A New Algorithm of Solving the Flow — Shop Problem

  • Józef Grabowski
Part of the Theory and Decision Library book series (TDLU, volume 32)

Abstract

The general flow — shop problem indicated by n|m|F|Cmax, can be formulated as follows. Each of n jobs J,…,Jn has to be processed on m machines M1,…,Mm in that order. Job Jj, j=1,…,n, thus consists of a sequence of m operations oj1..,,…,0. jm0jk corresponds to the processing of Jj on Mk during a processing time Pjk We want to find a processing order on each machine Mk such that the time required to complete all jobs is minimized. If the processing order is assumed to be the same on each machine, the resulting problem is called the permutation flow — shop problem, and indicated by n|m|F|Cmax.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    A.P.G. Brown and Z.A. Lomnicki, “Some Applications of the Branch-and-Bound Algorithm to the Machine Scheduling Problem”, Opl. Res. Quart. 17, 173–186 (1966).CrossRefGoogle Scholar
  2. [2]
    J. Grabowski, “On two-machine scheduling with release and due dates to minimize maximum lateness”, Opsearch 17, No. 4, 133–154 C 1980).Google Scholar
  3. [3]
    S. Johnson, “Optimal Two-and-Three-Stage Production Scheduls with Setup Times Included”, Naval Res. Logist. Quart. 61–68 CI 1954).Google Scholar
  4. [4]
    J.R. Jackson, “Scheduling a Production Line to Minimize Maximum Tardines”, Research Report 43, Management Science Research Project, University of California, Los Angeles, 1955.Google Scholar
  5. [5]
    B.J. Lageweg, J.K. Lenstra, and A.H.G. Rinnooy Kan, “Minimizing Maximum Lateness on One Machine: Computational Experience and Some Applications”, Statistics Neerlandica 30, 24–41 (1976).Google Scholar
  6. [6]
    B.J. Lageweg, J.K. Lenstra, and A.H.G. Rinnooy Kan, “A General Bounding Scheme for the Permutation Plow-Shop Problem”, Opns. Res. 26, 53–67 (1978).CrossRefGoogle Scholar
  7. [7]
    J.K. Lenstra, A.H.G. Rinnooy Kan, and P. Brucker, “Complexity of Machine Scheduling Problems”, Ann. Discrete Math. 1, 343–362 (1977).CrossRefGoogle Scholar
  8. [8]
    A.H.G. Rinnooy Kan, “Machine Scheduling Problems: Classification, Complexity and Computations”, Nijhoff, The Hague (1976).Google Scholar
  9. [9]
    W. Szwarc, “Johnson’s Approximate Method for the 3xn Job Shop Problem”, Naval Res. Logist. Quart. 24, 153–157 (1977).CrossRefGoogle Scholar

Copyright information

© D. Reidel Publishing Company 1982

Authors and Affiliations

  • Józef Grabowski
    • 1
  1. 1.Technical University of WrocławWrocławPoland

Personalised recommendations