Economic order quantity models modified by introducing discount of purchase price or increase of setup costs

The economic order quantity (EOQ)-Model of inventory problem can determine ordering cycle and quantity. When the purchase unit price is constant, ordering cycle and ordering quantity, which minimize the one day's average inventory cost, is not dependent on the purchase price. But if purchase price may change, the EOQ-Model must be modified. The purchase unit price is discounted as the ordering becomes larger. The discount of purchase price is described with a decreasing function of ordering quantity. This function is not always continuous with respect to the ordering quantity. Under this condition one day's average profit can be defined. And we can determine ordering cycle and ordering quantity, which maximize one day's average profit. Moreover, we consider the situations under which the setup cost depends on the ordering quantity. In this case the setup can be described with the increasing function of ordering quantity. We show that the EOQ-Model can be applied if it is modified by introducing the continuous setup cost function. This function is not differentiable at some levels of ordering quantity.