A Re-Solving Heuristic with Uniformly Bounded Loss for Network Revenue Management
针对网络收益管理中的维度灾难问题，研究了一类重新求解启发式算法，通过改进确定性线性规划的重新求解时机和阈值设定，实现了与时间跨度和资源容量无关的一致有界收入损失。
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.