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.
PDEs are very important in dynamics, aerodynamics, elasticity, heat transfer, waves, electromagnetic theory, transmission lines, quantum mechanics, weather forecasting, prediction of crime places, disasters, how universe behave ……. Etc., second order linear PDEs can be classified according to the characteristic equation into 3 types hyperbolic, parabolic and elliptic; Hyperbolic equations have two distinct families of (real) characteristic curves, parabolic equations have a single family of characteristic curves, and the elliptic equations have none. All the three types of equations can be reduced to its first canonical form finding the general solution or the second canonical form similar to 3 basic PDE models; Hyperbolic equations reduce to a form coinciding with the wave equation in the leading terms, the parabolic equations reduce to a form modeled by the heat equation, and the Laplace’s equation models the canonical form of elliptic equations. Thus, the wave, heat and Laplace’s equations serve as basic canonical models for all second order linear PDEs.
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