This Study Develops a Single-Supplier, Single-Retailer Inventory Model For Deteriorating Items With Ramp Type Demand Rate and a Fixed Shelf. In Practice There Are Many Commodity Such As Food, Medication Exist the Shelf Life. Therefore the Self-Life Expiration Date Has Become an Important Research Topic In Inventory Management. Shortages Are Allowed and Partially Backlogged, Where the Backlogging Rate Is Variable and Dependent on the Waiting Time For the Next Replacement. We Will Discuss Three Cases. the Major Objective Is to Minimize the Total Cost Per Unit Time of the System. By Using the Software Matlab, We Obtain the Optimal Solution and Numerical Examples Are Provided to Illustrate the Theoretical Results. a Sensitive Analysis of the Optimal Solution With Respect to the Major Parameters Is Also Carried Out.