Optimal pricing, lot-sizing and backordering decisions when a seller demands an advance-cash-credit payment scheme

An advance-cash-credit (ACC) payment scheme is commonly used in business transactions. For instance, a contractor usually demands that a customer prepay 10% of the total cost (i.e., an advance payment) when a letter of agreement is signed to install a new driveway, kitchen, garage, etc. Upon delivery of the materials, a cash-on-delivery (i.e., a cash payment) to cover the contractor's materials cost is then required. Finally, the customer will pay the remainder of the total cost after the work is completed and accepted as satisfactory (i.e., a credit payment). In fact, an ACC payment type is a generalized payment scheme which includes advance, cash, credit, advance-cash, advance-credit, and cash-credit payments as special cases. In this paper, we develop an inventory model interfaced with marketing, operations, and finance in a supplier-retailer chain in which: (1) the demand curve is downward sloping, (2) the seller demands the buyer use an ACC payment for the total cost, and (3) for generality, shortages are allowed with a fixed market tolerance period. As a result, the retailer must determine optimal selling price, replenishment cycle, and shortage interval simultaneously to maximize the total profit for various situations. We demonstrate that an increase in the fraction of advance payment raises selling price, while an increase in the fraction of credit payment reduces selling price. The computational results reveal that if the supplier grants a credit payment, then the retailer has the highest profit amongst all of the payment types. This also results in the lowest selling price.