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The simplex SON algorithm for LP/embedded network problems

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Network Models and Associated Applications

Part of the book series: Mathematical Programming Studies ((MATHPROGRAMM,volume 15))

Abstract

This paper develops a special partitioning method for solving LP problems with embedded network structure. These problems include many of the large-scale LP problems of practical importance, particularly in the fields of energy, scheduling, and distribution. The special partitioning method, called the simplex special ordered network (SON) procedure, applies to LP problems that contain both non-network rows and non-network columns, with no restriction on the form of the rows and columns that do not exhibit a network structure.

Preliminary computational results are reported for an all-FORTRAN implementation of the simplex/SON algorithm called NET/LP. The test problems are real-world models of physical distribution and scheduling systems. NET/LP has solved problems with 6200 rows and 22,000 columns in less than 3 minutes, counting all I/O, on an AMDAHL V-6 with a FORTRAN H compiler.

This research was partially supported by FEA contract CR-03-70128-00 with Analysis, Research, and Computation, Inc., and by ONR Projects NR047-172 and NR047-021 with the Center for Cybernetic Studies, The University of Texas at Austin.

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Authors and Affiliations

  1. Graduate School of Business, University of Colorado, 80309, Boulder, CO, USA

    Fred Glover

  2. Department of General Business, University of Texas, BEB 608, 78712, Austin, TX, USA

    Darwin Klingman

Authors
  1. Fred Glover
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  2. Darwin Klingman
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D. Klingman J. M. Mulvey

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© 1981 The Mathematical Programming Society

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Glover, F., Klingman, D. (1981). The simplex SON algorithm for LP/embedded network problems. In: Klingman, D., Mulvey, J.M. (eds) Network Models and Associated Applications. Mathematical Programming Studies, vol 15. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120942

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  • DOI: https://doi.org/10.1007/BFb0120942

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00807-8

  • Online ISBN: 978-3-642-00808-5

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