Dynamic pricing, quality investment, and replenishment model for perishable items

The deterioration of perishable items results not only in direct quantitative losses, but also in qualitative losses, which would reduce the customer acceptability. To maintain or improve the quality level, sellers usually invest in functionality, aesthetics, safety or any other attributes. In addition to quality, price also plays a critical role in influencing the purchase choice of consumers and the profit of a firm. Most inventory management models for perishables are restricted to physical quantity deterioration and do not address joint dynamic pricing and quality investment strategies. This paper studies an optimal replenishment model with dynamic pricing and quality investment for perishable products, where the quality and physical quantity deteriorate simultaneously. The demand rate is decreasing in sales price and increasing in quality level. A dynamic optimization model is proposed to maximize the total profit per unit time and solved on the basis of Pontryagin's maximum principle. The optimal joint dynamic pricing, quality investment, and replenishment policy is obtained. A numerical example and sensitivity analysis on the key system parameters are presented to illustrate the validity of the theoretical results. Some managerial implications for the pricing and quality investment for the perishables are provided.