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A systematic extreme point enumeration procedure for fixed charge problem

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Trabajos de estadistica y de investigacion operativa

Abstract

In this paper the fixed charge problem viz: Min\(\sum\limits_{j = 1}^n {(c_j x_j + F_j \delta _j )} \) subject toAX=b, X>-0

$$\delta _j = \left\{ \begin{gathered} 0 if x_j = 0 \hfill \\ 1 if x_j > 0 \hfill \\ \end{gathered} \right.$$

is solved by systematically enumerating extreme points of a linear programming problem viz:

$$Min \sum\limits_{j = 1}^n {(c_j x_j + F_j \delta _j )} $$

subject toAX= b, x j−dj °j≤0, X≥0 °≥0 where ° is an extreme point ofI n °≤1. The technique provides an exact solution of the problem. The theory is supported by a numerical example.

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References

  1. G. Hadley: “Linear Programming”, Addison-Wesley Publishing Company, Inc. Reading, Mass, U.S.A.

  2. G. Hadley: “Non-Linear and Dynamic Programming,” Addison-Wesley Publishing Company, Inc. Reading, Mass. Palo Alto. London.

  3. Hirsch, W. M., and G. B. Dantzig: “The Fixed Charge Problem,” RM-1383, The Rand Corp. 1954.

  4. M. C. Puri & Kanti Swarup: “An Algorithm for A Fixed Charge Problem”. Presented at 5th Annual Conference of O.R. Society of India held at Kharagpur, India 1972.

  5. M. C. Puri & Kanti Swarup: “Simple Enumerative Method For Fixed Charge Problem.” To appear in INSA, India.

  6. Dantzig, G. B.: “On the significance of Solving Linear Programming, Problems with some Integer Variables,” Econometrics, 28, 1960, pp. 30–44.

    Article  MATH  MathSciNet  Google Scholar 

  7. M. J. L. Kirby, H. R. Love and Kanti Swarup: “Extreme Point Mathematical Programming Problems”, ‘Management Science’, U.S.S., 1973.

  8. M. J. L. Kirby, H. R. Love and Kanti Swarup: “Enumeration Technique for Extreme Point Mathematical Programming Problems”, Research report, Dalhousie University, May, 1970.

  9. H. Kuhn and W. Baumol: “An approximate Algorithm for the Fixrd Charge Transportation Problem,” Naval Research Logistics Quarterly, 9, 1962, pp. 1–15.

    Article  MATH  MathSciNet  Google Scholar 

  10. Murty, K. G.: “Solving the fixed charge problem by Ranking the extreme points”. Operations Research Centre Report 66–7, University of California-Berkeley, Operations Research Centre (March 1966).

  11. Murty K. G.: “Solving the Fixed Charge Transportation Problem by Ranking the Extreme Points.” Operations Research, Vol. 16, 1968, Nr. 2, pp. 268–279.

    Article  MATH  Google Scholar 

  12. Gray, P.: “Exact Solution of the Fixed Charge Transportation Problem”. Paper presented at the 1968 joint ORSA/TIMS meeting at San Francisco, California, May 2, 1968.

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Authors and Affiliations

  1. University of Delhi, Delhi, India

    M. C. Puri & Kanti Swarup

Authors
  1. M. C. Puri
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  2. Kanti Swarup
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Puri, M.C., Swarup, K. A systematic extreme point enumeration procedure for fixed charge problem. Trab. Estad. Invest. Oper. 25, 99–108 (1974). https://doi.org/10.1007/BF03030153

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  • DOI: https://doi.org/10.1007/BF03030153

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