Optimal selling price, replenishment cycle and payment time among advance, cash, and credit payments from the seller's perspective.

Although research on pricing and lot-sizing decisions concerning payment types has been extensive, almost all of it has been done from the buyer's perspective. In this study, we incorporate the following relevant and essential facts. If a seller allows a buyer to pay on credit, it increases sales volume. But if a seller asks a buyer for an advance payment, it decreases sales volume. Sometimes, a seller offers a buyer a price discount for an advance payment to increase sales and profitability. Asking a buyer for an advance payment bears interest earned and has no default risk. If a seller offers a buyer the opportunity to pay on credit, then a longer credit period may mean a higher the sales volume, but the default risk is higher, too. The seller wants to set an optimal selling price, replenishment time, and payment method simultaneously so that the profit per unit time is maximized. To achieve this, we develop and compare the seller's profit per unit time under each of three payment methods-advance, cash and credit. Through numerical analyses, the following managerial insights are highlighted: (1) Under certain conditions, a specific payment type obtains the seller's highest profit among all three payment types. (2) If advance payment is required, then it is critically important for a seller to offer a price discount. (3) An advance payment generates more profit than a credit payment provided that sales volume from a credit payment to an advance payment declines insignificantly and vice versa.