the general problem is constructed and its worst-case bound is analyzed. Computational experiments show that the heuristic algorithm performs well on randomly generated problem instances.


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  1. 1.
    Ahmadi, J.H., Ahmadi, R.H., Dasu, S., Tang, C.S.: Batching and Scheduling Jobs on Batch and Discrete Processors. Operations Research 39, 750–763 (1992)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Cheng, T.C.E., Ding, Q., Lin, B.M.T.: A Concise Survey of Scheduling with Time-Dependent Processing Times. European Journal of Operational Research 152, 1–13 (2004)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman and Company, New York (1979)MATHGoogle Scholar
  4. 4.
    Leung, T.T., Ng, C.T., Cheng, T.C.E.: Minimizing Sum of Completion Times for Batch Scheduling of Jobs with Deteriorating Processing Times. European Journal of Operational Research 187, 1090–1099 (2008)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Pinedo, M.: Scheduling: Theory, Algorithm and Systems. Prentice-Hall, Englewood Cliffs (1995)Google Scholar
  6. 6.
    Riane, F., Artiba, A., Elmaghraby, S.E.: A Hybrid Three-stage Flowshop Problem: Efficient Heuristics to Minimize Makespan. European Journal of Operational Research 109, 321–329 (1998)MATHCrossRefGoogle Scholar
  7. 7.
    Soewandi, H., Elmaghraby, S.E.: Sequencing Three-stage Flexible Flowshops with Identical Machines to Minimize Makespan. IIE Transactions 33, 985–993 (2001)Google Scholar
  8. 8.
    Sung, C.S., Kim, Y.H.: Minimizing Makespan in a Two-machine Flowshop with Dynamic Arrivals Allowed. Computers Operations Research 29, 275–294 (2002)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Hua Gong
    • 1
  • Lixin Tang
    • 1
  1. 1.The Logistics InstituteNortheastern UniversityShenyangChina

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