## Price-Setting Models for Innovative Products

Modern organizations have abundant choices in selecting the right product supply chain. Functional products are items that are purchased regularly, are widely available from multiple sources, and have long life cycles. Alternatively, innovative products are new to the marketplace, have unpredictable demand, and usually have short life cycles.

Read this article. Researchers suggest that products belong to either a functional or innovative category, where innovative products are much more challenging to price. What innovative products do you own, and how do you know you are getting the value you paid for?

### Newsvendor Models with the OSDT

In this section, the decision-making procedure for a retailer of innovative products is introduced. Before the selling season, the retailer must decide the order quantity q. For one unit of the innovative product, the wholesale price is , and the retail price is and . If there is an excess, the unit salvage price is . The unit opportunity cost is for the shortage. The retailer's profit function is as follows:

(1)

The demand function of the innovative product is described by a random variable and the probability mass (density) function is .

**Definition 1. **Given the probability function for random vector and be a function satisfying

(2)

is the relative likelihood degree of if for and for . For a retailer, his/her satisfaction levels towards profits are represented by the satisfaction function.

**Definition 2.** The satisfaction function is a strictly increasing function of the profit ,

(3)

Obviously, the relative likelihood degrees and the satisfaction levels can be utilized to describe the relative position of the probabilities and the payoffs, respectively.

Usually, because of the short life cycle of the innovative product, there is only one chance given to the retailer to determine his/her order quantity and a unique demand will appear accordingly. Therefore, before ordering products, the retailer has to meditate which demand should be factored in. We take into account four types of demands (scenarios) for each order quantity with contemplating the likelihood degrees and the satisfaction levels, that is the demands with the higher satisfaction and likelihood (Type I), the lower satisfaction and higher likelihood (Type II), the higher satisfaction and lower likelihood (Type III), the lower satisfaction and likelihood (Type IV). It is intuitively acceptable that active, passive, daring and apprehensive retailers are inclined to take into account Type I, Type II, Type III and Type IV demands, respectively. Therefore, we call Type I, Type II, Type III and Type IV demands active, passive, daring and apprehensive focus points, respectively (shown in Table 1). Which kind of focus point is taking into account reflects the personality of the retailer under demand uncertainty.

**Table 1.** Four different focus points.

satisfaction | |||

higher | lower | ||

likelihood | higher | active focus point | passive focus point |

lower | daring focus point | Apprehensive focus point |

Following operators are introduced to characterize the focus points.

**Example 1.**There are four demands and . Their probabilities are 0.05, 0.15, 0.5 and 0.3 so that the corresponding relative likelihood degrees are 0.1, 0.3, 1.0 and 0.6, respectively. For an order quantity whose are, for instance, and , respectively. is which corresponds to . Thus, is . Clearly is the demand with a higher likelihood degree and satisfaction level.

**Comments:**Equations (6)–(9) are from four bi-objective optimization problems as follows: ; ; , and , . From Equations (6) to (9), there is no other satisfies and ; or and ; or and ; or and . It means that , , and are Pareto optimal solutions of the above four bi-objective optimization problems which are used to seek for the demands with the higher likelihood and satisfaction, the higher likelihood and lower satisfaction, the lower likelihood and satisfaction and the lower likelihood and higher satisfaction, respectively. In other words, for any no demand can cause an even higher satisfaction with an even higher likelihood than its active focus point ; no demand can provide an even lower satisfaction with an even higher likelihood than its passive focus point ; no demand can lead to an even lower satisfaction with an even lower likelihood than its apprehensive focus point ; no demand can generate an even higher satisfaction with an even lower likelihood degree than its daring focus point .

**Advantages in phenomena explanation**: Let us consider the following anecdotal evidence. In September 2014, Apple® released iPhone 6 and iPhone 6 Plus, but the Chinese market was left out the first wave of countries. The iPhone 6 was sold for as much as 10 times the U.S. price in Chinese black market, due to the delayed release. There were many scalpers trying to buy and resell the iPhone 6 in this risky and fragile market. Grothaus observed that some of the scalpers treat it as a "gamble" and just took into account the scenario that they can make profits and "feed their family". This kind of phenomena in an innovative product market can be explained by the behavior of a daring retailer. Even though some scenario may occur with a low likelihood, the high gain lures him/her to take action. On the other hand, this kind of phenomena is very hard to be explained by lottery-based models, including expected utility models, value at risk models or conditional value at risk models. The reason is that the expression of risk preferences in these models rely on the framework of weighting average, which ignored the importance of some unique and irreplaceable scenario (focus point) in the progress of decision-making.

**Example 2.**A fashion store is scheduled to order a kind of newly designed fashion. For a unit, retail price , wholesale price , salvage price and opportunity cost are all set, for example, as 10, 7, 1 and 4 (1000RMB), respectively. The profit of the store is

**Table 2.**The relative likelihood degrees of demands.

Demands | 350 | 450 | 550 | 650 | 750 |
---|---|---|---|---|---|

likelihood degrees | 0.22 | 0.35 | 1.00 | 0.73 | 0.29 |

**Table 3.**Profits for each order quantity.

Demands |
||||||

350 | 450 | 550 | 650 | 750 | ||

Orders |
350 | 1050 | 650 | 250 | −150 | −550 |

450 | 450 | 1350 | 950 | 550 | 150 | |

550 | −150 | 750 | 1650 | 1250 | 850 | |

650 | −170 | 150 | 1050 | 1950 | 1550 | |

750 | −1350 | −450 | 450 | 1350 | 2250 |

**Table 4.**Satisfaction levels obtained for order quantities.

Demands |
||||||

350 | 450 | 550 | 650 | 750 | ||

Orders |
350 | 0.67 | 0.56 | 0.44 | 0.33 | 0.22 |

450 | 0.50 | 0.75 | 0.64 | 0.53 | 0.42 | |

550 | 0.33 | 0.58 | 0.83 | 0.72 | 0.61 | |

650 | 0.17 | 0.42 | 0.67 | 0.92 | 0.81 | |

750 | 0.00 | 0.25 | 0.50 | 0.75 | 1.00 |

**Table 5.**Focus points of order quantities.

Order Quantities | |||||
---|---|---|---|---|---|

350 | 450 | 550 | 650 | 750 | |

Active | 550 | 550 | 550 | 650 | 650 |

Passive | 650 | 650 | 450 | 450 | 550 |

Apprehensive | 750 | 750 | 350 | 350 | 350 |

Daring | 350 | 450 | 750 | 750 | 750 |

In step 2, the optimal order quantities are chosen on the basis of satisfaction levels of focus points. The satisfaction levels for each order quantity with different types of focus points is easily calculated (see Table 6). Using (10–13), we get the optimal active, passive, apprehensive and daring order quantities, that is 650, 550, 450, and 750, respectively.

**Table 6.**Satisfaction levels for focus points.

Order Quantities | |||||
---|---|---|---|---|---|

350 | 450 | 550 | 650 | 750 | |

Active | 0.44 | 0.64 | 0.83 | 0.92 | 0.75 |

Passive | 0.33 | 0.53 | 0.58 | 0.42 | 0.50 |

Apprehensive | 0.22 | 0.42 | 0.33 | 0.17 | 0.00 |

Daring | 0.67 | 0.75 | 0.61 | 0.81 | 1.00 |