Weibull Model for Dynamic Pricing in e-Business

As is the case with traditional markets, the sellers on the Internet do not usually know the demand functions of their customers. However, in such a digital environment, a seller can experiment different prices in order to maximize his profits. In this paper, we develop a dynamic pricing model to solve the pricing problem of a Web-store, where seller sets a fixed price and buyer either accepts or doesn’t buy. Frequent price changes occur due to current market conditions. The model is based on the two-parameter Weibull distribution (indexed by scale and shape parameters), which is used as the underlying distribution of a random variable X representing the amount of revenue received in the specified time period, say, day. In determining (via testing the expected value of X) whether or not the new product selling price c is accepted, one wants the most effective sample size n of observations X1, ..., Xn of the random variable X and the test plan for the specified seller risk of Type I (probability of rejecting c which is adequate for the real business situation) and seller risk of Type II (probability of accepting c which is not adequate for the real business situation). Let 1 be the expected value of X in order to accept c, and 2 be the expected value of X in order to reject c, where 12, then the test plan has to satisfy the following constraints: (i) Pr{statistically reject c | E{X} = 1} = 1 (seller risk of Type I), and (ii) Pr{statistically accept c | E{X} = 2} = 2 (seller risk of Type II). It is assumed that 1 < 0.5 and 2 < 0.5. The cases of product pricing are considered when the shape parameter of the two-parameter Weibull distribution is assumed to be a priori known as well as when it is unknown.