Solving Large-scale Three-level Linear Fractional Programming Problem with Rough Coefficient in Objective Function

Abstract

In this paper a Large-Scale three level fractional problem is considered with random rough coefficient in objective function, in order to solve this problem, The intervals technique used to convert rough nature in objective into equivalent crisp , Then Tailor Series transformation is used to convert the Large-Scale three level fractional to an equivalent three level linear programming problem , then a Traditional Method used to constructed solution of the three-level programming problem, then we will use Decomposition Technique to solve Large-ScaleProblem. Finally an auxiliary problem is discussed as well as an example is presented.

A Survey on Rough Intervals Programming Formulation and Methodologies

“…A three level fractional programming problem with a random rough coefficient in constraints was considered [7]. At the first phase of the solution approaches and to avoid the complexity of the problem, fractional programming problems were converted into a linear model problem using Charnes & Cooper method.…”

“…where solves A solution algorithm to solve the TLFPRIC problems ( ) -( ) is described in a series of steps as follows [7]:…”

“…Omran et al [7] presented an algorithm for solving a three level fractional programming problem with rough coefficient in constraints.…”