Replenishment strategy is very important to any aid agency. A situation that an agency may handle is a disaster relief program. A good aid replenishment strategy during this period is critical. The fulfillment of any item needed is important to ensure the survival ability of the victim. The demand of items may have certain patterns, including a trend characteristic. The traditional Economic Order Quantity (EOQ) may not be suitable to be applied during this situation. Therefore, an alternative mathematical model is proposed. The model is developed by considering the increasing demand behavior, the deterioration of inventory item, the urgency of items during the period, and the shortage issue. An analytical calculation approach is performed to demonstrate how the model could be implemented. The result shows that the more often the replenishment is executed, the higher the service level will be, without compromising the cost. At the end of this research we also suggest some future potential work to perform.