Optimal ordering and discounting policy for a segmented market with price and freshness dependent demand for mixed quality product

Owing to various factors, fresh produce purchased by the retailer is initially of mixed quality. A random proportion of the lot would generally have lost some freshness before being received in stock, while the remaining items would still be fresh. This calls for some discount initially for the former, and later, when the latter product is not so fresh. For demand declining with increase in selling price and decrease in freshness, this paper deals with optimal ordering and discounting policy when the lot received is of mixed quality and the market has two segments differentiated by the initial product quality sold simultaneously at widely different prices. Sufficient conditions for existence and uniqueness of optimal cycle length and the optimal discount are obtained. Sensitivity analysis reveals that increase in freshness time and proportion of initially fresh items in the lot result in increased profit rate.