Due to bounded rationality, people often rush for instantaneous gratification if the decisions involve immediate rewards, but procrastinate if the decisions involve immediate costs. Present-biased preference and time-inconsistency will be more salient when people are making inter-temporal decisions to trade off rewards and costs in the future. People outweigh the present and their preference for the outcome in the future will decline over time. Incorporating present-biased preference and time-inconsistency under quasi-hyperbolic discounting, time value of money under inflation and time-varying demand with shortages completely backlogged, we develop an inventory replenishment model for a deteriorating item. Inventory replenishment policies that benefit the decision maker are as follows. With the increase of time-inconsistency, one can increase ordering number and decrease fraction of shortages; with the increase of hazard rate within an upper limit, one can increase ordering number and decrease fraction of shortage; with the increase of compounded discount rate, one can increase ordering number and fraction of shortage. Hyperbolic discounting increases the ordering number and decreases the final profit, and the degree of hyperbolic discounting strengthens such outcomes. As a result, the optimal policy for a decision maker is to keep as rational as possible when making inter-temporal decisions.