Price-Setting Models for Innovative Products
Price-Setting Newsvendor Models Based on OSDT
In the following model, a manufacturer who produces and sells an innovative product in the monopoly market is considered. Before selling season, the manufacturer produces units at unit cost W and setup cost is assumed to be zero. We consider the following widely used linear inverse demand function.
(15)
where shows the limit demand when the retail price equals to , and represents the decreasing of demand when the retail price increases by one unit. We call a as the price sensitivity of market demand. The demand's uncertainty is described by the parameter b with probability density function . The profit function is with the retail price and the production quantity as the decision variables. With considering (1), it can be expressed as:
(16)
If one considers Definitions 1 and 2, then we have the relative likelihood function of , i.e., and the satisfaction function, i.e., . Similar to the newsvendor model, the following types of focus points are considered.
Active focus point: For retail price and production quantity , the active focus point is
(17)
is the focused demand value with the relatively high likelihood degree and satisfaction level for the production quantity .
Passive focus point: For retail price and production quantity , the passive focus point is
(18)
is the focused demand value with the relatively high likelihood degree and relatively low satisfaction level for the production quantity .
Apprehensive focus point: For retail price and production quantity , the apprehensive focus point is
(19)
is the focused demand value with the relatively low likelihood degree and satisfaction level for the production quantity .
Daring focus point: For retail price and production quantity , the daring focus point is
(20)
is the focused demand value with the relatively low likelihood degree and relatively high satisfaction level for a production quantity .
The sets of the four types of focus points of the retail price and production quantity are denoted as , , and , respectively. The optimal production quantities for the manufacturers are
(21)
(22)
(23)
(26)