An EOQ model with controllable selling rate

According to the marketing principle, a decision maker may control demand rate through selling price and the unit facility cost of promoting transaction. In fact, the upper bound of willing-to-pay price and the transaction cost probably depend upon the subjective judgment of individual consumer in purchasing merchandise. This study therefore attempts to construct a bivariate distribution function to simultaneously incorporate the willing-to-pay price and the transaction cost into the classical economic order quantity (EOQ) model. Through the manipulation of the constructed bivariate distribution function, the demand function faced by the supplier can be expressed as a concrete form. The proposed mathematical model mainly concerns how to determine the initial inventory level for each business cycle, so that the profit per unit time is maximized by means of the selling price and the unit-transaction cost to control the selling rate. Furthermore, the sensitivity analysis of optimal solution is performed and the implication of this extended inventory model is also discussed.