In this article, we extend the classical economic production quantity (EPQ) model by proposing imperfect production processes and quality-dependent unit production cost. The demand rate is described by any convex decreasing function of the selling price. In addition, we allow for shortages and a time-proportional backlogging rate. For any given selling price, we first prove that the optimal production schedule not only exists but also is unique. Next, we show that the total profit per unit time is a concave function of price when the production schedule is given. We then provide a simple algorithm to find the optimal selling price and production schedule for the proposed model. Finally, we use a couple of numerical examples to illustrate the algorithm and conclude this article with suggestions for possible future research.
International Journal of Systems Science 42(1), pp.1-10