Traditional research studies on the Economic Production Quantity (EPQ) model propose that produced items have perfect quality. However, in real production systems the quality of the products depends on the production process reliability. EPQ models that consider reliability and the effect of imperfect items are much more complex, and in turn the objective function becomes much more complicated. It is challenging to solve this type of model analytically, and it is also time consuming. Hence, it is necessary to utilize non-traditional solution techniques, such as numerical methods and heuristic search algorithms, for solving this type of model. In this paper, the optimal solution of the EPQ based reliability model are obtained by analytical solution, a Generalized Reduced Gradient (GRG) algorithm, an Evolutionary Algorithm (EA), a Monte Carlo non-deterministic method and the LINGO™ commercial solver. The methodology of this work has been clearly presented, and the computational results are compared and discussed. The computational results show that the GRG, EA, and Monte Carlo methods result in feasible and similar solutions, while the analytical solution is not valid for the model studied. The model can be extended to solve more complicated inventory models considering rework, shortage and multiple products.