We discuss the effects of inflation and time discounting on an EOQ model for deteriorating items under stock-dependent demand and time-dependent partial backlogging. The inventory model is studied under the replenishment policy starting with no shortages. We then use MATLAB to find the optimal replenishment policies. The objective of this model is to maximize the total profit (TP) which includes the sales revenue, purchase cost, the set up cost, holding cost, shortage cost and opportunity cost due to lost sales. Analytical results are given to justify the model. Finally, numerical examples are presented to determine the developed model and the solution procedure. Sensitivity analysis of the optimal solution with respect to major parameters is carried out. We propose a solution procedure to find the solution and obtain some managerial results by using sensitivity analysis.