Solving multi-choice linear programming problems by interpolating polynomials

Multi-choice programming solves some optimization problems where multiple information exists for a parameter. The aim of this paper is to select an appropriate parameter from a set of multiple choices, which optimizes the objective function. We consider a linear programming problem where the right h...

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Bibliographic Details
Published in:Mathematical and computer modelling Vol. 54; no. 5; pp. 1405 - 1412
Main Authors: Biswal, M.P., Acharya, S.
Format: Journal Article
Language:English
Published: Kidlington Elsevier Ltd 01.09.2011
Elsevier
Subjects:
computer software
Exact sciences and technology
Interpolating polynomial
Linear programming
Mathematical analysis
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Mixed integer programming
Multi-choice programming
Nonlinear programming
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming
Numerical methods in mathematical programming, optimization and calculus of variations
Sciences and techniques of general use
Multi-choice programming
Linear programming
Mixed integer programming
Nonlinear programming
Interpolating polynomial
Polynomial
Optimization method
Nonlinear problems
Non linear programming
Integer
Integer programming
Numerical analysis
Applied mathematics
Software
Mixed problem
Mathematical model
Computer aided analysis
Mathematical programming
ISSN:0895-7177, 1872-9479
Online Access:Get full text
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Summary:Multi-choice programming solves some optimization problems where multiple information exists for a parameter. The aim of this paper is to select an appropriate parameter from a set of multiple choices, which optimizes the objective function. We consider a linear programming problem where the right hand side parameters are multi-choice in nature. In this paper, the multiple choices of a parameter are considered as functional values of an affine function at some non-negative integer nodes. An interpolating polynomial is formulated using functional values at non-negative integer nodes to take care of any multi-choice parameter. After establishing interpolating polynomials of all multi-choice parameters, a mathematical programming problem is formulated. The formulated problem is treated as a nonlinear programming problem involving mixed integer type variables. It can be solved by using standard nonlinear programming software. Finally, a numerical example is presented to illustrate the solution procedure.
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ISSN:0895-7177
1872-9479
DOI:10.1016/j.mcm.2011.04.009