Skip to main content
SpringerLink
Log in
Book cover

Extremal Methods and Systems Analysis pp 442–464Cite as

Rectilinear Distance Location-Allocation Problem: A Simplex Based Algorithm

  • Conference paper

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 174))

Abstract

Professor Charnes was the first to recognize the potentialities of adjacent extreme point methods to solve nonlinear problems. Subsequent research has substantiated his thoughts enunciated two decades ago on the power and limitations of such methods. The current paper deals with a Bilinear Program, i.e., a problem of the form to minimize ctx + dty + xtHy subject to x ε X and y ε Y, where X and Y are bounded polyhedral sets. In particular, it deals with a rectilinear distance location-allocation problem involving the determination of the locations of several new facilities, and the allocation of several products from these facilities to other, new or existing, facilities. An adjacent extreme point method is used along with cutting planes to overcome local optimality. The resulting algorithm converges to the global minimum. Computational results are provided.

This is a preview of subscription content, 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   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. BAZARAA, M. S., AND C. M. SHETTY: Nonlinear Programming: Theory and Algorithm, John Wiley and Sons, Inc., 1979.

    Google Scholar 

  2. BURDET, C. A.: “On Polaroid Intersections” in Mathematical Programming in Theory and Practice, Hammer, P. I. and Zoutendijk (eds.), North Holland Publishing Co., 1976.

    Google Scholar 

  3. CHARNES, A. AND W. W. COOPER: “Nonlinear Power of Adjacent Extreme Point Methods in Linear Programming,” Econometrica, 25, 1956, 132–153.

    Article  Google Scholar 

  4. FRANCIS, R. L. AND J. A. WHITE: Facility Layout and Location: An Analytic Approach, Prentice Hall, 1974.

    Google Scholar 

  5. GLOVER, F.: “Polyhedral Convexity Cuts and Negative Edge Extensions,” Zeitschrift fur Operations Research, 18, 1974, 181–186.

    Article  Google Scholar 

  6. GLOVER, F.: “Polyhedral Annexation in Mixed Integer and Combinatorial Programming,” Mathematical Programming, 8, 1975, 161–188.

    Article  Google Scholar 

  7. HILL, T. W. J. AND A. RAVINDRAN: “Technical Note on Programming with Absolute Value Functions,” Journal of Optimization Theory and Applications, 17, 1975, 181–183.

    Article  Google Scholar 

  8. JEROSLOW, R. G.: “The Principles of Cutting Plane Theory: Part I,” (with an addendum), GSIA, Carnegie-Mellon University, February 1974.

    Google Scholar 

  9. KONNO, H.: “A Cutting Plane Algorithm for Solving Bilinear Programs,” Mathematical Programming, 11, 1976, 14–27.

    Article  Google Scholar 

  10. MALLOWS, C. L.: “Some Comments on Cp” Technometrics, 15, 1973, 661–675.

    Article  Google Scholar 

  11. MARTOS, B.: “The Direct Power of Adjacent Vertex Programming Methods, Management Science, 17, 1965, 241–252.

    Article  Google Scholar 

  12. MURTY, K.: “Solving the Fixed Charge Problem by Ranking the Extreme Points,” Operations Research, 16, 1968, 268–279.

    Article  Google Scholar 

  13. SHERALI, A. D. AND C. M. SHETTY: “The Rectilinear Distance Location Allocation Problem,” AIIE Transactions, 9, 1977, 136–142.

    Article  Google Scholar 

  14. SHERALI, H. D. AND C. M. SHETTY: “A Primal Simplex Based Solution Procedure for the Rectilinear Distance Multifacility Location Problem, Operational Research Quarterly, 29, 1978, 373–381.

    Google Scholar 

  15. SHETTY, C. M. R. W. LANGLEY AND J. KENNINGTON:“Efficient Computational Devices for the Constrained Transportation Problem,” Naval Res. Logistics Quarterly, 21, 1974, 637–347.

    Article  Google Scholar 

  16. VAISH, H.: “Nonconvex Programming with Applications to Production and Location Problems,” unpublished Ph.D. dissertation, Georgia Institute of Technology, 1974.

    Google Scholar 

  17. VAISH, H. AND C. M. SHETTY: “A Cutting Plane Algorithm for the Bilinear Programming Problem,” Naval Res. Logistics Quarterly, 24, 1977, 83–93.

    Article  Google Scholar 

  18. VAISH, H. AND C. M. SHETTY: “The Bilinear Programming Problem,” Naval Res. Logistics Quarterly, 23, 1976, 303–309.

    Article  Google Scholar 

Download references

Authors
  1. C. M. Shetty
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. D. Sherali
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Operations Research Institute for Management Science and Engineering, The Washington University, 20052, Washington, DC, USA

    Anthony V. Fiacco

  2. Department of Mathematics, Carnegie-Mellon University, 15213, Pittsburgh, PA, USA

    Kenneth O. Kortanek

Rights and permissions

Reprints and permissions

Copyright information

© 1980 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Shetty, C.M., Sherali, H.D. (1980). Rectilinear Distance Location-Allocation Problem: A Simplex Based Algorithm. In: Fiacco, A.V., Kortanek, K.O. (eds) Extremal Methods and Systems Analysis. Lecture Notes in Economics and Mathematical Systems, vol 174. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46414-0_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-46414-0_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09730-3

  • Online ISBN: 978-3-642-46414-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation