Skip to main content
SpringerLink
Log in

Graph Theoretical Approaches

  • Chapter
Computer-Aided Production Management

Part of the book series: IFIP State-of-the-Art Reports ((IFIP))

Abstract

For the production engineer one great virtue of graphs is their primitive simplicity and therefore their ability to represent a variety of structures of production planning and control problems.

Peter Falster is Associate Professor in the Electric Power Engineering Department, Technical University of Denmark. His Ph.D. is in Systems Science and Graph-oriented Production Models in APL. Dr. Falster is Chairman of IFIP WG 5.7: Computer Aided Production Management, and the Danish Representative to IFIP TC 5. He is also a member of the Danish Data Processing Association’s TC on CIM.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Vazsonyi, A., The use of mathematics in production and inventory control. Management Science, Vol. 1, 1954 and Vol. 1, Nos. 3-4, 1955

    Google Scholar 

  2. Vazsonyi, A., Scientific Programming in Business and Industry. John Wiley, 1958

    MATH  Google Scholar 

  3. Falster P., Graph-Oriented Production Models in APL. Electric Power Engineering Department, Technical University of Denmark, Pubi. 7710, October 1977

    Google Scholar 

  4. Falster, P., Dataoperations in production systems. In O. Bjorke and O. I. Franksen (eds): System Structures in Engineering - Economic Design and Production. Tapir Publishers, 1978

    Google Scholar 

  5. Giffler, B., Mathematical Solution of Production Planning and Scheduling Problems. IBM Technical Report 09.01028. 026 ( ASDD ), White Plains, NY, October 1960

    Google Scholar 

  6. Kelley, J. and Walker, M., Critical-path planning and scheduling. In Proceedings of the Eastern Joint Computer Conference, 1959

    Google Scholar 

  7. Cuninghame-Green, R. A., Describing industrial processes with interference and approximating their steady-state behaviour. Operations Research Quarterly, Vol. 13, 1962 pp 95 - 100

    Article  Google Scholar 

  8. Yoeli, M., A note on a generalization of Boolean matrix theory. American Mathematical Monthly, Vol. 68, 1961 pp. 552–557

    Article  MathSciNet  MATH  Google Scholar 

  9. Giffler, B., Schedule algebra: a progress report. Naval Research Logistic Quarterly, Vol. 15, No. 2, June 1968

    Google Scholar 

  10. Cuninghame-Green, R. A., Minimax Algebra, Lecture Notes in Economics and Mathematical Systems, Vol. 166. Springer-Verlag, New York, 1979

    Google Scholar 

  11. Gleiberman, L., The engineering change of the total requirements matrix for a bill of materials. Management Science, Vol. 10, No. 3, April 1964, pp. 488–493

    Article  Google Scholar 

  12. Falster, P., On datastructures and algorithms in factory management systems. In O. Bjerke & O. I. Franksen (eds): Structures and Operations in Engineering and Management Systems. Tapir Publishers, 1981

    Google Scholar 

  13. Warshall, S., A theorem on Boolean matrices. Journal of the ACM, Vol. 9, 1962

    Google Scholar 

  14. Giffler, B. and Thompson, G. L., Algorithms for solving production-scheduling problems. Operations Research, Vol. 8, No. 4, July 1960

    Google Scholar 

  15. Balas, E., Finding a minimaximal path in a disjunctive PERT network. Theory of Graphs, Int. Symp., Rome, Dunrod, 1966

    Google Scholar 

  16. Conway, R. W. et al., Theory of Scheduling. Addison-Wesley, Reading, MA, 1967

    MATH  Google Scholar 

  17. Franksen, O. I., Numerical Examples and Comments to Vazsonyi’s Two Articles. Lecture Notes, Spring Semester, 1968, 27 pp. and A Graph Theoretic Approach to Production Problems. Special Seminar, Dept. of Systems Design, Univ. of Waterloo, Canada, 2 June, 1975, 14 pp

    Google Scholar 

  18. Bellman, R., Some mathematical aspects of scheduling theory. J. Soc. Ind. and Appl. Math., Vol. 4, No. 3, September 1956

    Google Scholar 

  19. Ford, L. R. and Fulkerson, D. R., Flows in Networks. Princeton University Press, Princeton, NJ, 1962

    MATH  Google Scholar 

  20. Dantzig, G. B., All shortest routes in a graph theory of graphs. Int. Symp., Rome, 1966

    Google Scholar 

  21. Carré, B. A., An algebra for network routing problems. J. Inst. Math. Appi., Vol. 7, 1971 pp. 273–294

    Article  MATH  Google Scholar 

  22. Cohen, G. et al., A linear-system theoretic view of discrete-event processes and its use for performance evaluation in manufacturing. IEEE Trans, on Automatic Control, Vol. AC-30, No. 3, March 1985

    Google Scholar 

  23. Loewner, P. G., Fabrication and assembly operations, Part III: matrix methods for processing configuration data. IBM Systems Journal, Vol. 4, No. 2, 1965

    Google Scholar 

  24. Langefors, B., Computation of Parts Requirements for Production Scheduling. BIT Vol. 2, 1962 pp. 91–111

    Article  MATH  Google Scholar 

  25. Dzubak, B. J. and Warburton, C. R., The organization of structural files. Comm. of the ACM, Vol. 8, No. 7, July 1985, pp. 446–452

    Article  Google Scholar 

  26. Francis, N. D., Computation of material requirements for production planning. BIT, Vol. 19, 1979 pp. 34–38

    Article  MathSciNet  MATH  Google Scholar 

  27. IBM Corporation APL Language, GC 26-3847, 1983

    Google Scholar 

  28. Berge, C., The Theory of Graphs and its Applications. Methuen & Co., 1962

    MATH  Google Scholar 

  29. Harary F., Norman, R. Z., and Cartwright, D., Structural Models: An Introduction to the Theory of Directed Graphs. John Wiley, New York, 1965

    MATH  Google Scholar 

  30. Franksen, O. I., Mr. Babbage’s Secret: The Tale of a Cypher - and APL. Strandberg Publishers, Birkerod, Denmark, 1984. International Edition by Prentice-Hall Inc., Englewood Cliffs, NJ, 1985

    Google Scholar 

Download references

Authors
  1. Peter Falster
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Production Engineering Laboratory, NTH-SINTEF, Richard Birkelandsv. 2b, N-7034, Trondheim-NTH, Norway

    Asbjørn Rolstadås

Rights and permissions

Reprints and permissions

Copyright information

© 1988 IFIP International Federation for Information Processing

About this chapter

Cite this chapter

Falster, P. (1988). Graph Theoretical Approaches. In: Rolstadås, A. (eds) Computer-Aided Production Management. IFIP State-of-the-Art Reports. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-73318-5_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-73318-5_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-73320-8

  • Online ISBN: 978-3-642-73318-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation