Sensitivity Analysis on Linear Programming Problems with Trapezoidal Fuzzy Variables

Sensitivity Analysis on Linear Programming Problems with Trapezoidal Fuzzy Variables

Seyed Hadi Nasseri, Ali Ebrahimnejad
DOI: 10.4018/978-1-4666-2925-7.ch004
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In the real word, there are many problems which have linear programming models and sometimes it is necessary to formulate these models with parameters of uncertainty. Many numbers from these problems are linear programming problems with fuzzy variables. Some authors considered these problems and have developed various methods for solving these problems. Recently, Mahdavi-Amiri and Nasseri (2007) considered linear programming problems with trapezoidal fuzzy data and/or variables and stated a fuzzy simplex algorithm to solve these problems. Moreover, they developed the duality results in fuzzy environment and presented a dual simplex algorithm for solving linear programming problems with trapezoidal fuzzy variables. Here, the authors show that this presented dual simplex algorithm directly using the primal simplex tableau algorithm tenders the capability for sensitivity (or post optimality) analysis using primal simplex tableaus.
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Fuzzy set theory has been used in many fields such as control theory, mathematical modeling, Operations research and many industrial applications. Pahlavani (2010) presented a model to support the banking managerial decisions in the evaluation of investment plans, especially on rejecting inappropriate plans that can be done in short time (less than hour) and with minimal cost. Because there are some uncertainties in the evaluation process, their proposed model utilized fuzzy set theory to define the problem space in which an acceptance or rejection decision for a submitted investment plan is made. Wang and Liang (2009), based on Enhanced Russell measure model, proposed a fuzzy DEA model to deal with the efficiency evaluation problem with the given fuzzy input and output data, by using a ranking method based on the comparison of 978-1-4666-2925-7.ch004.m01-cuts. They illustrated our approach through an application to performance assessment of flexible manufacturing system.

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