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 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.

[1]  Ching-Ter Chang,et al.  Multi-choice goal programming , 2007 .

[2]  Chin-Nung Liao,et al.  Formulating the multi-segment goal programming , 2009, Comput. Ind. Eng..

[3]  J. Stoer,et al.  Introduction to Numerical Analysis , 2002 .

[4]  Srikumar Acharya,et al.  Transformation of a multi-choice linear programming problem , 2009, Appl. Math. Comput..

[5]  He-Yau Kang,et al.  Fuzzy multiple goal programming applied to TFT-LCD supplier selection by downstream manufacturers , 2009, Expert Syst. Appl..

[6]  James J. Solberg,et al.  Operations Research: Principles And Practice, 2Nd Ed , 2007 .

[7]  Frederick S. Hillier,et al.  Introduction of Operations Research , 1967 .

[8]  Edward Y. H. Lin,et al.  Multiple Choice Programming: A State‐of‐the‐Art Review , 1994 .

[9]  W. C. Healy.  Multiple Choice Programming A Procedure for Linear Programming with Zero-One Variables , 1964 .

[10]  Ching-Ter Chang.  Revised multi-choice goal programming , 2008 .

[11]  Ralph D. Snyder,et al.  Linear Programming with Special Ordered Sets , 1984 .

[12]  Turan Paksoy,et al.  Revised multi-choice goal programming for multi-period, multi-stage inventory controlled supply chain model with popup stores in Guerrilla marketing , 2010 .

[13]  Kendall E. Atkinson.  An introduction to numerical analysis , 1978 .

[14]  Hsing-Pei Kao,et al.  Supplier selection model using Taguchi loss function, analytical hierarchy process and multi-choice goal programming , 2010, Comput. Ind. Eng..