Economic production lot size model with variable production rate and imperfect quality

The classical economic production lot size (EPL) model assumes a constant production rate that is predetermined and inflexible, and perfect quality. Recent models have removed the assumption of perfect quality while maintaining the inflexible production rate assumption. Production rates in many cases, such as orders filled by a machine, can be changed. Moreover, unit production cost and process quality depend on the production rate. This paper extends the EPL model to cases where the production rate is a decision variable. Unit production cost becomes a function of the production rate. Also, the quality of the production process deteriorates with increased production rate. The paper solves the proposed model for special cost and quality functions and illustrates the results with a numerical example. The results show that, for cases where increases in the production rate lead to a significant deterioration in quality, the optimal production rate may be smaller than the rate that minimizes unit production cost. For cases where quality is largely independent of the production rate, the optimal production rate may be larger than the rate that minimizes unit production cost.