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Revised Dual Simplex Algorithm

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Book cover Linear Programming Using MATLAB®

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 127))

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Abstract

In Section 2.6, we presented the basic duality concepts. This chapter extends these concepts and presents the dual simplex algorithm. The dual simplex algorithm is an attractive alternative for solving linear programming problems (LPs). The dual simplex algorithm is very efficient on many types of problems and is especially useful in integer linear programming. This chapter presents the revised dual simplex algorithm. Numerical examples are presented in order for the reader to understand better the algorithm. Furthermore, an implementation of the algorithm in MATLAB is presented. The implementation is modular allowing the user to select which scaling technique and basis update method will use in order to solve LPs. Finally, a computational study over benchmark LPs and randomly generated sparse LPs is performed in order to compare the efficiency of the proposed implementation with the revised primal simplex algorithm presented in Chapter 8

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References

  1. Bixby, R. E. (1992). Implementing the simplex method: The initial basis. ORSA Journal on Computing, 4, 267–284.

    Article  MathSciNet  Google Scholar 

  2. Carstens, D. M. (1968) Crashing techniques. In W. Orchard-Hays (Ed.), Advanced linear-programming computing techniques (pp. 131–139). New York: McGraw-Hill.

    Google Scholar 

  3. Forrest, J. J., & Goldfarb, D. (1992). Steepest-edge simplex algorithms for linear programming. Mathematical Programming, 57(1–3), 341–374.

    Article  MathSciNet  Google Scholar 

  4. Fourer, R. (1994). Notes on the dual simplex method. Draft report.

    Google Scholar 

  5. Gould, N. I. M., & Reid, J. K. (1989). New crash procedures for large systems of linear constraints. Mathematical Programming, 45, 475–501.

    Article  MathSciNet  Google Scholar 

  6. Lemke, C. E. (1954). The dual method of solving the linear programming problem. Naval Research Logistics Quarterly, 1(1), 36–47.

    Article  MathSciNet  Google Scholar 

  7. Maros, I., & Mitra, G. (1998). Strategies for creating advanced bases for large-scale linear programming problems. INFORMS Journal on Computing, 10, 248–260.

    Article  MathSciNet  Google Scholar 

  8. Paparrizos, K., Samaras, N., & Stephanides, G. (2003). A new efficient primal dual simplex algorithm. Computers & Operations Research, 30(9), 1383–1399. ISO 690

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Applied Informatics, University of Macedonia, Thessaloniki, Greece

    Nikolaos Ploskas & Nikolaos Samaras

Authors
  1. Nikolaos Ploskas
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  2. Nikolaos Samaras
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9.1 Electronic Supplementary Material

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chapter 9 (Zip 6 kb)

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Ploskas, N., Samaras, N. (2017). Revised Dual Simplex Algorithm. In: Linear Programming Using MATLAB® . Springer Optimization and Its Applications, vol 127. Springer, Cham. https://doi.org/10.1007/978-3-319-65919-0_9

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