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Generalized transformation techniques for multi-choice linear programming problems

Journal Name:

  • An International Journal of Optimization and Control: Theories & Applications

Publication Year:

  • 2013
DOI: 
10.11121/ijocta.01.2013.00132

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Abstract (Original Language): 
The multi-choice programming allows the decision maker to consider multiple number of resources for each constraint or goal. Multi-choice linear programming problem can not be solved directly using the traditional linear programming technique. However, to deal with the multi-choice parameters, multiplicative terms of binary variables may be used in the transformed mathematical model. Recently, Biswal and Acharya [2] have proposed a methodology to transform the multi-choice linear programming problem to an equivalent mathematical programming model, which can accommodate a maximum of eight goals on the right hand side of any constraint. In this paper we present two models as generalized transformation the multi-choice linear programming problem. Using any one of the transformation techniques a decision maker can handle a parameter with finite number of choices. Binary variables are introduced to formulate a non-linear mixed integer programming model. Using a non-linear programming software optimal solution of the proposed model can be obtained. Finally, a numerical example is presented to illustrate the transformation technique and the solution procedure.
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