Geometric Programming with Stochastic Parameter

Subject Areas : Statistics

R. Khanjani Shiraz ¹ (School of Mathematics Science, University of Tabriz, Tabriz, Iran)

Received: 2016-06-23 Accepted : 2016-09-01 Published : 2016-06-21

Keywords: برنامه ریزی هندسی, برنامه ریزی تصادفی, محدودیتهای تصادفی, دوگان,

Abstract :

Geometric programming is efficient tool for solving a variety of nonlinear optimizationproblems. Geometric programming is generalized for solving engineering design. However,Now Geometric programming is powerful tool for optimization problems where decisionvariables have exponential form.The geometric programming method has been applied with known parameters. However,the observed values of the parameters in real-life GP problems are often imprecise or vague.This data may be different faces such as bounded, interval, fuzzy and random. In this paper,geometric programming with random parameters to be considered. Then stochasticprogramming has converted to geometric programming with deterministic parameters. Byusing dual of geometric programming, optimal solutions of stochastic geometricprogramming can be obtained. Two illustrative examples are presented to demonstrate theefficacy of our method.