Genetic Algorithms (GA) and Evolutionary Programming (EP) are two well-known optimization methods that belong to the class of Evolutionary Algorithms (EA). Both methods have generally been recognized to have successfully solved many problems in recent years, especially with respect to engineering and industrial problems. Even though they are two different types of EA, the two methods share a lot of commonalities in the genetic operators they use and the way they mimic natural evolution. This paper aims to bring forth an introductory review on how these two methods tackle the one-dimensional Cutting Stock Problem (CSP). We draw comparison on the effectiveness of GA and EP in solving CSP, and propose an improved algorithm using a combination of the two methods based on our observations. In the concluding remarks, some future works are suggested for further investigations.