A Decomposition Algorithm for Solving a Three Level Large Scale linear Programming Problem

Abstract

This paper presents a three level large scale linear programming problem in which the objective functions at every level are to be maximized. A three level programming problem can be thought as a static version of the Stackelberg strategy. An algorithm for solving a three planner model and a solution method for treating this problem are suggested. At each level we attempt to optimize its problem separately as a large scale programming problem using Dantzig and Wolfe decomposition method. Therefore, we handle the optimization process through a series of sub problems that can be solved independently. Finally, a numerical example is given to clarify the main results developed in this paper.

An Interactive Model for Fully Rough Three Level Large Scale Integer Linear Programming Problem

“…At that point, constraint method [6] can be used by embedding the FLDM decision variables to the SLDM in order to get the optimal solution using the decomposition algorithm [8]. The SLDM defines his/her problem in point of view of the FLDM by setting 1 = 1 , 1 , 1 , 1 , = 1,2, … , to the SLDM constraints, so the SLDM can be reformulated as follow: At last, by embedding the FLDM and the SLDM decision variables to the TLDM constraints.…”

“…The vast majority of the optimization problems emerged in real-world applications incorporates vast numbers of variables and constraints, which are called Large-Scale Programming Problems (LSPP) [6]. One prominent structure of the LSPP is the block angular structure.…”

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

“…Then by inserting the FLDM decision variable to the SLDM for him/her to seek the optimal solution using Dantzig and Wolf decomposition method [10] then the decomposition method break the large scale problem into n-sub problems that can be solved directly.…”

“…To obtain the optimal solution of the SLDM problem; the SLDM solves his master problem by the decomposition method [10] as the FLDM.…”

On Fuzzy Bi-Level Multi-Objective Large Scale Integer Quadratic Programming Problem

“…The vast majority of the optimization problems emerged in real-world applications incorporates vast numbers of variables and constraints, which are called Large-Scale Programming Problems (LSPP) [7]. One prominent structure of the LSPP is the block angular structure.…”