Positive sensitivity analysis in linear programming

Chan Kyoo Park, Woo Je Kim, Sangwook Lee, Soondal Park

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

Positive sensitivity analysis (PSA) is a sensitivity analysis method for linear programming that finds the range of perturbations within which positive value components of a given optimal solution remain positive. Its main advantage is that it is applicable to both an optimal basic and nonbasic optimal solution. The first purpose of this paper is to present some properties of PSA that are useful for establishing the relationship between PSA and sensitivity analysis using optimal bases, and between PSA and sensitivity analysis using the optimal partition. We examine how the range of PSA varies according to the optimal solution used for PSA, and discuss the relationship between the ranges of PSA using different optimal solutions. The second purpose is to clarify the relationship between PSA and sensitivity analysis using an optimal basis, and the relationship between PSA and sensitivity analysis using the optimal partition. We show that sensitivity analysis using the optimal partition is a special case of PSA, and its properties can be derived from the properties of PSA. The comparison among the three sensitivity analysis methods will lead to a better understanding of the difference among sensitivity analysis methods.

Original languageEnglish
Pages (from-to)53-68
Number of pages16
JournalAsia-Pacific Journal of Operational Research
Volume21
Issue number1
DOIs
StatePublished - Mar 2004

Keywords

  • Linear programming
  • Optimal basis
  • Optimal partition
  • Positive sensitivity analysis
  • Sensitivity analysis

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