Discrete dynamic pricing and application of network revenue management for FlixBus

We consider a real discrete pricing problem in network revenue management for FlixBus. We improve the company's current pricing policy by an intermediate optimization step using booking limits from standard deterministic linear programs. We pay special attention to computational efficiency. FlixBus' strategic decision to allow for low-cost refunds might encourage large group bookings early in the booking process. In this context, we discuss counter-intuitive findings comparing booking limits with static bid price policies. We investigate the theoretical question whether the standard deterministic linear program for network revenue management does provide an upper bound on the optimal expected revenue if customer's willingness to pay varies over time.

A Re-Solving Heuristic with Uniformly Bounded Loss for Network Revenue Management

We consider a canonical quantity-based network revenue management problem where a firm accepts or rejects incoming customer requests irrevocably in order to maximize expected revenue given limited resources. Because of the curse of dimensionality, the exact solution to this problem by dynamic programming is intractable when the number of resources is large. We study a family of re-solving heuristics that periodically re-optimize an approximation to the original problem known as the deterministic linear program (DLP), where random customer arrivals are replaced by their expectations. We find that, in general, frequently re-solving the DLP produces the same order of revenue loss as one would get without re-solving, which scales as the square root of the time horizon length and resource capacities. By re-solving the DLP at a few selected points in time and applying thresholds to the customer acceptance probabilities, we design a new re-solving heuristic with revenue loss that is uniformly bounded by a constant that is independent of the time horizon and resource capacities. This paper was accepted by Kalyan Talluri, revenue management and market analytics.

An Approximation Algorithm for Network Revenue Management Under Nonstationary Arrivals

Many revenue management problems require making capacity control and pricing decisions for multiple products. The decisions for the different products interact because either the products use a common pool of resources or the customers choose and substitute among the products. When pricing airline tickets, for example, different itinerary products use the capacities on common flight legs and the customers choose and substitute among different itinerary products that serve the same origin-destination pair. Finding the optimal capacity control and pricing decisions in such problems can be challenging because one needs to simultaneously consider the capacities available to serve a large pool of products. In “An Approximation Algorithm for Network Revenue Management under Nonstationary Arrivals,” Ma, Rusmevichientong, Sumida, and Topaloglu develop efficient methods to make decisions with performance guarantees in high-dimensional capacity control and pricing problems.