In this paper we develop an inventory model for deteriorating items with price sensitive demand. Generally the vendor offers a cash discount or fix time period to the retailer to pay all the dues. According to the availability of money the retailer chooses his/her option. In this paper we discuss the possible cases of permissible delay and cash discount. The shortages are allowed in this model and are partially backlogged. Holding cost is considered as varying function of time, which reflects a more realistic concept. The purpose of this study is to optimize the overall cost of the system and to compute optimal ordering quantity. Numerical examples for different cases are also presented to illustrate the study. A sensitivity analysis with regard to distinct associated parameters is shown to make sure the constancy of the model.