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Solving multi-choice linear programming problems by interpolating polynomials. (English) Zbl 1228.90051

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.

MSC:

90C05 Linear programming
90C30 Nonlinear programming
65K05 Numerical mathematical programming methods
90C11 Mixed integer programming

Software:

LINDO; LINGO
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Full Text: DOI

References:

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