Jiaqi Shi

We study pricing in a vehicle sharing network with N locations and C vehicles, motivated by on-demand bike, scooter, and car sharing, as well as robotaxi and ride-sharing services. Customers request directed trips between locations, with travel times following general distributions, and leave without service if no vehicle is available. Pricing affects both demand for trips and the distribution of vehicles across locations. Computing an optimal dynamic pricing policy is challenging because the system state depends on the number of vehicles available at each location and on vehicles in transit (including how long they have been traveling), motivating the use of simple static policies. For any number of vehicles and locations, we establish a tight performance guarantee for static pricing relative to optimal dynamic pricing. The guarantee holds for any concave revenue rate functions and general travel time distributions. Our tight guarantee is bounded below by C/(2C - 1) , achieving the first universal, non-asymptotical 50% guarantee, improving on the best previously known guarantees that can approach zero. We also prove that the optimal static policy can be efficiently computed by solving a concave optimization problem. Finally, we extend our performance guarantee to the general setting with supply redirection.

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 brand 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 show a surprising result that uniform pricing is optimal which implies it has the same optimal pricing solution and value as the traditional MNL model. Although adding an opaque product may enhance revenue given arbitrary traditional product prices, our result shows that this advantage disappears when all prices are optimized jointly. For the assortment problem, we first study the setting where the seller chooses both the offered assortment and the support of the opaque product, and prove that there exists an optimal assortment that is nested by revenue. We then study the case where the opaque support is required to coincide with the offered assortment which is common in practice. Here, we show that the optimal assortment is nested-by-valuation for uniformly priced products. For arbitrary prices, we propose a nested-by-revenue-and-valuation heuristic with a theoretical approximation guarantee that performs extremely well in our 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 time distribution, 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 97.55% of the optimal inventory-based 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.