Lot-sizing and pricing decisions for perishable products under three-echelon supply chains when demand depends on price and stock-age

In economics, a demand curve is almost always downward-sloping, reflecting the willingness of consumers to purchase more of the commodity at lower price levels. In addition, the demand for seasonal products (such as fashion apparels, beverages etc.) or perishable goods (such as meat and seafood, dairy products, fruit and vegetables, pharmaceutical products, and chemicals) decreases over time. Hence, demand is a function of price and stock-age. With large business transactions, a seller usually demands a down payment (i.e., an advance payment) to ensure that the buyer is making a serious offer. Conversely, a buyer frequently requests to hold a fraction of total purchase cost until the business transaction is completed and satisfactory (i.e., a credit payment). As a result, a combination of advance, cash, and credit (ACC) payments is commonly used in business transactions. This paper develops a supplier–retailer–customer chain in which the retailer receives an upstream ACC payment from the supplier while in return offers a down-stream cash-credit (some in cash and the remainder in credit) payment to customers, the demand is influenced by the combined effect of selling price and stock age, and the deterioration rate is time-varying. The retailer must determine optimal unit price and replenishment time to maximize the present value of total profit, which is strictly concave in selling price and strictly pseudo-concave in replenishment time. Finally, a sensitivity analysis is performed, and several managerial insights are obtained. For instance, an increase in the fraction of advance payment forces the retailer to raise selling price.