Two-period pricing and inventory decisions of perishable products with partial lost sales

Food waste has become one of the most critical issues for individuals and organizations involved in food marketing and policy across the world, which poses serious challenges to sustainable development. To reduce food waste, we develop a two-period dynamic pricing and inventory decision model for perishable products with partial lost sales. Faced with random demand, the firm has two opportunities to make inventory decisions during the selling season. The first inventory decision (for Period 1) is made at the beginning of the selling season and used to detect the market information, and the second decision (for Period 2) is to update the inventory level by reordering or returning based on the fully-realized market demand information. The firm may carry the unsold units left from Period 1 to Period 2, and there may be two types of stocks for the same products, but with different perceived levels of quality (old v.s. fresh) in Period 2. Both price competition and product substitutability exist between the fresh and old units. Using a dynamic programming approach, we derive the optimal solutions for the order quantities and retail prices of products under various quality conditions. We find that the reorder quantity at the middle of the season decreases with the quantity and the quality of old units. The pricing of fresh units does not depend on the quality or quantity of old units, while the pricing of old units increases with their quality and decreases with respect to the quantity.