Title: Multi-level linear programming problem involving some multi-choice parameters

Authors: Avik Pradhan; M.P. Biswal

Addresses: Department of Mathematics, Indian Institute of Technology, Kharagpur – 721 302, India ' Department of Mathematics, Indian Institute of Technology, Kharagpur – 721 302, India

Abstract: In a multi-level decision making problem the decision is taken jointly by several decision makers who are at different levels. In this paper, we consider a multi-level linear programming problem where some of the cost coefficients of the objective functions and some of the right hand side parameters of the constraints are multi-choice type. The aim of this paper is to establish a suitable solution procedure to solve the stated multi-level programming problem. To tackle the multi-choice parameters of the multi-level programming problem, we use some interpolating polynomials and transform the stated problem into a multi-level mixed integer non-linear programming problem. Then we apply fuzzy programming method to solve the transformed multi-level programming problem. One numerical example is included to illustrate the solution procedure of the multi-level linear programming problem which has some multi-choice parameters.

Keywords: multi-level programming; interpolating polynomial; fuzzy programming; multi-choice programming; MCP; linear programming; decision making; mixed integer nonlinear programming; multi-level MINLP.

DOI: 10.1504/IJMOR.2015.069150

International Journal of Mathematics in Operational Research, 2015 Vol.7 No.3, pp.297 - 317

Received: 05 Sep 2013
Accepted: 16 Jan 2014
Published online: 30 Apr 2015 *

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