Seller's optimal replenishment policy and payment term among advance, cash, and credit payments

It is evident that granting a short-term interest-free loan (i.e., a credit payment) stimulates more sales than asking for an advance payment. In addition, it is obvious that a 30-year mortgage has a higher default risk than a 15-year mortgage. As a result, it can be inferred that the longer the credit period, the higher the sales volume as well as the higher the default risk. Conversely, there are no default risks with an advance payment. Also, the longer the prepayment period (i.e., advance period), the lower the sales volume but the higher the interest earned. In this paper we incorporate the above mentioned important and relevant phenomena into the proposed model. Hence, the payment period and the replenishment cycle time are decision variables. We then derive the seller's profit under each of the three payment terms: advance payment, cash payment, and credit payment. In addition, we obtain explicit closed-form solutions to the problem, and explain them by simple economic interpretations. Furthermore, we demonstrate that an increase in selling price elevates the payment period, while an increase in purchasing cost reduces the payment period. Finally, we perform sensitivity analyses to examine the impacts of financial related parameters on the seller's decisions and profits, and then provide several managerial insights. For example, if the impact of advance payment on demand is relatively smaller than that of credit payment, then it is more profitable for the seller to ask for an advance payment than to offer a credit payment, and vice versa.