Abstract: This paper develops inventory models for deteriorating item; the rate of deterioration is Weibull distribution deterioration with two parameters. It considers ramp-type demand. Shortage is allowed and it is completely backlogged. In these models, we consider time dependent holding cost. These models are developed under two different replenishment policies; (i) without shortage (ii) with shortage. The aim of these models is to find the optimal solution for minimizing the total inventory costs for both the above mentioned policies. To optimize the models numerical illustrations have been carried out and sensitivity analysis occurred to evaluate the result of parameters on assessment variables and the entire cost of these models.