Pricing and lot-sizing decisions on buy-now-and-pay-later installments through a product life cycle

Buy-Now-Pay-Later (BNPL) service is one of the fastest-growing segments of financial technology in 2021. The BNPL program is a type of short-term finance that allows consumers to make purchases and pay for them interest-free over a predetermined brief period of time, usually weeks or months. In general, BNPL payment is instant-approval and no-credit-check right at checkout. As a result, BNPL payment is appealing to young adults who have existing student loans and cannot access credit. In this paper, we develop a brand-new model interfaced with finance, marketing, and operations in which a young store owner orders a product, receives a BNPL program at checkout with a good-faith down payment, and then pays off the remainder in interest-free installments. The store owner sells the product to consumers with price- and timing-dependent demand. The objective for the store owner is to determine an optimal selling price and replenishment time simultaneously to maximize total profit. We then derive the optimal solution and characterize its properties based on theoretical results. Furthermore, we present three examples and find that the optimal price moving through its life cycle coincides with price skimming. Finally, we perform a sensitivity analysis to gain managerial insights. For instance, an increase in fraction of installments or initial demand significantly raises total profit and order quantity meanwhile tremendously reduces selling price and cycle time. Also, an increase in demand slope or return rate on investment compels the store owner substantially to increase the unit price, cycle time, order quantity, and total profit.