In the business transactions, the supplier usually offers a permissible delay in payment to his retailer to attract more sales. In addition, a permissible delay in payment may be applied as an alternative to price discount. Based on the above phenomena, we incorporate a permissible delay in payment into the model of Yang  and develop a two-warehouse partial backlogging inventory model for deteriorating items with permissible delay in payment under inflation. The objective of this study is to derive the retailer’s optimal replenishment policy that maximizes the net present value of the profit per unit time. The necessary and sufficient conditions for an optimal solution are characterized. An algorithm is developed to find the optimal solution. Finally, numerical examples are provided to illustrate the proposed model. Sensitivity analysis is made and some managerial implications are presented.