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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| Vydáno v: | Mathematical and computer modelling Ročník 54; číslo 5; s. 1405 - 1412 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Kidlington
Elsevier Ltd
01.09.2011
Elsevier |
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| ISSN: | 0895-7177, 1872-9479 |
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| Abstract | 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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| AbstractList | 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. |
| Author | Acharya, S. Biswal, M.P. |
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| Keywords | 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 |
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| SubjectTerms | 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 |
| Title | Solving multi-choice linear programming problems by interpolating polynomials |
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