New Formulation for Linear and Quadratic Production Models
Abstract
In this paper, we present a new formulation for some applications of the dynamic mathematical programming problems using time scale. These applications include linear and quadratic objective function. Also, this formulation is an extension for the existing one. In addition, the continuous models and quantum models are obtained by choosing T = R and T = qN0 receptively. Moreover, the primal and the dual of the dynamic mathematical programming models on time scales are constructed for the linear and quadratic production model. This concepts of the duality theory will help the decision maker to choose either the primal model or the dual model for finding the optimal solution in particular for isolated time scales set. Furthermore, using this formulation the optimal solution can be obtained easily using some well-known discrete optimization methods such us simplex method and interior point method.
