TITLE:
Optimal Solution of Multi-Choice Mathematical Programming Problem Using a New Technique
AUTHORS:
Tarek A. Khalil, Yashpal Singh Raghav, N. Badra
KEYWORDS:
Multi-Choice Mathematical Programming, Transformation Technique, Optimization
JOURNAL NAME:
American Journal of Operations Research,
Vol.6 No.2,
March
10,
2016
ABSTRACT: The study deals with the multi-choice mathematical programming problem, where the right hand side of the constraints is multi-choice in nature. However, the problem of multi-choice linear programming cannot be solved directly by standard linear or nonlinear programming techniques. The aim of this paper is to transform such problems to a standard mathematical linear programming problem. For each constraint, exactly one parameter value is selected out of a multiple number of parameter values. This process of selection can be established in different ways. In this paper, we present a new simple technique enabling us to handle such problem as a mixed integer linear programming problem and consequently solve them by using standard linear programming software. Our main aim depends on inserting a specific number of binary variables and using them to construct a linear combination which gives just one parameter among the multiple choice values for each choice of the values of the binary variables. A numerical example is presented to illustrate our analysis.