Decision Making with Uncertainty: Applications to Queueing Theory and Market Research.

Abstract

In the first section, a firm with two servers must decide how to dynamically route arriving customers and allocate servers to two separate queues. The servers may work together or separately, and we provide insights into how the firm should optimally route customers and assign servers to queues. Reflecting operational systems in practice such as health care facilities or call centers, the uncertainty in the systems we analyze arises due to random customer arrival and service times.

In the second section, a firm seeks to optimize its pricing decision for an innovative product where the firm has limited information on the willingness of customers to pay for the item. To learn the true willingness-to-pay distribution, the firm holds a series of auctions to elicit consumers' valuations for the product. The primary decision making problem the firm faces is when to stop holding auctions, where a limited number of units can be sold, and turn to a traditional sales campaign, where a large number of units can be sold. In this problem, the main source of uncertainty is in the randomness in both the amount and importance of future auction bid data, which affect the quality of the firm’s estimate of the willingness-to-pay distribution.

Finally, motivated by the learning problem in the second section, we consider four auction mechanisms which can be used to elicit consumer valuations for a product which is initially sold at auction and later at a fixed price. The auction may follow either a first-price or a second-price format. After setting the fixed price, a rebate may, or may not, be offered to the auction winner if the price paid at auction exceeds the fixed price. Symmetric Nash equilibrium bidding strategies are found for these mechanisms. We show that the second-price auction with rebate induces truthful revelation.