Joint optimization of price and cycle length under two-stage credit policy with credit-linked demand

The objective of this paper is to jointly optimize the retailer's selling price and replenishment cycle under two-stage credit policy to reflect the real-life situations. Usually it is assumed that the supplier would offer the retailer a delay period but the retailer in turn would not offer the trade credit to his customers, which is unrealistic, because in reality retailer does offer the delay period to his customers in order to stimulate his own demand. Moreover the interaction between delay period and demand of an item ignored by the researchers, but it is observed that demand of an item does depend upon the credit period offered by the retailer to its customers. In order to incorporate this phenomenon, it is assumed that retailer's sales are divided in two categories (i) on cash, which is taken as a decreasing function of unit price and (ii) on credit, which is taken as a function of customer's credit period offered by the retailer. We then provide a solution procedure for determining the retailer's optimal price and cycle length simultaneously. Finally, a numerical example is given to illustrate the theoretical results followed by the sensitivity analysis of parameters on the optimal solution.