This paper presents an order level inventory system with time dependent Weibull deterioration and quadratic demand rate where holding costs as a linear function of time. The proposed model considered here to allows for shortages, and the demand is partially backlogged. The model is solved analytically by minimizing the total inventory cost. The implementation of the proposed model is illustrated using some numerical examples. Sensitivity analysis is performed to show the effect of changes in the parameters on the optimum solution. © 2015, Springer India Pvt. Ltd.