Pricing and lot-sizing decision for fresh goods when demand depends on unit price, displaying stocks and product age under generalized payments

The demand decreases as the price increases. Also, the demand rate for fresh goods depends on its freshness, which can be assessed by its sell-by date. Furthermore, a large pile of consumer goods displayed in a supermarket often provokes consumers to buy more due to its freshness, variety, or visibility. With larger business transactions, the supplier usually requests a good-faith deposit (or an advance payment) to discourage the order cancelation. On the other hand, the retailer likes to hold some portion of the purchase amount until the business transaction is completed and satisfactory (or a credit payment). Consequently, an advance-cash-credit (ACC) payment scheme, which is a combination of advance, cash, and credit payments, becomes commonly used in business transactions. In this study, we explore an inventory system in which: demand curve depends on unit price, displayed volume, and sell-by date; and the supplier and the retailer agree with an ACC payment scheme. The objective for grocery stores is to maximize the total profit by finding its price and order cycle simultaneously. We derive theoretical results, and then propose an algorithm. Finally, we perform sensitivity analyses to gain the following managerial insights: (i) An increase in stock efficiency significantly reduces selling price and cycle time while tremendously raising total profit. (ii) Credit payment generates the lowest selling price but the highest profit among all payment types. (iii) An increase in shelf life through preservation technology investment significantly raises total profit while slightly increasing the unit price and cycle time.