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Über das Transportproblem mit beliebigen zusätzlichen linearen Nebenbedingungen

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Zusammenfassung

Das klassische Transportproblem wurde durch zusätzliche Bedingungen ergänzt, die in Form beliebiger linearer Gleichungen oder Ungleichungen vorgegeben sind und allenfalls auch zusätzliche Variable beinhalten können. Für das so entstandene lineare Programm wurde ein rationeller Speicherraum sparender Algorithmus entwickelt. Es wird allerdings angenommen, daß die Anzahl der Zusatzbedingungen verhältnismäßig klein ist. Das Verfahren wurde an einer IBM 7040 (16 K) erprobt. Ein in Fortran IV abgefaßtes Rechenprogramm ist im Anhang wiedergegeben.

Summary

The classical transportation problem is augmented by a set of additional constraints, which are arbitrary linear equalities or inequalities and may contain also some additional variables. A special algorithm for this linear program is described. The method is thought to be efficient, if the number of the additional constraints is comparitively small. The algorithm has been tested on a IBM 7040 (16 K) Computer. A Fortran IV program is included in the appendix.

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Literatur

  1. Dantzig, G. B.: Linear Programming and extensions. Princeton 1963.

  2. Dantzig, G. B.: Application of the simplex method to a Transportation problem. InT. C. Koopmanns (ed) Activity Analysis of Production and Allocation. J. Wiley, 1951.

  3. Prager, W.: A Generalisation of Hitchcocks Transportations Problem. J. of Math. and Phys. Vol.36 (1957), S. 99ff.

    Google Scholar 

  4. Williams, A. C.: A treatment of transportation problems by decomposition. J. Soc. Indust. Appl. Math. Vol.10, No. 1, March 1962. S. 35.

    Google Scholar 

  5. Craven, B. D.: A Generalisation of the Transportation Method to Linear Programming. Op. Res. Quart., Vol.14 (1963), S. 157.

    Google Scholar 

  6. Eberl, W.: Lineare Planungsrechnung. MTW10. Jg. (1963), S. 9.

    Google Scholar 

  7. Dantzig, G. B.: Upper bounds, secondary constraints and block triangularity in linear programming. Econometrica Vol.23 (1955), S. 174ff.

    Google Scholar 

  8. Rosen, J. B.: Primal Partitioning Programming for Block Diagonal Matrices. Num. Math6 (1964), 250–260.

    Google Scholar 

  9. Beale, E. M. L.: The Simplex Method Using Pseudobasic Variables for Structured Linear Programming Problems. In R. L. Graves (ed.) and Ph. Wolfe (ed.), Recent advances in Mathematical Programming. Mc. Graw-Hill 1963, p. 133.

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  1. Institut für Rechentechnik, Technische Hochschule Wien, Karlsplatz 13, 1040, Wien

    P. Meissl Dozent am

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  1. P. Meissl Dozent am
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Meissl, P. Über das Transportproblem mit beliebigen zusätzlichen linearen Nebenbedingungen. Computing 1, 18–38 (1966). https://doi.org/10.1007/BF02235850

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  • DOI: https://doi.org/10.1007/BF02235850

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