Jiaqi Shi

An opaque product is a product for which only partial information is disclosed to the buyer at the time of purchase. Opaque products are common in sectors such as travel and online retail, where the car type or product color is hidden in the opaque product. Opaque products enable sellers to target customers who prefer a price discount in exchange for being flexible about the product they receive. In this paper, we integrate opaque products and traditional products together into the multinomial logit (MNL) choice model and study the associated price and assortment optimization problems. For the price optimization problem, we surprisingly show that uniform pricing is optimal which implies it has the same optimal pricing solution and value as the traditional MNL model. While adding an opaque product priced at the revenue-maximizing price may enhance revenue given arbitrary traditional product prices, this advantage disappears when all prices are optimized jointly. For the assortment optimization problem, we show that the revenue-maximizing assortment is nested-by-valuation for uniformly priced products. For non-uniformly priced cases, we propose a natural nested-by-revenue-and-valuation heuristic that performs extremely well in an extensive numerical study.

We consider the problem of pricing a reusable resource service system. Potential customers arrive according to a Poisson process and purchase the service if their valuation exceeds the price. If no units are available, customers immediately leave. Serving a customer corresponds to using one unit for an exponential service time. The objective is to maximize the steady-state revenue rate. Although an optimal policy is fully dynamic, we provide two main results that show a simple static policy is universally near-optimal for any service rate, arrival rate, and number of units in the system. When there is one class of customers who have a monotone hazard rate (MHR) valuation distribution, we prove that a static pricing policy guarantees 90.2% of the optimal policy. When there are multiple classes of customers, we prove that static pricing guarantees 78.9% of the optimal policy.

Considering the real-world situations where past purchases could influence future prices, this research examines the multi-product price optimization problem under a multi-stage choice model. Particularly, the seller commits to a multi-stage pricing policy and determines product prices based on the customer’s purchase history, and the customer makes purchase decisions such that the expected utility is maximized. We show that the pricing problem has a unique optimal solution under some mild conditions and the optimal solution satisfies a modified equal adjusted markup property. Moreover, the optimal pricing policy has an important property, namely, the product with a higher adjusted markup in earlier stages should always lead to lower prices in subsequent stages. We also show that compared to customers that are myopic, the seller should offer higher first-stage prices and lower second-stage prices to forward-looking customers, which will lead to a higher profit.