随机需求下旅行商问题中的最优服务承诺

中文摘要 AI 辅助

在拼车服务中，移动出行提供商必须在客户决定是否预订之前告知预计到达时间。雄心勃勃的承诺比保守的承诺能吸引更高的需求，但相应地也更难兑现。因此，提供商的收入由所宣布的承诺与其诱导的需求之间的内生相互作用所支配。我们在所有客户共享一辆班车前往共同目的地的旅行商情境下研究这种相互作用，将其形式化为带服务承诺的旅行商问题（TSP-SC），这是一个两阶段随机优化问题。在第一阶段，提供商向所有对行程感兴趣的客户宣布到达承诺，每个客户独立地以随承诺时间递减的概率接受或拒绝该要约。在第二阶段，一个定向运动问题确定在承诺时间内服务的接受客户中收入最大化的子集；其余客户被拒绝。我们证明最优承诺位于由客户子集的旅行长度诱导的有限候选集中，并开发了两种精确算法，一种通用算法和一种针对同质客户的更快变体，以及一种用于更大实例的自适应二项式采样启发式算法（BSH）。在对多达100个客户的实例进行的数值研究中，该启发式算法在所有可精确求解的规模上，与最优期望收入的平均偏差至多为0.32%。结果进一步揭示了一个显著的运营规律：随着客户群的增长，收入最大化策略收敛到一种状态，即大约每三个接受客户中就有一个被拒绝，这一拒绝率在各种实例规模中保持稳定。

英文摘要

In ridepooling services, mobility providers must communicate an expected arrival time before customers decide whether to book. An ambitious commitment attracts higher demand than a conservative one, but is correspondingly harder to fulfill. Provider revenue is therefore governed by an endogenous interplay between the announced commitment and the demand it induces. We study this interplay in a traveling salesman setting in which all customers share a shuttle to a common destination, formalizing it as the Traveling Salesman Problem with Service Commitments (TSP-SC), a two-stage stochastic optimization problem. In the first stage, the provider announces an arrival commitment to all customers interested in the trip, each of whom independently accepts or rejects the offer with a probability decreasing in the committed time. In the second stage, an Orienteering Problem determines a revenue-maximizing subset of accepting customers to be served within the commitment; the remaining customers are rejected. We show that optimal commitments lie in a finite candidate set induced by the tour lengths of customer subsets, and develop two exact algorithms, a general and a faster variant for homogeneous customers, together with an Adaptive Binomial Sampling Heuristic (BSH) for larger instances. In a numerical study on instances with up to 100 customers, the heuristic deviates from the optimal expected revenue by at most 0.32~\% on average across all exactly solvable sizes. The results further reveal a striking operational regularity: as the customer base grows, the revenue-maximizing policy converges to a regime in which roughly one in three accepting customers is rejected, a rejection rate that remains stable across instance sizes.

发表机构

• University of Hamburg Business School（汉堡大学商学院）

机构由 AI 辅助整理，请以论文原文为准。