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.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Vazsonyi, A., The use of mathematics in production and inventory control. Management Science, Vol. 1, 1954 and Vol. 1, Nos. 3-4, 1955
Vazsonyi, A., Scientific Programming in Business and Industry. John Wiley, 1958
Falster P., Graph-Oriented Production Models in APL. Electric Power Engineering Department, Technical University of Denmark, Pubi. 7710, October 1977
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
Giffler, B., Mathematical Solution of Production Planning and Scheduling Problems. IBM Technical Report 09.01028. 026 ( ASDD ), White Plains, NY, October 1960
Kelley, J. and Walker, M., Critical-path planning and scheduling. In Proceedings of the Eastern Joint Computer Conference, 1959
Cuninghame-Green, R. A., Describing industrial processes with interference and approximating their steady-state behaviour. Operations Research Quarterly, Vol. 13, 1962 pp 95 - 100
Yoeli, M., A note on a generalization of Boolean matrix theory. American Mathematical Monthly, Vol. 68, 1961 pp. 552–557
Giffler, B., Schedule algebra: a progress report. Naval Research Logistic Quarterly, Vol. 15, No. 2, June 1968
Cuninghame-Green, R. A., Minimax Algebra, Lecture Notes in Economics and Mathematical Systems, Vol. 166. Springer-Verlag, New York, 1979
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
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
Warshall, S., A theorem on Boolean matrices. Journal of the ACM, Vol. 9, 1962
Giffler, B. and Thompson, G. L., Algorithms for solving production-scheduling problems. Operations Research, Vol. 8, No. 4, July 1960
Balas, E., Finding a minimaximal path in a disjunctive PERT network. Theory of Graphs, Int. Symp., Rome, Dunrod, 1966
Conway, R. W. et al., Theory of Scheduling. Addison-Wesley, Reading, MA, 1967
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
Bellman, R., Some mathematical aspects of scheduling theory. J. Soc. Ind. and Appl. Math., Vol. 4, No. 3, September 1956
Ford, L. R. and Fulkerson, D. R., Flows in Networks. Princeton University Press, Princeton, NJ, 1962
Dantzig, G. B., All shortest routes in a graph theory of graphs. Int. Symp., Rome, 1966
Carré, B. A., An algebra for network routing problems. J. Inst. Math. Appi., Vol. 7, 1971 pp. 273–294
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
Loewner, P. G., Fabrication and assembly operations, Part III: matrix methods for processing configuration data. IBM Systems Journal, Vol. 4, No. 2, 1965
Langefors, B., Computation of Parts Requirements for Production Scheduling. BIT Vol. 2, 1962 pp. 91–111
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
Francis, N. D., Computation of material requirements for production planning. BIT, Vol. 19, 1979 pp. 34–38
IBM Corporation APL Language, GC 26-3847, 1983
Berge, C., The Theory of Graphs and its Applications. Methuen & Co., 1962
Harary F., Norman, R. Z., and Cartwright, D., Structural Models: An Introduction to the Theory of Directed Graphs. John Wiley, New York, 1965
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
Editor information
Editors and Affiliations
Rights 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