On number problems for the open shop problem

  • H. Bräsel
  • M. Kleinau
II Mathematical Programming II.2 Discrete Optimization
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 180)


In discrete optimization problems investigations of the number of feasible or optimal solutions are very difficult. Some interesting results we have found for the so-called open shop problem. By modelling this problem with latin rectangles we can describe the above problems as problems of determing the cardinality of sets of special latin rectangles. Therefore for small parameters well-known results about the number of latin rectangles are useful. Further results are obtained by generalization of investigations on the number of feasible solutions of the job shop problem.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Adiri, I.,Amit, N.: Openshop and flowshop scheduling to minimize sum of completion times, Comput.Ops.Res., Vol 11, No3(1984), pp 275–289zbMATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    Akers, S.,Friedman, J.: A non-numerical approach to production scheduling problems, Operations Research, Vol.3,No.4,1955,pp.429–442CrossRefGoogle Scholar
  3. [3]
    Bräsel,H.: Lateinische Rechtecke und Maschinenbelegung, Dissertation B, TU Magdeburg, 1990Google Scholar
  4. [4]
    Bräsel,H.,Kleinau,M.: On the number of feasible solutions of the open shop problem — an application of special latin rectangles, to appear in optimizationGoogle Scholar
  5. [5]
    Dènes, J.,Keedwell, A.D.: Latin Squares and their Applications, Akademia Kiado, Budapest, 1974zbMATHGoogle Scholar
  6. [6]
    Gonzales, T.,Sahni, S.: Open shop scheduling to minimize finish time, J.Ass.Comp.Mach., Vol.23,No.4,1976,pp.665–679Google Scholar
  7. [7]
    Kleinau,M.: On the number of feasible solutions for the job shop and the open shop problem with two jobs or two machines, Preprint, Math 18/91, TU MagdeburgGoogle Scholar
  8. [8]
    Riordan, J.: Three-line latin rectangles, Bull.Amer.Math.Soc. 53, 1946, pp.18–20MathSciNetGoogle Scholar
  9. [9]
    Танаев, В.С., Сотсков, Ю. Н., Струсевич, В.А.: Теория расписании стадииные системы, Наука, Москва 1989Google Scholar

Copyright information

© International Federation for Information Processing 1992

Authors and Affiliations

  • H. Bräsel
    • 1
  • M. Kleinau
    • 1
  1. 1.Fakultät für Mathematik, Institut für Mathematische OptimierungTechnische Universität MagdeburgMagdeburg

Personalised recommendations