In this paper, we propose an appropriate inventory model for a non-instantaneous deteriorating items having Ramp-type demand rate with time dependent deterioration rate. In this model, the shortages are allowed and, which is partially backlogged. The backlogging rate is variable and time dependent on the waiting time for the next replenishment. One of the best tools for delaying cash outflow of any cash-strapped or new retail business is the trade credit or delay in payments available from suppliers. This model serves in minimizing the total inventory cost by finding an optimal replenishment policy. Some useful lemmas have been delineated to illustrate the optimal solution. Several numerical examples are given to test and verify the theoretical results. The sensitivity analysis of the optimal solution with respect to major parameters is developed. Finally, the managerial implications and conclusion are presented
