Economic production quantity model with variable machining rates and product quality

The literature has several models that jointly determine the economic production quantity (EPQ) and the rate of production. Very few models define production rate explicitly. In this article, the cutting speed controls the production rate and the proportion nonconforming. Thus, we propose a model that integrates EPQ, machining economics and quality. Even though the objective function of the model is non-convex, we show for realistic values of some technical parameters that a local minimum of the proposed mathematical model is also global. Examples clearly show the effect of the production economics factors on the optimal machining speed and production quantity.