An economic production quantity model for an imperfect production system with selling price, advertisement frequency and green-level dependent demand

The consumer’s demand for certain products must be grown through frequent promotion. Also, maintaining the green level of the products can catch customers’ attention. The demand can be boosted by lowering the selling price per unit quantity. These essential issues should be considered while modelling the demand function for a production-retail scenario. The production of commodities cannot be error-free. A small part of the production may be imperfect, and the rate of the imperfect output must be increased as time forwards. The production cost increases as the advertisement frequency, maintenance of green level advances, and time forwards. The inventory carrying cost per unit product also hikes with time. This paper presents a comprehensive inventory optimization model, including the mentioned issues in its hypotheses. The result shows that the average profit is significantly sensitive to the selling price and production cost per unit. The resultant managerial insights after solving the proposed model are as follows. First, the average profit increases with the selling price hike and frequent advertisement. Second, the green level cannot increase average profit, though it causes surplus demand, because maintaining green levels of items incurs additional costs. Third, accumulating defective items during production diminishes average profit as the sellable products are lowered.