Dynamic Pricing of Perishable Products with Competition

With the development of product development technology and the rapid rise of online retailing, the market competition becomes increasingly fierce. Based on consumer utility function, this article established a two-stage dynamic pricing model and discussed pricing strategies under consumer behavior and market competition. Findings indicate that product quality difference and consumer valuation decreasing coefficient determine the order of the consumer purchase decisions. The firm who provides lower-quality products suffered more loss than the firm who provides high-quality products.


Introduction
With the development of Internet, competition between firms becomes increasingly fierce.Besides, replacement of product is becoming faster and faster, consumers also are becoming more and more "smart".These all increase competition among firms.In the competitive environment, firms not only consider consumers' behavior, but also consider the impact of competitors' pricing strategies.
Literature related to this paper is dynamic pricing with competition in revenue management.Based on discounted competition, Granot D, Granot F and Mantin B established a dynamic pricing model with two homogeneous perishable goods retailers [1].Levin Y, McGill J and Nediak M selected single and multiple-choice model to describe different choices of consumers in the case of monopoly and competition [2] [3].Dasci A and Karakul M discussed difference between static and dynamic pricing, and studied the effects of these two pricing methods to manufacturers' equilibrium price and revenue [4].Chen and Zhang found dynamic pricing improved revenue of the two firms, and social welfare is improved [5].Hao Li have done a lot of research of manufacturers' dynamic pricing in competitive environment [6] [7].
This paper considers the sales period is divided into two stages.There exist two firms whose product qualities are different.And there exists myopic and strategic consumers in the market.According to consumers' different utility, we establish demand and revenue function and obtain optimal pricing decision.

Problem Description and Basic Assumptions
Assuming there are two firms (A, B) whose product qualities are different.Their products are alternate, when product A is out of stock, consumer would consider buying product B. For some parameters and variables, we do the following settings: (1) Price of A, B in the first stage: (3) ϕ represents product quality difference between A, B, 0 1 ϕ ≤ ≤ .We assume firm A provides higher quality products.
(4) Consumer number in the market is N, the strategic customers proportion is α , 0 1

Model and Solution
Due to the difficulty of multi-stage dynamic programming solving, this paper study the dynamic pricing in the two stages.The sales period [ ] 0,T is divided into full price sales period [ ] 1 0,T and discount sales period In the first stage, consumer's utility of buying product A is 1 . Consumers' demand in the different stages is shown in Table 1.According to consumers' different demand for product A, B, we can obtain revenue function of firm A, B. ( ( ) We use the reverse solving method, for firm A, we set . We can solve the optimal price 1 p and obtain optimal revenue of firm A, B.

Numerical Experiments and Parameter Analysis
(1) When 0 1 a ϕ < < < , we set 20 V = , 5 . Assuming variable a changes within this range ( ) 0, 0.8 , we do sensitivity analysis for variable a. From Figure 1, we can know consumer's buying decision order is 1  A , p increases.Consumer's utility of buying product B in the first stage is larger than buying product A in the second stage.Consumers are more willing to buy product B, thus price of product B is priced higher.
From Figure 2, we can know consumer's buying decision order is 1 While ϕ increases, consumers' willingness to buy product B enhances, consumers' de- mand for product B increases and prices of manufacturer B in both two stages increase.In order to curb consumers turn to buy the product of firm B, firm A would reduce the price of product A in the second stage.
In Figure 3, when 0 1 a ϕ < < < , 0.7 ϕ = , when there exists strategic consumers, both firms' revenue decrease.Profit difference between firm A and B increases when α increases.When there exist strategic con- sumers in the market, firm B suffers more loss.

Conclusion
This article assumes that two firms provide different-quality products and consumer's reservation price of products is heterogeneous.Under consumers' strategic behavior, we establish a two-stage model and obtain consumers' buying decision and two firms' optimal pricing strategies in different situations.Product quality difference

2 Bp
, and obtain the optimal revenue of firm A, B.

Figure 1 .
Figure 1.Effect of a on price p.

Figure 2 .
Figure 2. Effect of ϕ on price p.

Figure 3 .
Figure 3.Effect of α on price R.