Author(s)

Tarek A. Khalil¹, Yashpal Singh Raghav^2*, N. Badra³

¹Mathematics Department, Higher Institute of Engineering and Technology, New Cairo Academy, Cairo, Egypt.
²Department of Mathematics, Faculty of Science, Jazan University, Jazan, KSA.
³Department of Physics and Engineering Mathematics, Faculty of Engineering, Ain Shams University, Cairo, Egypt.

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.

Multi-Choice Mathematical Programming, Transformation Technique, Optimization

Khalil, T. , Raghav, Y. and Badra, N. (2016) Optimal Solution of Multi-Choice Mathematical Programming Problem Using a New Technique. American Journal of Operations Research, 6, 167-172. doi: 10.4236/ajor.2016.62019.