Optimization is the magic key for most engineering projects. It concerns to minimize costs / losses or to maximize returns. In both cases, all existed constraints are to be satisfied. There are many optimization techniques that are widely employed in order to achieve the optimum solutions. In this paper, the dynamic programming, as a powerful optimization technique, is employed for this purpose. The dynamic programming is used by two different methods. The first method is the ordinary technique that called recursive dynamic programming. While the second method is a combination between the dynamic programming and the linear programming, and is called a simplified approach.

Two different models are established. The first model represents a production scheduling for a factory producing pipes. While the second model represents pollution in a river. The optimum solutions are obtained by the PC for the two models applying the two mentioned techniques for each model. These optimum solutions are compared showing high degree of tendency.

It is concluded that the simplified approach is an effective tool to get the optimum solutions for the two models. It is easy, simple, accurate, fast and is solved by a common PC software. It is recommended to provide more study for the simplified approach. Also, it is recommended to investigate its application to problems with maximization objective functions.