Pricing and lot-sizing decisions for perishable goods when demand depends on selling price, reference price, product freshness, and displayed stocks

Price is an important factor affecting demand rate based on economic and marketing theory. In addition, today's health-conscious consumers prefer a product further from its expiration date because it is fresher and can be stored longer. Furthermore, a large display of goods in a supermarket induces customers to buy more due to its visibility, variety, and seasonality. As a result, we develop a joint pricing and lot-sizing model for retailers selling perishable products in which the demand depends on not only the selling price and reference price but also the product freshness linked to expiration date and displayed stock level. We then formulate the problem as a deterministic model in which the retailer determines the optimal selling prices and ending inventory levels to maximize the discounted total profit. Furthermore, we discuss the retailer's optimal decisions under two scenarios of demand behavior: loss neutrality and loss aversion. Our theoretical analysis shows that the optimal pricing and ending inventory level strategies are both monotonic in time, and the equilibrium of the system is unique for these two scenarios of demand behavior. Finally, a set of structural properties and sensitivity analysis is also developed to characterize the impacts of model parameters on the optimal decisions.