A mathematical model for inventory-dependent demand and backorder.

Good and properly organized inventory management is essentially needed for a company in order to ensure that its production process runs smoothly. There are many factors to be considered since they can distract the inventory management such as demand behavior, the life time of goods, uncertain replenishment time, the political and economic situation, and unexpected natural disaster. There are certain risks involved with bulk replenishment such as the higher holding cost and the possibility of damage to the stored goods. On the other hand, if we order too little, the risks lie in the possibility that the production process will stop, resulting in lost sales due to the unavailability of goods. One strategy to overcome this unavailability of goods is backorder, where the customers will wait until the next replenishment to obtain their goods. This paper develops a mathematical model for inventory-dependent demand with the backorder policy applied. The decisions variables in our model are the optimal order quantity and the number of backorders, which minimize the total inventory cost. We also performed a sensitivity analysis of the optimal solution and found that the decreasing rate of the inventory is affected by the autonomous demand (α) and the increasing demand factor (β). Inventory will deplete faster as α and β increase. The number of backorders is affected by the high demand when inventory reaches zero and backorders entail a certain cost. When demand is higher and the backorder cost is relatively cheap, the number of backorders becomes higher. [ABSTRACT FROM AUTHOR]