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 X-1, . . . , X-n 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 IT (probability of accepting c which is not adequate for the real business situation). Let mu(1) be the expected value of X in order to accept c, and mu(2) be the expected value of X in order to reject c, where mu(1)>mu(2) then the test plan has to satisfy the following constraints: (i) Pr {statistically reject c vertical bar E{X} = mu(1)} = alpha(1) (seller risk of Type I), and (ii) Pr{statistically accept c vertical bar E{X} = mu(2)} = alpha(2) (seller risk of Type II). It is assumed that alpha(1) < 0.5 and alpha(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.