An economic order quantity model with continous quantity discount and probabilistic demand

In this research we develop mathematical model of inventory problem which considers interaction of unit cost and order quantity. It is assumed that demand is a function of selling price which depends on unit cost. Furthermore, unit cost is a function of order quantity. We develop two kinds of relationship between unit cost and order quantity, which are linear and hyperbolic. Customer demand is probabilistic with known mean and standard deviation. Service level is calculated based on the number of fulfilled demand. We assume that backorder policy will be decided if there is a shortage. The result shows that there is no significant difference between linear and hyperbolic relationship. However, hyperbolic model is considered more realistic than linear model because it can ensure that the unit cost is not less than minimum determined unit cost.