Abstract: Considering a market with demand uncertainty, the supplier provides the retailer with wholesale price related to the payment time—that is, the longer the retailer delays the payment, the higher the wholesale price of the product. Then, the retailer's optimal payment time and target inventory at the order point are addressed in order to obtain the maximum expected unit cycle revenue. Combining the relationship between the time when the retailer's inventory level drops to 0, the order time and the payment time, three inventory scenarios of the retailer are analyzed and the retailer's expected unit cycle revenue derived. The results show that the retailer's expected unit cycle revenue is a concave function of target inventory and there is a unique solution of target inventory. When the variation parameter of wholesale price is small, the retailer's expected unit cycle revenue is a concave function of payment time. The numerical results show that when the standard deviation of market demand increases, the retailer's optimal payment time, optimal target inventory and expected unit cycle revenue decrease; When the average market demand increases, the retailer's optimal payment time, optimal target inventory and expected unit cycle revenue increase.

Key words: stochastic demand, payment time, inventory policy, wholesale price